Papers I find interesting---mostly, but not solely, in Process Algebra---, and some fun stuff in Mathematics and Computer Science at large and on general issues related to research, teaching and academic life.

## Sunday, December 24, 2006

### Christmas Reading

The January 2007 issue of Scientific American features an article by Bill Gates entitled A Robot in Every Home.

Happy reading and merry Christmas.

## Friday, December 22, 2006

### Sussex in 1987

Julian tells me that it is a strange time at Sussex. Half of the department is moving buildings, so the department office and all of the secretaries are gone, the good old debugging room (the unofficial coffee room of the department at a time when the university regulations essentially did not allow for such rooms, hence the name) is also no more. Just an empty shell of a room now. Very sad.

Reading Julian's description prompted me to look back to a windy September-October 1987, when I arrived in Brighton to work for a year as a research assistant under Matthew Hennessy. The department of computer science was very small then. Yet, there was already a tightly knit group of theory people that created a very good atmosphere for intellectual growth. At that time, Marek Bedcnarzyk was putting the final touches to his PhD thesis, and Allen Stoughton was finalizing his monograph on fully abstract models of programming languages. Mark Millington, one of Matthew's former Edinburgh students, was there teaching Software Engineering. (It is a pity that Mark's PhD thesis is not very well known. It was a good piece of work.) I shared an office with Rance Cleaveland, a freshly minted PhD from Cornell, where he had formalized theories of processes using NuPRL. (Rance was working on the development of the Concurrency Workbench, but did a lot more than that---not least, he taught me a lot over beers at our local pub :-)) Across the fire doors leading to the Mathematics department, Andy Pitts was spending some time at Sussex, supported by a grant from the Royal Society.

Already the year after, the theory group grew substantially in size, with the arrival of PhD students from Britain and from abroad, postdocs, and later new members of staff. The rest, as they say, is history. It is a pity that not so much is left of that theory group at Sussex. (The linchpin, Matthew Hennessy, is still there, but many people have come and gone in the meantime.)

This is one of the pros and cons of academic life. One travels from place to place, possibly grows attached to each of the departments/centres one works for, and the colleagues one meets there, but eventually we all leave for somewhere else.

Good luck to Julian for his new job at Southampton, and congratulations to Vladi for having enticed an excellent collaborator like Julian to join his new department.

## Monday, December 18, 2006

### Being Head of Department: A New Experience

Not surprisingly, I am trying to gather some useful advice on how to survive this new experience, and hopefully live to tell the tale as far as research, teaching and service to the academic community are concerned. So far, I have found some useful information on the CRA web site, but I'd love to hear any advice you might have on how to manage one's time while being head of department, and what aspects of the job one should be particularly aware of. Drop me a line, or use the comments section. I'll be grateful for any piece of information you might provide.

I apologize to those of you who kindly invited me to serve on PCs for conferences during the first half of 2007. I was honoured by your consideration, but decided to politely decline all of those invitations rather than do a bad job. (I must freely admit that the prospect of chairing the department is worrying me somewhat :-() I hope that I made the right choice.

## Saturday, December 16, 2006

### Research in Italy

I am afraid that I do not know enough about the developments to express an informed opinion about the whole thing. However, I have always sternly refused to buy the argument that, unlike other countries, Italy does not have the cash to support universities and research. How can a member state of the G8 elite be short of money to support its future? Let's not mask lack of interest in science and technology as supposed poverty. By way of example, BRICS and the other research centres of the Danish National Research Foundation were richly funded for five-year periods (14 years for BRICS) with the interests resulting from the privatization of an insurance company! The outcome for Danish science is for everybody to see.

Why shouldn't the same type of investment in basic research be possible in a country like Italy? The reasons must be the same that prevent Italy from investing in its schools and universities. Three figures in the article I was reading yesterday paint an amazingly bleak picture. Italy boasts only about 3 researchers every 1000 workers. This is less than each of the other countries mentioned in the list. We (Italians) spend only about 1.2% of the GNP in research. Only Greece, Spain and Portugal invest less. Last but not least, Italy spends only 8000$ a year per university student. This is the same as Hungary, and half of what Sweden spends. Why are we Italians so masochistic?

Still, if I look at Italian research in TCS, I can only classify it as being very strong, despite the lack of money for research and the sub-optimal support. Yes, I know that I am biased. Even though I have never worked in an Italian university myself, I try to maintain good ties with my colleagues based in Italy. It is, however, an incontrovertible fact that there are many very active and very strong Italian TCS researchers. The strongest Italian CS departments are high class, and Italy exports talent. Off the top of my head, I could come up with the following list of Italian TCS researchers working abroad (with apologies to those whose names have not crossed my mind right now):

- Luca de Alfaro
- Roberto Amadio
- Antonio Bucciarelli
- Cristiano Calcagno
- Luca Cardelli
- Ilaria Castellani
- Giuseppe Castagna
- Roberto Di Cosmo
- Luigi Liquori (who is from Pescara like me)
- Giuseppe Longo
- Sergio Maffeis
- Pasquale Malacaria
- Silvio Micali
- Catuscia Palamidessi
- Luigi Santocanale
- Vladimiro Sassone
- Luca Trevisan
- Daniele Varacca
- Luca Viganò
- Francesco Zappa Nardelli

Addendum 19/12/2006: Yesterday I read an article by Princeton philosopher Peter Singer, on the subject of philantropy, poverty and ethics. (Thanks to Luca Trevisan for his post on this very interesting article, which is a must read during the crazy Christmas period.)

The following excerpt from that article struck me as being very relevant to this disjointed post of mine:

The Nobel Prize-winning economist and social scientist Herbert Simon estimated that “social capital” is responsible for at least 90 percent of what people earn in wealthy societies like those of the United States or northwestern Europe. By social capital Simon meant not only natural resources but, more important, the technology and organizational skills in the community, and the presence of good government. These are the foundation on which the rich can begin their work.

If instead of wealth, we consider "intellectual output", how much would Italian researchers produce in the presence of better technology and organizational skills in the community, and in the presence of good government? What if they could devote more of their time to not fighting against the system?

