Reachability analysis of reversal-bounded automata on series–parallel graphs

Reachability analysis of reversal-bounded automata on series–parallel graphs Extensions to finite-state automata on strings, such as multi-head automata or multi-counter automata, have been successfully used to encode many infinite-state non-regular verification problems. In this paper, we consider a generalization of automata-theoretic infinite-state verification from strings to labelled series–parallel graphs. We define a model of non-deterministic, 2-way, concurrent automata working on series–parallel graphs and communicating through shared registers on the nodes of the graph. We consider the following verification problem: given a family of series–parallel graphs described by a context-free graph transformation system (GTS), and a concurrent automaton over series–parallel graphs, is some graph generated by the GTS accepted by the automaton? The general problem is undecidable already for (one-way) multi-head automata over strings. We show that a bounded version, where the automata make a fixed number of reversals along the graph and use a fixed number of shared registers is decidable, even though there is no bound on the sizes of series–parallel graphs generated by the GTS. Our decidability result is based on establishing that the number of context switches can be bounded and on an encoding of the computation of bounded concurrent automata that allows us to reduce the reachability problem to the emptiness problem for pushdown automata. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Informatica Springer Journals

Reachability analysis of reversal-bounded automata on series–parallel graphs

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2016 by The Author(s)
Subject
Computer Science; Logics and Meanings of Programs; Computer Systems Organization and Communication Networks; Software Engineering/Programming and Operating Systems; Data Structures, Cryptology and Information Theory; Theory of Computation; Information Systems and Communication Service
ISSN
0001-5903
eISSN
1432-0525
D.O.I.
10.1007/s00236-016-0290-1
Publisher site
See Article on Publisher Site

Abstract

Extensions to finite-state automata on strings, such as multi-head automata or multi-counter automata, have been successfully used to encode many infinite-state non-regular verification problems. In this paper, we consider a generalization of automata-theoretic infinite-state verification from strings to labelled series–parallel graphs. We define a model of non-deterministic, 2-way, concurrent automata working on series–parallel graphs and communicating through shared registers on the nodes of the graph. We consider the following verification problem: given a family of series–parallel graphs described by a context-free graph transformation system (GTS), and a concurrent automaton over series–parallel graphs, is some graph generated by the GTS accepted by the automaton? The general problem is undecidable already for (one-way) multi-head automata over strings. We show that a bounded version, where the automata make a fixed number of reversals along the graph and use a fixed number of shared registers is decidable, even though there is no bound on the sizes of series–parallel graphs generated by the GTS. Our decidability result is based on establishing that the number of context switches can be bounded and on an encoding of the computation of bounded concurrent automata that allows us to reduce the reachability problem to the emptiness problem for pushdown automata.

Journal

Acta InformaticaSpringer Journals

Published: Dec 18, 2016

References

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