Behavioral Equivalences

Beahvioral equivalences serve to establish in which cases two reactive (possible concurrent) systems offer similar interaction capabilities relatively to other systems representing their operating environment. Behavioral equivalences have been mainly developed in the context of process algebras, mathematically rigorous languages that have been used for describing and verifying properties of concurrent communicating systems. By relying on the so called structural operational semantics (SOS), labelled transition systems, are associated to each term of a process algebra. Behavioral equivalences are used to abstract from unwanted details and identify those labelled transition systems that react “similarly” to external experiments. Due to the large number of properties which may be relevant in the analysis of concurrent systems, many different theories of equivalences have been proposed in the literature. The main contenders consider those systems equivalent that (i) perform the same sequences of actions, or (ii) perform the same sequences of actions and after each sequence are ready to accept the same sets of actions, or (iii) perform the same sequences of actions and after each sequence exhibit, recursively, the same behavior. This approach leads to many different equivalences that preserve significantly different properties of systems

On the Rationality of Escalation

Escalation is a typical feature of infinite games. Therefore tools conceived for studying infinite mathematical structures, namely those deriving from coinduction are essential. Here we use coinduction, or backward coinduction (to show its connection with the same concept for finite games) to study carefully and formally the infinite games especially those called dollar auctions, which are considered as the paradigm of escalation. Unlike what is commonly admitted, we show that, provided one assumes that the other agent will always stop, bidding is rational, because it results in a subgame perfect equilibrium. We show that this is not the only rational strategy profile (the only subgame perfect equilibrium). Indeed if an agent stops and will stop at every step, we claim that he is rational as well, if one admits that his opponent will never stop, because this corresponds to a subgame perfect equilibrium. Amazingly, in the infinite dollar auction game, the behavior in which both agents stop at each step is not a Nash equilibrium, hence is not a subgame perfect equilibrium, hence is not rational.Comment: 19 p. This paper is a duplicate of arXiv:1004.525

Generalized Vietoris Bisimulations

We introduce and study bisimulations for coalgebras on Stone spaces [14]. Our notion of bisimulation is sound and complete for behavioural equivalence, and generalizes Vietoris bisimulations [4]. The main result of our paper is that bisimulation for a $\mathbf{Stone}$ coalgebra is the topological closure of bisimulation for the underlying $\mathbf{Set}$ coalgebra

Intelligent escalation and the principle of relativity

Escalation is the fact that in a game (for instance in an auction), the agents play forever. The $0,1$-game is an extremely simple infinite game with intelligent agents in which escalation arises. It shows at the light of research on cognitive psychology the difference between intelligence (algorithmic mind) and rationality (algorithmic and reflective mind) in decision processes. It also shows that depending on the point of view (inside or outside) the rationality of the agent may change which is proposed to be called the principle of relativity.Comment: arXiv admin note: substantial text overlap with arXiv:1306.228

Loosening the notions of compliance and sub-behaviour in client/server systems

In the context of "session behaviors" for client/server systems, we propose a weakening of the compliance and sub-behaviour relations where the bias toward the client (whose "requests" must be satisfied) is pushed further with respect to the usual definitions, by admitting that "not needed" output actions from the server side can be "skipped" by the client. Both compliance and sub-behaviour relations resulting from this weakening remain decidable, though the proof of the duals-as-minima property for servers, on which the decidability of the sub-behaviour relation relies, requires a tighter analysis of client/server interactions.Comment: In Proceedings ICE 2014, arXiv:1410.701

Logic programming and bisimulation

The logic programming encoding of the set-theoretic graph property known as bisimulation is analyzed. This notion is of central importance in non-well-founded set theory, semantics of concurrency, model checking, and coinductive reasoning. From a modeling point of view, it is particularly interesting since it allows two alternative high-level characterizations. We analyze the encoding style of these modelings in various dialects of Logic Programming. Moreover, the notion also admits a polynomial-time maximum fixpoint procedure that we implemented in Prolog. Similar graph problems which are instead NP hard or not yet perfectly classified (e.g., graph isomorphism) can inherit most from the declarative encodings presented

Producing Enactable Protocols in Artificial Agent Societies

This paper draws upon our previous work [7, 16] in which we proposed the organisation of services around the concept of artificial agent societies and presented a framework for representing roles and protocols using LTSs. The agent would apply for a role in the society, which would result in its participation in a number of protocols. We advocated the use of the games-based metaphor for describing the protocols and presented a framework for assessing the admission of the agent to the society on the basis of its competence. In this work we look at the subsequent question: what information should the agent receive upon entry?. We can not provide it with the full protocol because of security and overload issues. Therefore, we choose to only provide the actions pertinent to the protocols that the role the agent applied for participates in the society. We employ branching bisimulation for producing a protocol equivalent to the original one with all actions not involving the role translated into silent (τ) actions. However, this approach sometimes results in non-enactable protocols. In this case, we need to repair the protocol by adding the role in question as a recipient to certain protocol messages that were causing the problems. We present three different approaches for repairing protocols, depending on the number of messages from the original protocol they modify. The modified protocol is adopted as the final one and the agent is given the role automaton that is derived from the branching bisimulation process

Proving Continuity of Coinductive Global Bisimulation Distances: A Never Ending Story

We have developed a notion of global bisimulation distance between processes which goes somehow beyond the notions of bisimulation distance already existing in the literature, mainly based on bisimulation games. Our proposal is based on the cost of transformations: how much we need to modify one of the compared processes to obtain the other. Our original definition only covered finite processes, but a coinductive approach allows us to extend it to cover infinite but finitary trees. After having shown many interesting properties of our distance, it was our intention to prove continuity with respect to projections, but unfortunately the issue remains open. Nonetheless, we have obtained several partial results that are presented in this paper.Comment: In Proceedings PROLE 2015, arXiv:1512.0617

Coinductive soundness of corecursive type class resolution

This work has been partially supported by the EU Horizon 2020 grant “RePhrase: Refactoring Parallel Heterogeneous Resource-Aware Applications - a Software Engineering Approach” (ICT-644235), by COST Action IC1202 (TACLe), supported by COST (European Cooperation in Science and Technology), and by EPSRC grant EP/K031864/1-2 “‘Coalgebraic Logic Programming for Type Inference”.Horn clauses and first-order resolution are commonly used for the implementation of type classes in Haskell. Recently, several core- cursive extensions to type class resolution have been proposed, with the common goal of allowing (co)recursive dictionary construction for those cases when resolution does not terminate. This paper shows, for the first time, that corecursive type class resolution and its recent extensions are coinductively sound with respect to the greatest Herbrand models of logic programs and that they are inductively unsound with respect to the least Herbrand models.Postprin