## Thursday, December 14, 2006

### Zeilberger's 76th Opinion

Zeilberger writes:

All the problems in, say, Garey and Johnson, are essentially

**one**problem, since they are all trivially equivalent.

Well, I am not sure that I agree that those problems are "trivially" equivalent. "Triviality" is in the eye of the beholder, and maybe one has to be a top notch mathematician like Zeilberger in order to find all of the reductions between NP-complete problems trivial. I admit that I do not find most of them to be trivial at all.

I also find the characterization of the work of complexity theorists as "just proving yet-another reduction theorem" somewhat restrictive.

I am expecting to see some comments on this opinion on the complexity theoretic blogs.

Addendum posted on 15 December 2006: Read Luca Trevisan's thoughtful comments.

Let me also mention another statement of Zeilberger's from opinion 76:

There is no hope, as smart and "creative" as you and your cronies are, that you will be able to prove it by yourselves. Your only hope is to enlist that

*"simple" mechanical device*, that ironically, you

**computer**-scientists, do not use very much, not even for spell-checking!

Now that I have algebraic combinatorialists working near me, I can vouch that they use computers a fair amount in their work---possibly more than many theoretical computer scientists. However, in concurrency theory, people construct and use software tools to make models of computing devices and to analyze their behaviour algorithmically. Readers who have never used such tools might wish to play with Uppaal or HyTech to mention but two such tools.

## Wednesday, December 13, 2006

### Accepted Papers for FOSSACS 2007

## Tuesday, December 12, 2006

### Accepted Papers at ETAPS 2007

Multi-Objective Model Checking of Markov Decision Processes by Kousha Etessami, Marta Kwiatkowska, Moshe Y. Vardi, and Mihalis Yannakakis.

ESOP features a list of accepted papers that is definitely of interest to concurrency theorists.

Most accepted papers at TACAS and ESOP have at least three authors, further confirming the trend to higher and higher degrees of collaboration in most fields of TCS.

Happy browsing! I am still awaiting the list of accepted papers for FOSSACS 2007. In any event, the tenth anniversary edition of ETAPS looks already like a conference one should attend. I myself, however, will be attending a marriage of mathematicians that will be held in Chicago at around that time.

## Monday, December 11, 2006

### RIP (Research In Peace)

**research programs**in specialized areas of mathematics, and I am told that it is a great place to visit.

One of their programmes is called RIP (Research in Peace). This is a programme allowing mathematicians from Scandinavian universities, who are not directly connected to the current scientific programme, to visit the Institute for shorter periods. My colleague, and frequent indirect contributor to this blog, Anders Claesson is presently visiting Mittag-Leffler using the RIP programme.

Maybe some of you will be interested in organizing a programme on some topic in TCS at that institution.

## Friday, December 08, 2006

### Characteristic Formulae for Timed Automata

The first construction of a characteristic formula for timed bisimilarity over timed automata I am aware of was presented in the paper

François Laroussinie, Kim G. Larsen, and Carsten Weise. From Timed Automata to Logic - and Back. Jirí Wiedermann, Petr Hájek (Eds.): Mathematical Foundations of Computer Science 1995, 20th International Symposium, MFCS'95, Prague, Czech Republic, August 28 - September 1, 1995, Proceedings. Lecture Notes in Computer Science 969 Springer 1995, ISBN 3-540-60246-1.

In that paper, the authors propose a timed version of Hennessy-Milner logic Lnu, and show thateach timed automaton can be uniquely characterized by a single formula in that logic up to timed bisimilarity.

The construction in that paper relied on the region graph of the timed automaton, and thus produces "large" formulae. (See yesterday's post on the number of regions in a timed automaton.) In the setting of timed automata without invariants, the construction by Laroussinie, Larsen and Weise was improved upon in the paper

Luca Aceto, Anna Ingólfsdóttir, Mikkel Lykke Pedersen, and Jan Poulsen. Characteristic Formulae for Timed Automata. ITA 34(6): 565-584 (2000).

That paper offers characteristic formula constructions in the real-time logic Lnu for several behavioural relations between (states of) timed automata. The behavioural relations studied in op. cit. are timed (bi)similarity, timed ready simulation, faster-than bisimilarity and timed trace inclusion. The characteristic formulae delivered by the constructions offered in the aforementioned paper have size which is linear in that of the timed automaton they logically describe.

Finally, the paper

Luca Aceto, Patricia Bouyer, Augusto Burgueño, Kim G. Larsen. The power of reachability testing for timed automata. Theor. Comput. Sci. 300(1-3): 411-475 (2003)

uses a property language characterizing the power of reachability testing over timed automata in the context of "test automata" to provide a definition of characteristic properties with respect to a timed version of the ready simulation preorder, for nodes of τ-free, deterministic timed automata.

I am not aware of a timed counterpart of the results by Browne, Clarke and Grümberg on the characterization of bisimulation-like equivalences over Kripke structures using characteristic formulae in fragments of CTL. Is Timed CTL expressive enough to describe characteristic formulae for timed bisimilarity? This has been an item on my "to do" list for quite some time, but I have never had the guts to start working on the problem yet.

## Thursday, December 07, 2006

### Number of Regions in a Timed Automaton

There is a characterization of the number of regions where all clocks lie between 0 and 1 in terms of Stirling numbers of the second kind in this paper (page 13 bottom).

Peter Kopke's PhD thesis available from Tom's web page at http://mtc.epfl.ch/~tah/Students/kopke.pdf also contains that characterization. The section that starts on page 164 (of the file) offers the following formula:

Regions(2n) = sum

_{k=1}

^{2n}S

_{k}

^{2n}k!

where Regions(2n) is the number of equivalence classes over 2n clocks each constrained to lie in the interval (0,1), and S

_{k}

^{2n}is the number of ways of partitioning a set with 2n elements into k subsets. So Regions(2n) is exactly the number of ways of partitioning a set with 2n elements into k ordered subsets.

