Last year, the CONCUR conference series inaugurated its Test-of-Time Award, whose purpose is to recognise important achievements in Concurrency Theory that were published at the CONCUR conference and have stood the test of time. This year, the following four papers were chosen to receive the CONCUR Test-of-Time Awards for the periods 1994–1997 and 1996–1999 by a jury consisting of Rob van Glabbeek (chair), Luca de Alfaro, Nathalie Bertrand, Catuscia Palamidessi, and Nobuko Yoshida:

- David Janin and Igor Walukiewicz. On the Expressive Completeness of the Propositional mu-Calculus with respect to Monadic Second Order Logic.
- Uwe Nestmann and Benjamin C. Pierce. Decoding Choice Encodings.
- Ahmed Bouajjani, Javier Esparza, and the late Oded Maler. Reachability Analysis of Pushdown Automata: Application to Model-checking.
- Rajeev Alur, Thomas A. Henzinger, Orna Kupferman, and Moshe Y. Vardi.
Alternating Refinement Relations.

Last year, I interviewed the CONCUR 2020 Test-of-Time Award recipients and was asked by Javier Esparza (chair of the CONCUR SC) and Ilaria Castellani (outgoing chair of the IFIP WG 1.8 on Concurrency Theory) to do the same with the current batch of awardees. (In passing, let me thank Nathalie Bertrand and Nobuko Yoshida for their kind help with the interviews!)

This post is devoted to the interview I conducted via email with Rajeev Alur, Thomas A. Henzinger, Orna Kupferman and Moshe Y. Vardi. Reading the answers I received from that dream team of colleagues was like a masterclass for me and I trust that their thoughts on their award-winning paper will be of interest to many of the readers of this blog. Enjoy!

**Luca:** You receive the CONCUR ToT Award 2021 for your paper Alternating Refinement Relations, which appeared at CONCUR 1998. In that article, you gave what I consider to be a fundamental contribution, namely the introduction of refinement relations for alternating transition systems. Could you briefly explain to our readers what alternating transition systems are? Could you also tell us how you came to study the question addressed in your award-winning article and why you focused on simulation- and trace-based refinement relations? Which of the results in your paper did you find most surprising or challenging?

**Answer:** When we model a system by a graph, our model abstracts away some details of the system. In particular, even when systems are deterministic, states in the model may have several successors. The nondeterminism introduced in the model often corresponds to different actions taken by the system when it responds to different inputs from its environment. Indeed, a transition in a graph that models a composite system corresponds to a step of the system that may involve some components.
Alternating transition systems (ATSs) enable us to model composite systems in more detail. In an ATS, each transition corresponds to a possible move in a game between the components, which are called agents. In each move of the game, all agents choose actions, and the successor state is deterministically determined by all actions. Consequently, ATSs can distinguish between collaborative and adversarial relationships among components in a composite system. For example, the environment is typically viewed adversarially, meaning that a component may be required to meet its specification no matter how the environment behaves.

In an earlier paper, some of us introduced ATSs and Alternating Temporal Logics, which can specify properties of agents in a composite system. The CONCUR 1998 paper provided refinement relations between ATSs which correspond to alternating temporal logics. Refinement is a central issue in a formal approach to the design and analysis of reactive systems. The relation “I refines S '' intuitively means that system S has more behaviors than system I. It is useful to think about S being a specification and I an implementation. Now, if we consider a composite implementation I||E and specification S||E and we want to check that the component I refines the component S, then the traditional refinement preorders are inappropriate, as they allow I to achieve refinement of I||E with respect to S||E by constraining its environment E. Alternating refinement relations are defined with respect to ATSs that model the interaction among the underlying components, and they enable us to check, for example, that component I has fewer behaviors than component S no matter how component E behaves. They are called “alternating” because refinement may restrict implementation actions but must not restrict environment actions. In other words, refinement may admit fewer system actions but, at the same time, more environment actions.

It was nice to see how theoretical properties of preorders in the traditional setting are carried over to the game setting, and so are the results known then about the computational price of moving to a game setting. First, the efficiency of the local preorder of simulation with respect to the global preorder of trace containment is maintained. As in the traditional setting, alternating simulation can be checked in polynomial time, whereas alternating trace-containment is much more complex. Second, the branching vs. linear characterizations of the two preorders is preserved: alternating simulation implies alternating trace containment, and the logical characterization of simulation and trace-containment by CTL and LTL, respectively, is carried over to their alternating temporal logics counterparts. The doubly-exponential complexity of alternating trace containment, as opposed to the PSPACE complexity of trace containment, is nicely related to the doubly-exponential complexity of LTL synthesis, as opposed to its PSPACE model-checking complexity,

**Luca:** In your paper, you give logical characterisations of your alternating refinement relations in terms of fragments of alternating temporal logic. Logical characterisations of refinement relations are classic results in our field and I find them very satisfying. Since I teach a number of those results in my courses, I'd be interested in hearing how you would motivate their interest and usefulness to a student or a colleague. What would your "sales pitch" be?

