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

A Logic for True Concurrency

We propose a logic for true concurrency whose formulae predicate about events in computations and their causal dependencies. The induced logical equivalence is hereditary history preserving bisimilarity, and fragments of the logic can be identified which correspond to other true concurrent behavioural equivalences in the literature: step, pomset and history preserving bisimilarity. Standard Hennessy-Milner logic, and thus (interleaving) bisimilarity, is also recovered as a fragment. We also propose an extension of the logic with fixpoint operators, thus allowing to describe causal and concurrency properties of infinite computations. We believe that this work contributes to a rational presentation of the true concurrent spectrum and to a deeper understanding of the relations between the involved behavioural equivalences.Comment: 31 pages, a preliminary version appeared in CONCUR 201

The Logic of Exact Covers: Completeness and Uniform Interpolation

We show that all (not necessarily normal or monotone) modal logics that can be axiomatised in rank-1 have the interpolation property, and that in fact interpolation is uniform if the logics just have finitely many modal operators. As immediate applicatio

Requirements, specifications, and minimal refinement

Refinement is usually employed to produce more concrete versions of a specification, or to add new requirements to it. However, during specification revision one may over-refine, thus incorporating unnecessary requirements. In this paper, we argue that this process can be formalised by the notion of minimal refinements, hence avoiding over-refinement, and prove that this definition is well-behaved theoretically as well as computationall

On the Complexity of Deciding Behavioural Equivalences and Preorders. A Survey

This paper gives an overview of the computational complexity of all the equivalences in the linear/branching time hierarchy [vG90a] and the preordersin the corresponding hierarchy of preorders. We consider finite state or regular processes as well as infinite-state BPA [BK84b] processes. A distinction, which turns out to be important in the finite-state processes, is that of simulation-like equivalences/preorders vs. trace-like equivalencesand preorders. Here we survey various known complexity results for these relations. For regular processes, all simulation-like equivalences and preorders are decidable in polynomial time whereas all trace-like equivalences and preorders are PSPACE-Complete. We also consider interesting specialclasses of regular processes such as deterministic, determinate, unary, locally unary, and tree-like processes and survey the known complexity results inthese special cases. For infinite-state processes the results are quite different. For the class of context-free processes or BPA processes any preorder or equivalence beyond bisimulation is undecidable but bisimulation equivalence is polynomial timedecidable for normed BPA processes and is known to be elementarily decidable in the general case. For the class of BPP processes, all preorders and equivalences apart from bisimilarity are undecidable. However, bisimilarityis decidable in this case and is known to be decidable in polynomial time for normed BPP processes

Querying Schemas With Access Restrictions

We study verification of systems whose transitions consist of accesses to a Web-based data-source. An access is a lookup on a relation within a relational database, fixing values for a set of positions in the relation. For example, a transition can represent access to a Web form, where the user is restricted to filling in values for a particular set of fields. We look at verifying properties of a schema describing the possible accesses of such a system. We present a language where one can describe the properties of an access path, and also specify additional restrictions on accesses that are enforced by the schema. Our main property language, AccLTL, is based on a first-order extension of linear-time temporal logic, interpreting access paths as sequences of relational structures. We also present a lower-level automaton model, Aautomata, which AccLTL specifications can compile into. We show that AccLTL and A-automata can express static analysis problems related to "querying with limited access patterns" that have been studied in the database literature in the past, such as whether an access is relevant to answering a query, and whether two queries are equivalent in the accessible data they can return. We prove decidability and complexity results for several restrictions and variants of AccLTL, and explain which properties of paths can be expressed in each restriction.Comment: VLDB201

Characteristic Formulae for Timed Automata

This paper offers characteristic formula constructions in the real-time logic L for several behavioural relations between (states of)timed automata. The behavioural relations studied in this work aretimed (bi)similarity, timed ready simulation, faster-than bisimilarityand timed trace inclusion. The characteristic formulae delivered byour constructions have size which is linear in that of the timed automaton they logically describe. This also applies to the characteristicformula for timed bisimulation equivalence, for which an exponentialspace construction was previously offered by Laroussinie, Larsen andWeise

Second-Order Logic and Related Systems : a game-semantical perspective (Mathematical Logic and its Applications)

This is based on tutorial lectures on second-order logic in SAML 2022. Among others, we here discuss monadic second-order logic (MSO) from a game-theoretical view-point. Although the validity of MSO in terms of standard structures is not decidable (not axiomatizable), the MSO theory of full binary tree is decidable and modal μ-calculus can be viewed as a decidable fragment of MSO