As the algebraic combinatorialists here at Reykjavík University know well, I am always very impressed by these counting formulae :-)

## Tuesday, December 05, 2006

### IFIP WG1.8 Workshop at CONCUR

---------------------------------------

TITLE: IFIP WG 1.8 Workshop on Applying Concurrency Research in Industry (7 or 8 September 2007)

DURATION: Half a day

ORGANIZERS: Luca Aceto, Jos Baeten, Wan Fokkink, Anna Ingolfsdottir, and Uwe Nestmann (on behalf of WG1.8)

SUMMARY: This strategic workshop, held under the auspices of IFIP Working Group 1.8 on Concurrency Theory, aims at highlighting the challenges that arise in applying concurrency theory research in an industrial setting, broadly construed. Its purpose is to be a forum for the discussion of the state-of-the-art in the transfer of results from concurrency theory to industry, and for distilling the lessons to be learned from the successes and failures so far. Moreover, we shall discuss, e.g., how to increase the impact that concurrency research can have in industry, the role of software tools in this technology transfer effort, and what are possible novel industrial application areas of concurrency theory research. The ultimate goal of the meeting, and subsequent discussions, will be to establish road map(s) for the concurrency theory community, or parts thereof, in applying its research in industrial settings.

The topic of the workshop is strongly related to all of the areas of CONCUR interest. Semantics, logics, and verification techniques for concurrent systems are necessary for the development of languages and methods for use in industrial applications. Conversely, the industrial applications of methods from concurrency theory research stimulate further advances in the basic theory covered by the CONCUR conference series. Successful applications of concurrency theory in industry further highlight the fundamental scientific and technological relevance of work done within the CONCUR community.

SELECTION OF PAPERS: The workshop will consist of three-four invited presentations, followed by discussions. We might summarize the presentations and discussions in an article for the concurrency column of the Bulletin of the EATCS. The theme of the workshop could form the basis for a special issue of a journal (for instance JLAP), but such a special issue would not be necessarily based upon presentations at the workshop. There would be a separate call for contributions for that volume.

## Monday, December 04, 2006

### Italian Success in Logic

Matteo Viale finished his doctorate last September at the University of Turin and the University of Paris VII (co-supervised by Alessandro Andretta and Boban Velickovic) . In his thesis, he has solved one of the major open problems in logic and set theory by showing that the proper forcing axiom (PFA) implies the singular cardinal hypothesis (SCH). The result is reported in this paper.

Congrats to Matteo!

### News from EATCS

The Call for Nominations for the 2007 Gödel Prize has been posted on the EATCS web site. The deadline for nominations is January 31, 2007.

The Call for Nominations for the 2007 EATCS Award has been published (page 13 of Bulletin issue 90). The nominations should be sent to Wolfgang Thomas by December 15, 2006. Hurry up if you do intend to nominate one of our colleagues in concurrency theory!

## Friday, December 01, 2006

### A Google Talk by Luis von Ahn

http://video.google.com

(Thanks to Anders Claesson for this pointer.)

Luis von Ahn is the winner of one of the MacArthur genius awards for 2006. I just tried his ESP game ( http://www.espgame.org/) for the first time. It is actually rather smart, in a way, and apparently some people play it a lot (even over 10 hours a day, according to von Ahn). In so doing, they help label images on the web, using all those human brain cycles devoted to game playing for a good cause.

## Thursday, November 30, 2006

### Characteristic Formulae (continued)

A classic result on characteristic formulae was obtained in the paper

Browne, M. C.; Clarke, E. M.; Grümberg, O.

*Characterizing finite Kripke structures in propositional temporal logic*.

*Theoret. Comput. Sci.*59 (1988), no. 1-2, pp. 115-131.

The above paper shows that for any finite Kripke structure, i.e., a labelled transition graph with an initial state, it is possible to construct a Computation Tree Logic formula uniquely characterizing that finite Kripke structure. Browne, Clarke and Grümberg call the notion of equivalence matching "logical equivalence wrt CTL" E-equivalence. Two states are said to be E-equivalent if they have the same labelling of atomic propositions, and transitions to other states preserve the E-equivalence. (Surprise, surprise! This is just bisimilarity for Kripke structures.) It turns out that, modulo E-equivalence, finite Kripke structures are characterized by CTL formulae containing the "next-time" operator. (A formula of the form

**X**φ, read "next φ", states that φ has to hold at the next state of the computation path.)

Another characteristic formula result is presented in that paper for an equivalence between states called S-equivalence (equivalence with respect to stuttering) . Two state sequences are said to correspond if each can be partitioned into finite blocks of identically labelled states such that each state of the ith block in one sequence is E-equivalent to each state in the ith block of the other sequence. Two states are said to be S-equivalent if, for each state sequence starting at one, there is a corresponding state sequence that starts at the other.

Theorem: S-equivalence classes of states in a finite Kripke structure are completely characterized by next-time-free CTL formulae.

The absence of the next-time operator is expected in light of the inability of S-equivalence to "count" the number of steps in a stuttering sequence. S-equivalence is closely related to van Glabbeek's and Weijland's branching bisimilarity. Logical characterizations of branching bisimilarity have been offered by De Nicola and Vaandrager in the paper:

R. De Nicola and F.W. Vaandrager. Three logics for branching bisimulation.

*Journal of the ACM*,

**42**(2):458-487, 1995.

Kucera and Schnoebelen have presented a refinement of the above classic theorem by Browne, Clarke and Grümberg in the paper

A. Kucera and Ph. Schnoebelen. A general approach to comparing infinite-state systems with their finite-state specifications. Theor. Comput. Sci. 358(2-3): 315-333 (2006).

In a follow-up post, I'll try to wind up this brief three-part discussion of characteristic formulae by mentioning a couple of results on characteristic formulae for timed automata.

## Monday, November 27, 2006

### Bulletin of the EATCS, October 2006

I firmly believe that having the Bulletin open access will further increase its quality and impact, turning it into an even more useful and widely read publication than it already is. Thanks to Vladimiro Sassone for his great editorial work on the Bulletin.

This issue of the Bulletin has at least two papers of direct interest to concurrency theorists (see the concurrency column and the programming languages column). I also enjoyed reading Leonid Libkin's contribution to the logic in computer science column.

