Game-Theoretic Semantics for ATL+ with Applications to Model Checking

Game-theoretic semantics for ATL+ with applications to model checking

We introduce a new game-theoretic semantics (GTS) for the modal mu-calculus. Our so-called bounded GTS replaces parity games with alternative evaluation games where only finite paths arise; infinite paths are not needed even when the considered transition system is infinite. The novel games offer alternative approaches to various constructions in the framework of the mu-calculus. For example, they have already been successfully used as a basis for an approach leading to a natural formula size game for the logic. While our main focus is introducing the new GTS, we also consider some applications to demonstrate its uses. For example, we consider a natural model transformation procedure that reduces model checking games to checking a single, fixed formula in the constructed models, and we also use the GTS to identify new alternative variants of the mu-calculus with PTime model checking.

We introduce versions of game-theoretic semantics (GTS) for Alternating-Time Temporal Logic (ATL). In GTS, truth is defined in terms of existence of a winning strategy in a semantic evaluation game, and thus the game-theoretic perspective appears in the framework of ATL on two semantic levels: on the object level, in the standard semantics of the strategic operators, and on the meta-level, where game-theoretic logical semantics can be applied to ATL. We unify these two perspectives into semantic evaluation games specially designed for ATL. The novel game-theoretic perspective enables us to identify new variants of the semantics of ATL, based on limiting the time resources available to the verifier and falsifier in the semantic evaluation game; we introduce and analyse an unbounded and bounded GTS and prove these to be equivalent to the standard (Tarski-style) compositional semantics. We also introduce a non-equivalent finitely bounded semantics and argue that it is natural from both logical and game-theoretic perspectives.

A Compositional Automata-based Approach for Model Checking Multi-Agent Systems

In this thesis, we introduce and examine four new temporal logic formalisms that can be used as specification languages for the automated verification of the reliability of hardware and software designs with respect to a desired behavior. The work is organized in two parts. In the first one, we reason about two logics for computations, GCTL* and MCTL*, which are useful to describe a correct execution of monolithic closed systems. In the second one, instead, we focus on two logics for strategies, SL and mATL*, which are useful to formalize several interesting properties about interactive plays in multi-entities systems modeled as multi-agent games. In the “Logics for Computations” part, we first study the immersion of the idea of graded quantifications into the temporal-logic framework. In first order logic, existential and universal quantifiers express the concepts of the existence of at least one individual object satisfying a formula, or that all individual objects satisfy a formula. In other logics, these quantifiers have been generalized to express that, for a given non-negative integer n, at least n or all but n individuals satisfy a particular formula. Here, we consider GCTL, a temporal logic with graded path quantifiers, which allows to describe properties like “there exist at least n different classes of computational fluxes in which a system reaches a predetermined state”, where the classes over paths are computed by means of a predetermined equivalence relation. More precisely, we uniformly extend the classic concept of graded quantifiers from states to paths, through the use of a concept of path equivalence with respect to a given path formula. About this logic, in particular, we study the expressiveness and succinctness relationships with respect to GµCalculus and the complexity of the satisfiability problem, which results to be ExpTime-Complete. This research is partially based on the works [BMM09] “Graded Computation Tree Logic” and [BMM10] “Graded Computation Tree Logic with Binary Coding” published, respectively, in the proceedings of the “IEEE Symposium on Logic in Computer Science, 2009” and “EACSL Annual Conference on Computer Science Logic, 2010”. Preliminary results can be also found in [Mog07]. Furthermore, we consider special quantifiers over substructures, which allow to select, using parametric criteria, small critical parts of a system to be successively verified. In literature, there are some attempts to define a logic that allows to modify the underlying structure under exam and then to verify on it some assigned property. However, as far as we know, none of them is able to select minimal submodels of a given property describing the criteria on which then execute the verification process. Here, we base our work on the search of a new operator that merges the concept of quantifiers on structures with that one derived by a generalization of the concept of pruning. The results of this work, is a class of three different extensions of CTL* with minimal model quantifiers, which we name MCTL*. Regarding these logics, we study several reductions among them, as well as the satisfiability problem that we prove to be highly undecidability, i.e., Σ_1^1-Hard, for two out of the three cases. This research is partially based on the work [MM09] “Branching-Time Temporal Logics with Minimal Model Quantifiers” published in the proceedings of the “International Conference on Developments in Language Theory, 2009”. In the “Logics for Strategies” part, we first study the problem of defining a new specification language through which it is possible to express several important properties of multi-entities systems that are neither expressible using classical monolithic temporal logics, such as CTL*, nor using two-agent-teams temporal logics, such as ATL*. In literature, we can found some proposal of logics that try to achieve this goal, but unfortunately, none of them succeeds completely on all the aspects. Among them, one of the most important attempts is CHP-SL, a logics in which one can use variables over strategies. However, this logic has a deep weakness, since it does not allow to describe games with more than two players and even two-players concurrent games. Here, we introduce SL, a logic with a syntax similar in some aspects to the first order logic, in which the strategies of the agent building the game are treated as first order objects on which we can quantify. This logic generalizes CHP-SL, by allowing the specification of the correct behavior of multi-agent concurrent games. In SL, for example, we are able to express very complex but useful Nash equilibria that are not expressible with CHP-SL. We enlighten that Nash equilibrium is one of the most important concepts in game theory. For the introduced logic, we solve two problems left open in the work on CHP-SL. Precisely, we show that the related model-checking problem is 2ExpTime-Complete, thus not harder of the same problem for several subsumed logics, while we prove that its satisfiability problem is highly undecidable, i.e., Σ_1^1-Hard. This research is partially based on the work [MMV10a] “Reasoning About Strategies” published in the proceedings of the “IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, 2010”. Finally, we consider the concept of relentful strategic reasoning, i.e., a formalism that expresses the ability of a strategy to be used not only to achieve a first given goal, but also to change its final goal in dependence of the history of the play. In the context of planning, memoryful quantification, i.e., quantification over computations that does not lose information about the past along the time, is one of the principal way to express the fact that a system is able to achieve a desired result, and shift to a different goal if some event happens. However, this kind of quantification was not considered before in the context of multi-agent planning. Here, we introduce mATL*, a fusion of the classic alternating temporal logic ATL* with memoryful quantification, with the aim of covering the previous idea. About this logics, we prove that, although it is equivalent to ATL*, it is exponentially more succinct. Nevertheless, we prove that both the model-checking and the satisfiability problems remain 2ExpTime-Complete, as for ATL*. This research is partially based on the work [MMV10b] “Relentful Strategic Reasoning in Alternating-Time Temporal Logic” published in the proceedings of the “International Conference on Logic for Programming Artificial Intelligence and Reasoning, 2010”.

