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Parametrized verification diagrams: temporal verification of symmetric parametrized concurrent systems

Parametrized verification diagrams: temporal verification of symmetric parametrized concurrent... This paper studies the problem of verifying temporal properties (including liveness properties) of parametrized concurrent systems executed by an unbounded number of threads. To solve this problem we introduce parametrized verification diagrams (PVDs), that extend the so-called generalized verification diagrams (GVDs) adding support for parametrized verification. Even though GVDs are known to be a sound and complete proof system for non-parametrized systems, the application of GVDs to parametrized systems requires using quantification or finding a potentially different diagram for each instantiation of the parameter (number of threads). As a consequence, the use of GVDs in parametrized verification requires discharging and proving either quantified formulas or an unbounded collection of verification conditions. Parametrized verification diagrams enable the use of asinglediagram to represent the proof that all possible instances of the parametrized concurrent system satisfy the given temporal specification. Checking the proof represented by a PVD requires proving only a finite collection of quantifier-free verification conditions. The PVDs we present here assume that the parametrized systems are symmetric, which covers a large class of concurrent and distributed systems, including concurrent data types. Our second contribution is an implementation of PVDs and its integration into Leap, our prototype theorem prover. Finally, we illustrate empirically, using Leap, the practical applicability of PVDs by building and checking proofs of liveness properties of mutual exclusion protocols and concurrent data structures. To the best of our knowledge, these are the first machine-checkable proofs of liveness properties of these concurrent data types. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Mathematics and Artificial Intelligence Springer Journals

Parametrized verification diagrams: temporal verification of symmetric parametrized concurrent systems

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References (58)

Publisher
Springer Journals
Copyright
Copyright © 2016 by Springer International Publishing Switzerland
Subject
Computer Science; Artificial Intelligence (incl. Robotics); Mathematics, general; Computer Science, general; Complex Systems
ISSN
1012-2443
eISSN
1573-7470
DOI
10.1007/s10472-016-9531-9
Publisher site
See Article on Publisher Site

Abstract

This paper studies the problem of verifying temporal properties (including liveness properties) of parametrized concurrent systems executed by an unbounded number of threads. To solve this problem we introduce parametrized verification diagrams (PVDs), that extend the so-called generalized verification diagrams (GVDs) adding support for parametrized verification. Even though GVDs are known to be a sound and complete proof system for non-parametrized systems, the application of GVDs to parametrized systems requires using quantification or finding a potentially different diagram for each instantiation of the parameter (number of threads). As a consequence, the use of GVDs in parametrized verification requires discharging and proving either quantified formulas or an unbounded collection of verification conditions. Parametrized verification diagrams enable the use of asinglediagram to represent the proof that all possible instances of the parametrized concurrent system satisfy the given temporal specification. Checking the proof represented by a PVD requires proving only a finite collection of quantifier-free verification conditions. The PVDs we present here assume that the parametrized systems are symmetric, which covers a large class of concurrent and distributed systems, including concurrent data types. Our second contribution is an implementation of PVDs and its integration into Leap, our prototype theorem prover. Finally, we illustrate empirically, using Leap, the practical applicability of PVDs by building and checking proofs of liveness properties of mutual exclusion protocols and concurrent data structures. To the best of our knowledge, these are the first machine-checkable proofs of liveness properties of these concurrent data types.

Journal

Annals of Mathematics and Artificial IntelligenceSpringer Journals

Published: Nov 15, 2016

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