Support the Bulletin, an open access publication in theoretical computer science, by, amongst other things, becoming a member of the EATCS and publishing articles in the Bulletin. Feel free to contact me if you'd like to write a piece for the concurrency column.

### Characteristic Formulae

Why is this notion interesting at all? A classic result in the theory of concurrency is the characterization theorem of bisimulation equivalence in terms of Hennessy-Milner logic (HML) due to Matthew Hennessy and Robin Milner. (See this paper.) This theorem states that two bisimilar processes satisfy the same formulae in Hennessy-Milner logic, and if the processes satisfy a technical "image finiteness condition", then they are also bisimilar when they satisfy the same formulae in the logic. This means that, for bisimilarity and HML, logical equivalence coincides with behavioural equivalence, and that whenever two processes are not equivalent, then we can always find a formula in HML that witnesses a reason why they are not. This distinguishing formula is useful for debugging purposes, and can be algorithmically constructed for finite processes. (Algorithms for computing such distinguishing formulae for strong and weak bisimilarity are implemented in tools like the Edinburgh Concurrency Workbench.)

The characterization theorem of Hennessy and Milner is, however, less useful if we are interested in using it directly to establish when two processes are behaviourally equivalent using the logic. Indeed, that theorem seems to indicate that to show that two processes are equivalent we need to check that they satisfy the same formulae expressible in the logic, and there are countably many such formulae, even modulo logical equivalence. Isn't it possible to find a single formula that characterizes the equivalence of a process p?

To the best of my knowledge, this natural question was first addressed by Susanne Graf and Joseph Sifakis in their paper

Susanne Graf and Joseph Sifakis. A modal characterization of observational congruence on finite terms of CCS.

*Inform. and Control*, 60 (1986), no. 1-3, pp. 125--145.

In that paper, they offered a translation from recursion-free terms of Milner's CCS into formulas of a modal language representing their equivalence class with respect to observational congruence.

Can one characterize the equivalence class of an arbitrary finite process---for instance one described in the regular fragment of CCS---up to bisimilarity using HML? The answer is negative because each formula in that logic can only describe a finite fragment of the initial behaviour of a process. (The "sight" of a formula is limited by the maximum nesting of modal operators occurring in it.)

Consider, for instance, the automaton over set of labels {a,b} with only one state p and a self-loop edge labelled a. The characteristic formula for p modulo bisimulation should state the following properties, which together completely characterize the behavior of p.

- Process p affords an a-labelled transition leading to itself (that is, to a process that is bisimilar to p).
- No matter how p makes an a-labelled transition, it always ends up in a state that is bisimilar to p.
- Process p affords only a-labelled transitions.

F(p) = diamond(a) F(p) AND [a]F(p) AND [b] False,

where I write diamond(a) for the a-labelled may modality in HML to prevent the blogging software from interpreting the standard notation as a HTML tag :-)

The right-hand side of the above formula determines a monotonic endofunction over the collection of sets of processes. The famous Knaster-Tarski fixed-point theorem yields a complete lattice of fixed-points for that function. It turns out that the largest fixed-point is the collection of all processes that are bisimilar to p. So, we can give characteristic formulae modulo bisimulation for states of finite labelled transition systems using HML enriched with a facility for the recursive definition of formulae, where recursively defined formulae are interpreted using largest fixed-points.

I believe that this characteristic formula construction was first noticed in the relatively unknown MSc thesis

Anna Ingolfsdottir, Jens Christian Godskesen and Michael Zeeberg. Fra Hennessy-Milner Logik til CCS-Processer. Department of Computer Science, Aalborg University, 1987

The thesis, supervised by Kim G. Larsen, was unfortunately encrypted in Danish, and this is one of the reasons why it is not as well known as it deserves to be. Some of ideas and technical developments from that work then appeared in the paper

Bernhard Steffen, Anna Ingolfsdottir: Characteristic Formulae for Processes with Divergence Inf. Comput. 110(1): 149-163 (1994),

which is by now the standard reference for the development of characteristic formulae for bisimulation-like behavioural relations over finite processes.

## Friday, November 24, 2006

### New Rector at Reykjavík University

**Service Leadership: The Quest for Competitive Advantage**with Judith B. (Banks) Strother. (Check the price!)

I will refrain from passing judgement on this choice until I see her in action. One word about the selection process, though. One of our contacts at Columbia University wrote to us saying:

First, most established American universities would announce a Search Committee to search for a new president. The Search Committee would typically comprise members of the board of directors, faculty, and even a staff member and student. Second, once a Search Committee was in place, a formal announcement would be made, with a deadline for applications and nominations. The principal publication that most universities--American or European--use to make these announcements is The Chronicle of Higher Education and sometimes even The New York Times education employment section. The Search Committee would meet to review applications and nominations and typically will select between 7 and 10 potential candidates for initial interviews. Following that, finalists, perhaps 3 individuals, would be interviewed in-depth and even asked to write a statement of their vision for the university. The selection of a final candidate is usually a consensus process.

Whatever process they chose, it was nothing like this, and the decision was not a consensus one. I hope it was a good one, especially because Reykjavík University is at a watershed, and a clear message has to be sent out as to whether the university wants to be what the Americans call a "research university" or some kind of teaching and service institution. However, I can already say that I did not like hearing the chairman of the Board of Directors talk about the university as an "educational company". I might be old fashioned, but a university is not a firm, and has very different purposes from a company.

Fingers crossed.

## Monday, November 20, 2006

### Predicting the Future

A few well-known scientists talk about mathematics and computing. In fact, even one of the mathematics contributions focus on computer science! Tim Gowers' prediction discusses the P versus NP problem. He writes:

Thanks for the further publicity Timothy!

There are about half a dozen problems that almost all mathematicians agree are supremely important. One that I particularly like is the "P = NP" problem. ....

This problem gets to the heart of mathematics, because mathematical research itself has the property I have described: it seems to be easier to check that a proof is correct than to discover it in the first place. Therefore, if we found a solution to the P = NP problem it would profoundly affect our understanding of mathematics, and would rank alongside the famous undecidability results of Kurt Gödel and Alan Turing.