When specifying goals of agents, temporal logics such as linear temporal logic LTL and branching time temporal logic CTL are adopted as basic tools. In order to specify goals in view of multi-agent cooperation which is one aspect of social interaction, two logic frameworks are proposed in this paper based on alternating-time temporal logic ATL. Firstly, ATL is extended with strong and weak exceptions so as to facilitate non-monotonic reasoning of goals, and N-ATL whose model checking complexity is PTIME-complete is proposed. As far as we know, N-ATL is the first multi-agent cooperation logic that takes non-monotonic reasoning into account in the literature. Secondly, ATL is extended with goal operator which is one kind of modal operators, and ATL-G whose model checking complexity is also PTIME-complete is proposed. Examples are introduced to show the usage of these two new multi-agent cooperation logics whose properties are analyzed as well.

Dwyer et al. provide a language to specify dynamic properties based on a limited number of predefined patterns and scopes. The semantics of these properties is defined by translating each combination of a pattern and a scope into usual temporal logics (linear temporal logic, CTL, etc.). This translational semantics suffers from two main issues. It is not easily extensible to other patterns or scopes, and it is not always faithful to the natural semantics. In this article, we propose a compositional automata-based approach defining the semantics of each pattern and each scope by an automaton, after which the semantics is composed. Hence, the semantics is compositional and the language is easily extensible. We compare the two semantics by model checking. In some cases, our semantics reveals a lack of homogeneity within Dwyer et al.’s semantics. Finally, we apply this approach in the context of property-based testing, in order to evaluate the quality of a test suite, by measuring the coverage of the property automaton. To allow the tester to adapt the coverage criteria to its goals, we propose transformation rules over the patterns automata that implement relevant unfolding strategies for loops, or predicates labeling the automata transitions. We illustrate these principles by means of an industrial case study.