**Answer:** There is extensive research on the expressive power of different formalisms. Logical characterization of refinement relations tells us something about the distinguishing power of formalisms. For example, while the temporal logic CTL* is more expressive than the temporal logic CTL, the two logics have the same distinguishing power: if you have two systems and can distinguish between them with a CTL* formula (that is, your formula is satisfied only in one of the systems), then you should be able to distinguish between the two systems also with a CTL formula. Moreover, while CTL is not more expressive than LTL, we know that CTL is “more distinguishing” than LTL. These results have to do with the logical characterizations of trace containment and simulation. The distinguishing power of a specification formalism is useful when we compare systems, in particular an implementation and its abstraction: if we know that the properties we care about are specified in some formalism L, and our system refines the abstraction according to a refinement relation in which the satisfaction of specifications in L is preserved, then we can perform verification on the abstraction.

**Luca:** I am interested in how research collaborations start, as I like to tell "research-life stories" to PhD students and young researchers of all ages. Could you tell us how you started your collaboration on the award-winning paper?

**Answer:**
Subsets of us were already collaborating on other topics related to reactive models and model checking, and all of us shared a common belief that the field was in need to move from the limited setting of closed systems to a more general setting of open systems, that is, systems that interact with an environment. Open systems occur not only when the environment is fully or partly unknown, but also when a closed system is decomposed into multiple components, each of them representing an open system. To build “openness” into models and specifications as first-class citizens quickly leads to the game-theoretic (or “alternating”) setting. It was this realization and the joint wish to provide a principled and systematic foundation for the modeling and verification of open systems which naturally led to this collaboration.

**Luca:** Did any of your subsequent research build explicitly on the results and the techniques you developed in your award-winning paper? Which of your subsequent results on alternating transition systems and their refinement relations do you like best? Is there any result obtained by other researchers that builds on your work and that you like in particular or found surprising?

**Answer:
**
Various subsets of us pursued multiple research directions that developed the game-theoretic setting for modeling and verification further, and much remains to be done. Here are two examples. First, the game-theoretic setting and the alternating nature of inputs and outputs are now generally accepted as providing the proper semantic foundation for interface and contract formalisms for component-based design. Second, studying strategic behavior in multi-player games quickly leads to the importance of probabilistic behavior, say in the form of randomized decisions and strategies, of equilibria, when players have non-complementary objectives, and of auctions, when players need to spend resources for decisions. All of these are still very active topics of research in computer-aided verification, and they also form a bridge to the algorithmic game theory community.

**Luca:** One can view your work as a bridge between concurrency theory and multi-agent systems. What impact do you think that your work has had on the multi-agent-system community? And what has our community learnt from the work done in the field of multi-agent systems? To your mind, what are the main differences and points of contact in the work done within those communities?

**Answer:**
Modeling interaction in multi-agent systems is of natural interest to planning problems studied in the AI community. In 2002, the International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS) was formed and the annual International Conference on Autonomous Agents and Multiagent Systems (AAMAS) was launched. The models, logics, and algorithms developed in the concurrency and formal methods communities have had a strong influence on research presented at AAMAS conferences over the past twenty years. Coincidentally, this year our paper on Alternating-Time Temporal Logic was chosen for the IFAAMAS Influential Paper Award.

**Luca:**What are the research topics that you find most interesting right now? Is there any specific problem in your current field of interest that you'd like to see solved?

**Answer:**
Research on formal verification and synthesis, including our paper, assumes that the model of the system is known. Reinforcement learning has emerged as a promising approach to the design of policies in scenarios where the model is not known and has to be learned by agents by exploration. This leads to an opportunity for research at the intersection of reactive synthesis and reinforcement learning. A potentially promising direction is to consider reinforcement learning for systems with multiple agents with both cooperative and adversarial interactions.

The realization that reactive systems have to satisfy their specifications in all environments has led to extensive research relating formal methods with game theory. Our paper added alternation to refinement relations. The transition from one to multiple players has been studied in computer science in several other contexts. For the basic problem of reachability in graphs, it amounts to moving from reachability to alternating reachability. We recently studied this shift in other fundamental graph problems, like the generation of weighted spanning trees, flows in networks, vertex covers, and more. In all these extensions, we consider a game between two players that take turns in jointly generating the outcome. One player aims at maximizing the value of the outcome (e.g., maximize the weight of the spanning tree, the amount of flow that travels in the network, or the size of the vertex cover), whereas the second aims at minimizing the value. It is interesting to see how some fundamental properties of graph algorithms are lost in the alternating setting. For example, following a greedy strategy is not beneficial in alternating spanning trees, optimal strategies in alternating flow networks may use fractional flows, and while the vertex-cover problem is NP-complete, an optimal strategy for the maximizer player can be found in polynomial time. Many more questions in this setting are still open.

**Luca:** What advice would you give to a young researcher who is keen to start working on topics related to alternating transition systems and logics?

**Answer:**One important piece of advice to young researchers is to question the orthodoxy. Sometimes it is necessary to learn everything that is known about a topic but then take a step back, look at the bigger picture, reexamine some of the fundamental assumptions behind the established ways of thinking, change the models that everyone has been using, and go beyond the incremental improvement of previous results. This is particularly true in formal methods, where no single model or approach fits everything. And young researchers stand a much better chance of having a really fresh new thought than those who have been at it for many years.

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