As for Gregory Chaitin, he went on record as saying that:

I cannot believe that this statement will win him many friends :-) I, for one, am overawed to live in a research world which is full of very creative people. Sure, the heights of "creativity" are the realm of a chosen few, but one should never underestimate the importance of contributing small bricks of knowledge to the scientific enterprise. If everybody just looked for the next quantum leap in a field all of the time, the result will probably be stagnation.

In my own field, I hope the current desiccated, formal approach has died out and people are more adventurous and creative.

I'll try to get hold of a copy of that number of the New Scientist.

On a local note, I had my own personal peek at my crystal ball last October, when I forecast that the rector of Reykjavík University will be chosen as one of the candidates to run for parliament at the next Icelandic elections. It did not take special powers of predictions to come to that conclusion. I am eagerly waiting to see who the next rector will be. Above all, I hope that the new rector will be "research friendly".

## Saturday, November 18, 2006

### Spinoza

Reading Goldstein's warm account of Spinoza's philosophy and of his social and intellectual environment made me think that Spinoza's thought really has had a deep influence on the Dutch way of thinking (whatever that may be), and might indeed be one of the sources of the rationality that inbues Dutch society.

As Spinoza hints at in his writings, for every fact that is true, there is a reason why it is true. Since there are no arbitrary aspects of reality, logic itself must explain the world. In fact, logic itself is the world, which is just the collection of logical implications that make Nature.

Spinoza wrote:

"Thus in life it is before all things useful to perfect the understanding, or reason, as far as we can, and in this alone man's highest happiness, or blessedness, consists...."

I do not know whether I feel like endorsing Spinoza's vision completely, but I certainly feel that the intellectual process of beholding his vision of the world is an enriching one.

The closing words of Goldstein's book are a fitting climax to a well-written volume that I recommend heartily:

"The world has been transformed (though not enough) by a long and complicated chain of causes and effects that reaches back to Spinoza's choice to think out the world for himself."

I cannot help but feeling that the exercise of "thinking our way toward radical objectivity" would be a useful exercise for many of our leaders today.

You can also listen to a podcast interview with Rebecca Goldstein on the Nextbook website. Enjoy.

You might also wish to check out Rebecca Goldstein's other books. In particular, the novel The Mind-Body Problem is a favourite of mine. Readers of this blog will also enjoy the well-written, but at times somewhat flawed, Incompleteness: The Proof and Paradox of Kurt Gödel.

## Wednesday, November 15, 2006

### The Number of Labelled Trees over n Nodes

*n*nodes is

*n*Anders presented a bijective proof of this counting result due to André Joyal. (Concurrency theory buffs will recall that Joyal, together with Mogens Nielsen and Glynn Winskel, was one of the authors of the famous paper Bisimulations from Open Maps. Anders tells me that Joyal is also the father of the theory of combinatorial species.)

^{n-2}*.*

The proof is truly beautiful, and establishes a bijection between doubly rooted trees over {1,...,n}, and functional digraphs over that set. (A digraph is functional if the out-degree of each of its nodes is 1.) I encourage all of you to have a look at it.

Anders then showed how to obtain a proof of Cayley's theorem using the very general machinery of generating functions. (See this freely available book.) I must admit that I find the latter proof a little "magical", but this is due to my ignorance of the machinery of formal power series, generating functions and Lagrange inversion :-)

Addendum 18/11/2006: I have noticed that the classic textbook A Course in Combinatorics (2nd Edition) by J. H. van Lint and R. M. Wilson presents three different proofs of Cayley's theorem. (I think that the book offers five proofs of that result overall.)

As reading on generating functions, Anders recommends the draft book Analytic Combinatorics by Philippe Flajolet and Robert Sedgewick even more than Herbert Wilf's book.

## Tuesday, November 14, 2006

### Advice from David Patterson

Patterson's advice is crystallized into the following Patterson Rules for increasing productivity at work, and reducing the frustration that ensues from coming in earlier, staying later, and getting less work done. Other pieces of advice from him include the following nuggets.

(saying no lets you say yes later)

Do the Patterson rules apply to your work practices?

## Saturday, November 11, 2006

### Workshop on Emerging Trends in Concurrency Theory

*Emerging Trends in Concurrency Theory*will be held at LIX, École Polytechnique de Paris, during 13-15 of November 2006. The colloquium is organized by Catuscia Palamidessi and Frank D. Valencia, and will be held under the auspices of Working Group 1.8 on Concurrency Theory of IFIP TC1. The guest of honor will be Turing Award winner Robin Milner, who was awarded one of the prestigious Blaise Pascal International research chairs to visit LIX for the 2006-2007 academic year.

The event will have well over 10o participants, and has a programme of talks to whet anybody's appetite. I am really sorry to have to miss this event, which clashes with the exams for our courses in Reykjavík---a rather mundane reason for having to miss what will be a great event.

Fortunately, Wan (Fokkink), the co-chair of WG1.8, will be there, you will be able to discuss with him matters related to the proposal to hold a WG workshop at CONCUR 2007.

It would be great if one or more of the participants could report on the workshop using the blog. All you need to do is to email me your report(s), and I'll take care of posting them on this blog.

I, for one, would be happy to read about yet another great event I am missing.

## Thursday, November 09, 2006

### Book off to the Publisher

**Lester Burnham**: Remember those Posters that said, today is the first day of the rest of your life? Well that's true with everyday except one, the day you die.

I have just posted the final manuscript of the book "Reactive Systems: Modelling, Specification and Verification", co-authored with Anna Ingolfsdottir, Kim G. Larsen and Jiri Srba, off to Cambridge University Press.

We'll maintain a web site for the book, that will be published in the spring 2007. (At the moment it is empty, sorry!) On the web site, an instructor will find suggested schedules for his/her courses, exercises that can be used to supplement those in the textbook, links to other useful teaching resources that we will make available on the web, further suggestions for student projects and electronic slides that can be used for the lectures. We'll also make available CWB and Uppaal models for all of the proposed projects. Students will have access to the solutions for the mandatory and strongly recommended exercises in the book.

