Finding shortest witnesses to the nonemptiness of automata on infinite words

Orna Kupferman*, Sarai Sheinvald-Faragy

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

13 Scopus citations


In the automata-theoretic approach to formal verification, the satisfiability and the model-checking problems for linear temporal logics are reduced to the nonemptiness problem of automata on infinite words. Modifying the nonemptiness algorithm to return a shortest witness to the nonemptiness (that is, a word of the form uvω that is accepted by the automaton and for which |uv| is minimal) has applications in synthesis and counterexample analysis. Unlike shortest accepting runs, which have been studied in the literature, the definition of shortest witnesses is semantic and is independent on the specification formalism of the property or the system. In particular, its robustness makes it appropriate for analyzing counterexamples of concurrent systems. We study the problem of finding shortest witnesses in automata with various types of concurrency. We show that while finding shortest witnesses is more complex than just checking nonemptiness in the nondeterministic and in the concurrent models of computation, it is not more complex in the alternating model. It follows that when the system is the composition of concurrent components, finding a shortest counterexample to its correctness is not harder than finding some counterexample. Our results give a computational motivation to translating temporal logic formulas to alternating automata, rather than going all the way to nondeterministic automata.

Original languageAmerican English
Title of host publicationCONCUR 2006 - Concurrency Theory - 17th International Conference, CONCUR 2006, Proceedings
PublisherSpringer Verlag
Number of pages17
ISBN (Print)3540373764, 9783540373766
StatePublished - 2006
Event17th International Conference on Concurrency Theory, CONCUR 2006 - Bonn, Germany
Duration: 27 Aug 200630 Aug 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4137 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference17th International Conference on Concurrency Theory, CONCUR 2006


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