TY - GEN

T1 - Finding shortest witnesses to the nonemptiness of automata on infinite words

AU - Kupferman, Orna

AU - Sheinvald-Faragy, Sarai

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33749552643&partnerID=8YFLogxK

U2 - 10.1007/11817949_33

DO - 10.1007/11817949_33

M3 - Conference contribution

AN - SCOPUS:33749552643

SN - 3540373764

SN - 9783540373766

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 492

EP - 508

BT - CONCUR 2006 - Concurrency Theory - 17th International Conference, CONCUR 2006, Proceedings

PB - Springer Verlag

T2 - 17th International Conference on Concurrency Theory, CONCUR 2006

Y2 - 27 August 2006 through 30 August 2006

ER -