Model Checking Dynamic-Epistemic Spatial Logic

In this paper we focus on Dynamic Spatial Logic, the extension of Hennessy-Milner logic with the parallel operator. We develop a sound complete Hilbert-style axiomatic system for it comprehending the behavior of spatial operators in relation with dynamic/temporal ones. Underpining on a new congruence we define over the class of processes - the structural bisimulation - we prove the finite model property for this logic that provides the decidability for satisfiability, validity and model checking against process semantics. Eventualy we propose algorithms for validity, satisfiability and model checking

ATLsc with partial observation

Alternating-time temporal logic with strategy contexts (ATLsc) is a powerful formalism for expressing properties of multi-agent systems: it extends CTL with strategy quantifiers, offering a convenient way of expressing both collaboration and antagonism between several agents. Incomplete observation of the state space is a desirable feature in such a framework, but it quickly leads to undecidable verification problems. In this paper, we prove that uniform incomplete observation (where all players have the same observation) preserves decidability of the model-checking problem, even for very expressive logics such as ATLsc.Comment: In Proceedings GandALF 2015, arXiv:1509.0685

Model-Checking of Ordered Multi-Pushdown Automata

We address the verification problem of ordered multi-pushdown automata: A multi-stack extension of pushdown automata that comes with a constraint on stack transitions such that a pop can only be performed on the first non-empty stack. First, we show that the emptiness problem for ordered multi-pushdown automata is in 2ETIME. Then, we prove that, for an ordered multi-pushdown automata, the set of all predecessors of a regular set of configurations is an effectively constructible regular set. We exploit this result to solve the global model-checking which consists in computing the set of all configurations of an ordered multi-pushdown automaton that satisfy a given w-regular property (expressible in linear-time temporal logics or the linear-time \mu-calculus). As an immediate consequence, we obtain an 2ETIME upper bound for the model-checking problem of w-regular properties for ordered multi-pushdown automata (matching its lower-bound).Comment: 31 page

Real-time and Probabilistic Temporal Logics: An Overview

Over the last two decades, there has been an extensive study on logical formalisms for specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although numerous logics have been introduced for the formal specification of real-time and complex systems, an up to date comprehensive analysis of these logics does not exist in the literature. In this paper we analyse real-time and probabilistic temporal logics which have been widely used in this field. We extrapolate the notions of decidability, axiomatizability, expressiveness, model checking, etc. for each logic analysed. We also provide a comparison of features of the temporal logics discussed

Forward Analysis and Model Checking for Trace Bounded WSTS

We investigate a subclass of well-structured transition systems (WSTS), the bounded---in the sense of Ginsburg and Spanier (Trans. AMS 1964)---complete deterministic ones, which we claim provide an adequate basis for the study of forward analyses as developed by Finkel and Goubault-Larrecq (Logic. Meth. Comput. Sci. 2012). Indeed, we prove that, unlike other conditions considered previously for the termination of forward analysis, boundedness is decidable. Boundedness turns out to be a valuable restriction for WSTS verification, as we show that it further allows to decide all $\omega$-regular properties on the set of infinite traces of the system

Strategy Logic with Imperfect Information

We introduce an extension of Strategy Logic for the imperfect-information setting, called SLii, and study its model-checking problem. As this logic naturally captures multi-player games with imperfect information, the problem turns out to be undecidable. We introduce a syntactical class of "hierarchical instances" for which, intuitively, as one goes down the syntactic tree of the formula, strategy quantifications are concerned with finer observations of the model. We prove that model-checking SLii restricted to hierarchical instances is decidable. This result, because it allows for complex patterns of existential and universal quantification on strategies, greatly generalises previous ones, such as decidability of multi-player games with imperfect information and hierarchical observations, and decidability of distributed synthesis for hierarchical systems. To establish the decidability result, we introduce and study QCTL*ii, an extension of QCTL* (itself an extension of CTL* with second-order quantification over atomic propositions) by parameterising its quantifiers with observations. The simple syntax of QCTL* ii allows us to provide a conceptually neat reduction of SLii to QCTL*ii that separates concerns, allowing one to forget about strategies and players and focus solely on second-order quantification. While the model-checking problem of QCTL*ii is, in general, undecidable, we identify a syntactic fragment of hierarchical formulas and prove, using an automata-theoretic approach, that it is decidable. The decidability result for SLii follows since the reduction maps hierarchical instances of SLii to hierarchical formulas of QCTL*ii

Equivalence-Checking on Infinite-State Systems: Techniques and Results

The paper presents a selection of recently developed and/or used techniques for equivalence-checking on infinite-state systems, and an up-to-date overview of existing results (as of September 2004)