For the moment, you can read the preface, and have a look at the table of contents here. Then, tell your library to buy copies in due course, make a note to buy your own copy when the book is out, and consider it for course use :-)

I must say that it really feels like "the first day of the rest of my life", hence the quote from American Beauty. Now it is time to catch up with several outstanding other projects, hoping that my co-workers will still want to work with me at this stage.

## Wednesday, November 08, 2006

### Brief News from the Math World

Terence Tao continues to collect prizes and awards. He has also landed the SASTRA Ramanujan Prize.

Anders Claesson, from the combinatorics group at Reykjavík University, has pointed out the following two math blogs to me: Mathematics under the Microscope and A Neighbourhood of Infinity. Maybe some of you might enjoy looking at them.

Bill Gasarch has a guest post on the Complexity Weblog on the topic of private information retrieval. He mentions the following papers:

An Ω(n

^{1/3}) lower bound for bilinear group based Private Information Retrieval by Alexander Razborov and Sergey Yekhanin, FOCS 2006.

New Locally Decodable Codes and Private Information Retrieval Schemes, by Sergey Yekhanin

Apparently, the former paper models 2-Database-Private Information Retrieval via Latin Squares and then uses representation theory of finite groups to push through the lower bound. The latter uses Mersenne primes.

I have not looked at the papers, but that sounds like yet another application of very hard maths in volume A TCS.

## Thursday, November 02, 2006

### Process Algebra on Lambda the Ultimate

The references provided in that post are to the point. As Mohammad pointed out to me, relevant process algebraic work along those lines may also be found in the paper

H.M.A. van Beek. An algebraic approach to transactional processes. CS-Report 02/18, Department of Mathematics and Computing Science, Technische Universiteit Eindhoven, December 2002. Harm's Ph.D. thesis contains that report as a chapter (Chapter 8).

As far as I know, the earliest studies of "atomic transactions" within the field of process calculi were presented by Gérard Boudol and Ilaria Castellani in two papers that appeared in the late 1980s:

- Gérard Boudol,
*Atomic actions*, in EATCS Bulletin Vol. 38 (1989), 136-144.

[Abstract, PostScript, .ps.gz] - Gérard Boudol and Ilaria Castellani,
*Concurrency and atomicity*, in Theoretical Computer Science Vol. 59 (1988), 25-84.

[Abstract]

I encourage my readers to post further reading suggestions on the topic of process calculi for atomic transactions. As Charles Stewart writes on Lambda the Ultimate, this topic will repay a closer look.

## Wednesday, October 25, 2006

### Rock and TCS

One of the events at FOCS was a concert by Lady X and The Positive Eigenvalues, a band that includes Christos Papadimitriou on keyboards. As Luca Trevisan notes in his blog, apart from Christos Papadimitriou, Mike Jordan, and guest star Anna Karlin, that band includes "a number of other Berkeleites (for some reason, all Italians)."

This is not the first ever example of a rock concert held at a major theory conference. I recall that Dexter Kozen and his band performed at the Monterey aquarium during LICS 1989. Amongst others, they offered (T)CS renditions of songs by the Ramones (I wanna be promoted) and the Dead Kennedys (Categories über alles). At the time I collected a leaflet with the text of the songs Dexter's band played, but I lost it. Here is a scanned version of the leaflet, courtesy of Don Sannella. Enjoy it!

## Sunday, October 22, 2006

### Report on NWPT06

Anna and I organized the 18th Nordic Workshop on Programming Theory from Wednesday, 18 October, till Friday, 20 October, at Reykjavík University. The workshop was held under the auspices of the Icelandic Centre of Excellence in Theoretical Computer Science (ICE-TCS) and of the IFIP TC1 Working Group 1.8 on Concurrency Theory, and was partly sponsored by Reykjavík University.

The NWPT series of annual workshops is a forum bringing together programming theorists from the Nordic and Baltic countries (but also elsewhere). The previous workshops were held in Uppsala (1989, 1999 and 2004), Aalborg (1990), Gothenburg (1991 and 1995), Bergen (1992 and 2000), Turku (1993, 1998, and 2003), Aarhus (1994), Oslo (1996), Tallinn (1997 and 2002), Lyngby (2001), and Copenhagen (2005). Thus, this was the first ever NWPT workshop held in Iceland.

- There were no contributed talks from Sweden, and David Sands was therefore the only representative of Swedish computer science at the workshop.
- There was a good number of participants from Germany.)

- Gerd Behrmann, Aalborg University.
*How to become a successful tool builder - the dirty tricks* - Matthew Hennessy, University of Sussex.
*Some Remarks on Testing Probabilistic Processes*. - Hanne Riis Nielson, DTU.
*Analysis of Process Interactions* - David Sands, Chalmers University of Technology and University of Göteborg.
*Specifying and Verifying Dynamic Information Flow Properties*

Gerd Behrmann's talk offered a thought provoking and stimulating analysis of the role of tool development in algorithmic verification. Gerd gave the audience many good reasons for building tools, but also pointed out that empirical studies in this field are often of questionable quality, with results that are not reproducible and unfounded conclusions. He pledged for this situation to be improved if tool building is to become a respected scientific activity.

Not surprinsingly, Gerd's talk gave rise to a lively discussion (both during and after the presentation). Flemming Nielson made some very interesting remarks after the talk, explaining how a tool developer can obtain credit for his/her work at his institution (DTU), e.g., by means of innovation schemes and the writing of books about the lessons learned during tool building. He also defended, in case there was any need to do so, the hard work of theorists, and uttered the following eminently quotable sentence:

"The purpose of theory is insight, not theorems!"

Matthew Hennessy delivered a talk on testing probabilistic processes that presented work he did while visiting NICTA in Australia. This was a one hour version of a shorter talk he had delivered earlier at the symposium in honour of Gordon Plotkin's sixtieth birthday. Matthew gave a typically well polished lecture, which managed to present a lot of technical work without ever giving his audience the feeling of being overwhelmed by the mathematics. I am looking forward to reading the paper on which the talk was based.

