Live Report from CALCO - Part 2 Without further ado, here is my second report from CALCO. I will only give a short report of the two interesting keynote talks presented yesterday and today.
- Tuesday: Tuesday was the first day of CALCO 2007 main conference. There were some 40-50 participants (depending on when the snapshot is taken). Till Mossakowki opened the conference by mentioning that, despite initial doubts, CALCO 2007 was indeed a success and it attracted some 57 submissions from 3 continents and 14 countries.
Stephen Bloom gave the keynote speech of Tuesday on algebraic and regular words and trees formalized as continuous $\Sigma$-algebras. He mentioned a recent result of his together with Zoltan Esik (I&C, 197(1-2):55--89, 2005) in which they present a complete axiomatization for regular words modulo isomorphism. He quoted the following interesting statement from his teacher who taught him about ordinals.
"Ordinals are the numbers you use to count apples."
- Wednesday: Glynn Winskel delivered his keynote address on symmetry and concurrency. He motivated the choice of the topic by a few examples from Petri Nets and HD Automata and Strand Spaces to the effect that the lack of a notion of symmetry blocks universal treatment of some constructions (such as unfolding). He started off by introducing event structures (surprise, surprise!) and presented their application as types (in stable domain theory) and processes (in the semantics of process algebras and Petri Nets). Subsequently (total, rigid, and open) maps on event structures were presented as ways of relating them and in particular open maps are underscored as a notion of bisimulation among event structures. Semantics of nondeterministic dataflow programs was presented as a challenge to which event structure with some sort of maps to input and output even structures, called stable spans, provide a solution. Glynn mentioned that this is the same as the idea of pro-functors, but admittedly I could not appreciate the value of this fact! After some discussion on insufficiency of stable maps, he defined an abstract notion of symmetry using (a pair of) open maps on event structures. He ran a bit out of time and could not get into concrete applications of this notion of symmetry but the moral of the story, if I understand it correctly, is that by taking symmetry into account you get more general and universal constructions (maps) that are not too fine to distinguish between symmetric objects.
To conclude my reports on CALCO, I feel obliged to thank the local organizer for the excellent organization. Luca arrived here on Wednesday afternoon and I guess we will all have the chance to read about the rest from him.