In modern chip designs, shared resources are used extensively. Arbiters usage is crucial to settle conflicts when multiple requests compete for these shared resources. Making sure these arbiter circuits work correctly is vital not just for their proper functionality, but also for security reasons. The work in this paper introduces a method based on formal verification to thoroughly assess the proper functional aspects of various arbiter setups. This is achieved through SystemVerilog assertions and model checking. Additionally, we explore a non-invasive method for the modeling and insertion of different types of hardware Trojans. These Trojans, with their unique triggers and payloads, are modeled formally without the need for any alterations to the actual circuit. The results provide a detailed analysis of the cost involved in running the formal verification environment on versions of arbiters that are free from Trojans. This analysis is carried out using Questa PropCheck formal analysis tool, which offers valuable insights into the time and memory resources required. Furthermore, the results highlights how the formally modeled and inserted Trojans interfere with hold criteria of the arbiters’ properties, where at least a single property fires due to the inserted Trojan. This work can be extended to be a generic approach with the potential to validate both the proper operation and security aspects of complex systems.

In this paper we address the problem of distributing model checking of timed automata. We demonstrate through four real life examples that the combined processing and memory resources of multi-processor computers can be effectively utilized. The approach assumes a distributed memory model and is applied to both a network of workstations and a symmetric multiprocessor machine. However, certain unexpected phenomena have to be taken into account. We show how in the timed case the search order of the state space is crucial for the effectiveness and scalability of the exploration. An effective heuristic to counter the effect of the search order is provided. Some of the results open up for improvements in the single processor case.

We develop a sound, complete and practically implementable tableaux-based decision method for constructive satisfiability testing and model synthesis in the fragment ATL+ of the full Alternating time temporal logic ATL*. The method extends in an essential way a previously developed tableaux-based decision method for ATL and works in 2EXPTIME, which is the optimal worst case complexity of the satisfiability problem for ATL+. We also discuss how suitable parameterizations and syntactic restrictions on the class of input ATLP formulae can reduce the complexity of the satisfiability problem.KeywordsState FormulaElimination RuleFull ExpansionInput FormulaNegation Normal FormThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In this paper we present a logic to provide a framework for the formal specification of multiagent real-time systems which allows explicit reasoning about the actions of agents, the nondeterministic model of interaction between agents and environment, the cooperation and competition of agents and the reaction time limits of a system. The logic combines Propositional Dynamic Logic PDL and Alternating-time Temporal Logic ATL and extends the formalism with reaction time constraints. We introduce a multiagent system abstract model and show how the logic can be used to specify the model properties.

When specifying mental states such as belief and goal of agents, temporal logics are often adopted as basic tools. Although there are work on non-monotonic extension of linear temporal logic LTL and branching time temporal logic CTL, the non-monotonic extension of alternating-time temporal logic ATL which is an important kind of multi-agent cooperation logics has not been discussed yet in literature. To solve this problem, this paper proposed non-monotonic alternating-time temporal logic with belief and goal, namely N-ATL-GB to facilitate the non-monotonic reasoning of mental states of agents. Firstly, concurrent game structures of ATL are extended by strong and weak exceptions, two kinds of modal operators are introduced into the syntax of N-ATL-GB, and exceptions removing model is built. Secondly, the corresponding model checking algorithm which can be finished in polynomial time is proposed. Examples are given to show the usage of this new logic at last.

We consider models of multi-player games where abilities of players and coalitions are defined in terms of sets of outcomes which they can effectively enforce. We extend the well studied state effectivity models of one-step games in two different ways. On the one hand, we develop multiple state effectivity functions associated with different long-term temporal operators. On the other hand, we define and study coalitional path effectivity models where the outcomes of strategic plays are infinite paths. For both extensions we obtain representation results with respect to concrete models arising from concurrent game structures. We also apply state and path coalitional effectivity models to provide alternative, arguably more natural and elegant semantics to the alternating-time temporal logic ATL*, and discuss their technical and conceptual advantages.

We consider a combination of the strategic logic ATL with the description logic ALCO. In order to combine the logics in a flexible way, we assume that every individual can be (potentially) an agent. We also take the novel approach to teams by assuming that a coalition has an identity on its own, and hence its membership can vary. In terms of technical results, we show that the logic does not have the finite model property, though both ATL and ALCO do. We conjecture that the satisfiability problem may be undecidable. On the other hand, model checking of the combined logic is decidable and even tractable. Finally, we define a particular variant of realizability that combines satisfiability of ALCO with model checking of the ATL dimension, and we show that this new problem is decidable.

In the following paper we present a new semantics for the well-known\nstrategic logic ATL. It is based on adding roles to concurrent game structures,\nthat is at every state, each agent belongs to exactly one role, and the role\nspecifies what actions are available to him at that state. We show advantages\nof the new semantics, provide motivating examples based on sensor networks, and\nanalyze model checking complexity.\n