The last invited talk for the workshop was delivered by David Sands. Static verification of secure information flow has been a popular theme in recent programming language research, but the information flow policies considered are based on a static view of security levels. In his talk, Dave provided a road map of the main directions of current research, and introduced a simple mechanism, called flow locks, for specifying dynamic information flow policies, and a type-and-effect system for statically verifying flow lock policies. The talk was based on joint work with Niklas Broberg.

The 26 contributed talks were mostly of excellent quality, presenting work at different stages of development; some of it was definitely in progress, some other was "in infancy", and some was instead very mature. This is what a workshop should be like!

Some photos from the workshop, courtesy of MohammadReza Mousavi, are available.

The 2007 edition of the workshop will be held in Oslo, Norway. I trust that it'll be just as successful as we felt this one was. Good luck to Olaf Owe, who will take over the mantle of organizer from Anna and me.

## Tuesday, October 17, 2006

### Double Blind Refereeing

A computer scientist is preparing a submission to a conference in Language Technology that has double blind refereeing. He is just about the only person in the world doing tagging for Icelandic. Should he cite his own work in the submission?

This colleague realized that, by citing his own work, he would make his identity known to the reviewers, and was worried that this might influence them. We told him that a reviewer would be able to infer the name of the author from the paper anyway because he is really the only possible author of that paper. (In general, in TCS the set of possible authors of a paper is not very large, and, using tell-tale stylistic or notational usages, a reviewer of an authorless paper is often able to determine the author(s) of a paper with a rather large degree of accuracy.)

Consider also the following catch-22 situation. A reviewer of the paper by our colleague could reject it because the anonymous author X is neither citing the closely related work of author X nor comparing his work with that of author X! It would be just great to have one's paper rejected for not citing one's own work, wouldn't it?

I have never believed in double blind refereeing. This story has reinforced my lack of belief in this system.

## Friday, October 13, 2006

### Mini Course on Model Checking Real-time Systems in Reykjavík

*Model Checking for Real-time Systems*held by Kim G. Larsen. The course will be held on Monday, 16 October, at Reykjavík University. (In case you are interested in looking at some text in Icelandic, you can see the announcement that will appear tomorrow in one of the local newspapers.)

The course will be followed by an exercise session on Tuesday, 17 October, held by Alexandre David (Aalborg University). Feel free to drop by, if you happen to be in Reykjavík for the

*Iceland Airwaves*music festival.

### Teaching Reductions

After last Wednesday's lecture, however, I was totally drained of energy. Why? During Tuesday's lecture I introduced the concept of reduction, and used it to prove the undecidability of the emptiness, equality and regularity problem for Turing machines. The day after I started the lecture with a warm-up, peer instruction session asking the students to argue that it is undecidable whether a Turing machine accepts the language {Alan, Turing}. The reaction was summarized by the blank stare I got from most of my audience Even when we worked through the solution together, I still had the feeling that many of them were not comfortable with the notion of reduction. I had to work very hard to try and clarify it as best as I could, and it is not clear to me yet whether I succeeded.

Looking back to my previous experiences teaching this course, or variations on it, in Aalborg, this is not surprising. The notion of reduction is the bread-and-butter of computability and complexity, and one of the cornerstones of algorithmic thinking. Having mastered it, the rest of the material in my introductory courses becomes, I would venture to say, relatively easy. It is one of those powerful concepts that opens up new vistas, and, despite being very natural and ubiquitous in the theory of computing, requires some intellectual maturity to be understood fully.

A typical pitfall I have experienced over the years is that many students think that the pre-processing algorithm converting, say, the question "Does a Turing machine M accept the string w?" into an equivalent one of the form "Does the Turing machine M' accept the empty language?" actually runs M on input w when, while producing the code for M', it writes the line of code

Run M on input w.

Here I usually use the analogy with a compiler to try and dispel their doubts. (Basically, I tell them to view the pre-processing algorithm implementing the reduction as a compiler between inputs to two different problems. The pre-processing algorithm outputs a piece of code, but never runs it.) It is not up to me to say whether this works, but it seems to me that most of the students "crack the code", and start thinking naturally in terms of reductions between algorithmic problems.

Is it just my personal experience, or are reductions hard to grasp for many of our students? I'd be happy to hear how you go about teaching reductions in your classes on the theory of computation, and what analogies/metaphors you use to help your students understand such a fundamental notion.

## Monday, October 09, 2006

### Turing in the Notices of the AMS

I have already recommended it to the students who are taking my theory of computation course in Reykjavík.

Enjoy it!

## Wednesday, October 04, 2006

### Paul Halmos, 1914-2006

A few years ago, I had the pleasure of borrowing his "mathobiography" I Want to Be a Mathematician from Steffen Lauritzen in Aalborg, and enjoyed it immensely. I plan to buy a copy for my bookshelves at some point.

Bas Luttik has keeps telling me to read Halmos's expository work on algebraic logic. I keep postponing doing so, but maybe now it is time to start. At least after some pencil sharpening has taken place :-)

Let me end with a quotation from Halmos's mathobiography I like:

"I love to do research, I want to do research, I have to do research, and I hate to sit down and begin to do research---I always try to put it off just as long as I can.

....Isn't there something I can (must?) do first? Shouldn't I sharpen my pencils perhaps?"- --Paul Halmos,I Want to be a Mathematician

These days I sharpen my pencils a lot, alas.

## Saturday, September 30, 2006

### N is a Number

*N is a Number: A Portrait of Paul Erdös*by George Csicsery. I bought the DVD of this award winning documentary using my Springer author discount, and, rather than watching it at home, I decided to share it with my colleagues at Reykjavík University. I also hoped that some of our students would show up to watch the documentary. (Every opportunity is good to entice students to study TCS! Unfortunately, however, no student took the bait and joined us :-()

The documentary is good and I recommend it, even though it does not hold many surprises for people who have read the popular books on Paul Erdös. However, watching Paul Erdös strut his skills on the dias before diving into the mathematics was an enjoyable experience for somebody like me who never had the chance of seeing him "live".

I wonder whether he is still managing to keep the SF's score low wherever he may be now.

Addendum: The Erdös numbers of the members of ICE-TCS are here.

