Finding Shortest Witnesses to the Nonemptiness of Automata on Infinite Words

  • Orna Kupferman
  • Sarai Sheinvald-Faragy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4137)


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 uv ω 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.


Model Check Hamiltonian Cycle Linear Temporal Logic Acceptance Condition Input Word 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Orna Kupferman
    • 1
  • Sarai Sheinvald-Faragy
    • 1
  1. 1.School of Engineering and Computer ScienceHebrew UniversityJerusalemIsrael

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