Well-structured transition systems everywhere!

Abstract.Recently, LTL extended with atomic formulas built over a constraint language interpreting variables in Z has been shown to have a decidable satisfiability and model-checking problem. This language allows to compare the variables at different states of the model and include periodicity constraints, comparison constraints, and a restricted form of quantification. On the other hand, the CTL counterpart of this logic (and hence also its CTL * counterpart which subsumes both LTL and CTL) has an undecidable model-checking problem. In this paper, we substantially extend the decidability border, by considering a meaningful fragment of CTL * extended with such constraints (which subsumes both the universal and existential fragments, as well as the EF-like fragment) and show that satisfiability and model-checking over relational automata that are abstraction of counter machines are decidable. The correctness and the termination of our algorithm rely on a suitable well quasi-ordering defined over the set of variable valuations.

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“…[ACJT96,FS01]. Hence, one can define a decidable well-quasi ordering on the set of states, which is also a simulation.…”

Section: Temporal Logics Extended With Presburger Constraintsmentioning

confidence: 99%

Branching-Time Temporal Logic Extended with Qualitative Presburger Constraints

Bozzelli

Gascon

2006

Logic for Programming, Artificial Intelligence, and Reasoning

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“…As a result, we obtain a general decidability result for provenance verification problem, when the domain of provenance annotations is well-structured [1,8]. Specifically, we show verification is EXPSPACE-complete for the set provenance domain, that tracks the set of principals that have seen a message, as well as for the language provenance domain, in which provenance information is stored as ordered sequences of principals that have seen the message and policies are regular languages.…”

Section: Introductionmentioning

confidence: 83%

“…A send action increases the counter, a receive decrements it. We can then show that the transition system of a message passing program is well-structured [1,8]: an action that could be taken in a state can also be taken if there are more messages in the channels. Formally, we give a reduction to Petri nets, an infinite-state well-structured system with good decidability properties.…”

Section: Examplementioning

confidence: 99%

Static Provenance Verification for Message Passing Programs

2013

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Abstract. Provenance information records the source and ownership history of an object. We study the problem of provenance tracking in concurrent programs, in which several principals execute concurrent processes and exchange messages over unbounded but unordered channels. The provenance of a message, roughly, is a function of the sequence of principals that have transmitted the message in the past. The provenance verification problem is to statically decide, given a message passing program and a set of allowed provenances, whether the provenance of all messages in all possible program executions, belongs to the allowed set. We formalize the provenance verification problem abstractly in terms of well-structured provenance domains, and show a general decidability result for it. In particular, we show that if the provenance of a message is a sequence of principals who have sent the message, and a provenance query asks if the provenance lies in a regular set, the problem is decidable and EXPSPACE-complete. While the theoretical complexity is high, we show an implementation of our technique that performs efficiently on a set of Javascript examples tracking provenances in Firefox extensions. Our experiments show that many browser extensions store and transmit user information although the user sets the browser to the private mode.

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“…Though a transition system with an infinite state-space has an infinite reachability tree, for each WSTS with an effective ordering relation and computable transition relation a finite coverability tree can be effectively constructed [3]. For interacting automata it can be done as follows.…”

Section: Corollary 44 Let K K Be Two Configurations For Automata Cmentioning

confidence: 99%

Interacting Automata for Modelling Distributed Systems

Lomazova

2003

Lecture Notes in Computer Science

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Abstract.A community of interacting automata is a set of nondeterministic finite automata which can execute actions autonomously, synchronize with each other, or generate new members of the community. Thus interacting automata allow to model distributed systems with unlimited number of interacting agents. We show that the formalism of interacting automata has a clear semantics and nice semantic properties, leading to decidability of some important behavioral properties of modelled systems.

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Well-structured transition systems everywhere!

Cited by 571 publications

References 32 publications

Branching-Time Temporal Logic Extended with Qualitative Presburger Constraints

Branching-Time Temporal Logic Extended with Qualitative Presburger Constraints

Static Provenance Verification for Message Passing Programs

Interacting Automata for Modelling Distributed Systems

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