## Sunday, September 24, 2006

### MohammadReza Mousavi in Reykjavík

The 'group' has doubled in size since August this year, with the arrival of Silvio Capobianco (a mathematician from Rome) and Mohammad. Their arrival has also strengthened ICE-TCS considerably, and their presence is giving Anna and me a good intellectual environment to work in. Now it's up to us to make the most of this opportunity, and I hope that we'll be able to capitalize on their scientific strength. If we don't, then it's going to be solely our fault.

The problems we encountered in getting a visa for Mohammad at the last minute seem to have some positive consequences. Together with the Icelandic research council, we are pressing the politicians here to establish a fast-track for researchers seeking visas and work permits to come and work in Iceland. Having a "researcher visa" procedure might make it more attractive for scientists to come and work here in the North Atlantic, at times when access to other countries is becoming more and more difficult. I'll keep you posted on the developments.

## Friday, September 22, 2006

### New Perspectives on Fairness

*New Perspectives on Fairness*by Daniele Varacca and Hagen Voelzer.

Fairness is an important concept that appears repeatedly in various forms in different areas of computer science, and plays a crucial role in the semantics and verification of reactive systems. Entire books are devoted to the notion of fairness---see, for instance, the monograph by Nissim Francez published in 1986---, and researchers in our community have painstakingly developed a taxonomy of various fairness properties that appear in the literature, such as unconditional fairness, weak fairness, strong fairness, and so on. This research is definitely important in light of the plethora of notions of fairness that have been proposed and studied in the literature.

But when is a temporal property expressing a fairness requirement? The authors of this column have recently developed a very satisfying answer to this fundamental question by offering three equivalent characterizations of ``fairness properties'' in the setting of linear-time temporal logic: a language-theoretic, a topological, and a game-theoretic characterization. This survey discusses these recent results in a very accessible fashion, and provides also a beautiful link between the study of fairness and classic probability theory.

I trust that you will enjoy reading this piece by Daniele and Hagen as much as I did. It is not often that one sees notions and results from several areas of mathematics and computer science combine so well to offer a formalization of a concept that confirms our intuition about it.

## Tuesday, September 19, 2006

### MacArthur Genius Awards for 2006

- Luis von Ahn.

- Terence Tao.
- Claire Tomlin. The announcement makes very interesting reading for a concurrency theorist, and for anyone interested in formal verification:
Much of Tomlin's research concentrates on aeronautical applications of hybrid systems research, particularly aircraft flight control and air traffic conflict resolution. As the number of variables increases and their interactions become more complex, it becomes ever more difficult to guarantee that systems will always be within safe limits. Tomlin has developed practical algorithms for determining when unsafe conditions may arise, and for establishing feedback control laws for a hybrid system guaranteed to remain within a safe subset of all reachable states.

Congratulations to the winners of the awards!

### Jazz meets Process Algebra

## Saturday, September 16, 2006

### An Essay by Palamidessi and Valencia

This essay is a commendable example of `outreach activity´ from two very active members of the concurrency theory community. Let's give it to our students and colleagues from other areas of computer science to read, and let's try to sow the seeds of our research area in our departments. Something good is bound to come out of these kind of efforts. For the moment, thanks to Catuscia and Frank for offering a contribution in this direction.

## Thursday, September 14, 2006

### New Award to Moshe Vardi

See http://www2.informatik.hu-berlin.de/lics/#awards for a description of the award. I think that the idea to look back 20 years for the award is a good one, and look forward to seeing more awards in areas of logic related to concurrency theory and formal verification.

### Experimental Blog for the IFIP WG on Concurrency Theory

## Wednesday, September 06, 2006

### PC Chair for FOSSACS 2008

## Tuesday, September 05, 2006

### Gordon Plotkin is 60

This is really good to see. Gordon is one of the veritable giants in TCS, and he has had outstanding students and collaborators over the years. His contributions to the study of the semantics of programming languages (be it denotational, logical or operational) and to its mathematical underpinnings are well known, so I'll just limit myself to wishing Gordon a happy symposium.

## Sunday, September 03, 2006

### What Are the Most Important Open Problems in Concurrency?

Based upon this thought experiment, wouldn't it be a good thing to have a repository of open problems that identify the present state of development in concurrency theory, and suggest directions for further research?

At some point in the past, I started putting together a list of open problems, but I have not really maintained it for a while. Will you help me revive this enterprise by sending me, or posting as a comment to this blog entry, a description of your favourite open problems in concurrency theory, together with links to partial solutions and pointers to the literature? This input of yours might even form the basis for a useful installment of the Concurrency Column in the Bulletin of the EATCS, and generate a lot of research in our field following what Luca Trevisan has called in this very informative blog entry the "Hungarian approach to mathematics": pose very difficult problems, and let deep results, connections between different areas of math, and applications, come out as byproducts of the search for a solution.

By the way, Luca Trevisan has a few very interesting posts related to Szemeredi's theorem and other results in additive combinatorics. (See this one, and the five blog entries on Szemeredi's theorem.) Those posts give an inkling of the level of mathematical sophistication that has been reached in TCS research from the volume A camp. Check them out!

## Thursday, August 31, 2006

### A New Yorker Article on the Poincaré Conjecture

I do not know if the content of the article is truly trustworthy, but it makes for some interesting, and at times arresting, reading. This excerpt, for one, tells the remarkable story of the recent publication of what could be a key paper in the story of the solution of the Poincaré conjecture:

On April 13th of this year, the thirty-one mathematicians on the editorial board of the Asian Journal of Mathematics received a brief e-mail from Yau and the journal’s co-editor informing them that they had three days to comment on a paper by Xi-Ping Zhu and Huai-Dong Cao titled “The Hamilton-Perelman Theory of Ricci Flow: The Poincaré and Geometrization Conjectures,” which Yau planned to publish in the journal. The e-mail did not include a copy of the paper, reports from referees, or an abstract. At least one board member asked to see the paper but was told that it was not available. On April 16th, Cao received a message from Yau telling him that the paper had been accepted by the A.J.M., and an abstract was posted on the journal’s Web site.

Quite a remarkable refereeing process for a paper proving one of the Millennium Problems of the Clay mathematical institute!