Promptness in ω-regular automata

Shaull Almagor*, Yoram Hirshfeld, Orna Kupferman

*Corresponding author for this work

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

12 Scopus citations


Liveness properties of on-going reactive systems assert that something good will happen eventually. In satisfying liveness properties, there is no bound on the "wait time", namely the time that may elapse until an eventuality is fulfilled. The traditional "unbounded" semantics of liveness properties nicely corresponds to the classical semantics of automata on infinite objects. Indeed, acceptance is defined with respect to the set of states the run visits infinitely often, with no bound on the number of transitions taken between successive visits. In many applications, it is important to bound the wait time in liveness properties. Bounding the wait time by a constant is not always possible, as the bound may not be known in advance. It may also be very large, resulting in large specifications. Researchers have studied prompt eventualities, where the wait time is bounded, but the bound is not known in advance. We study the automata-theoretic counterpart of prompt eventually. In a prompt-Büchi automaton, a run r is accepting if there exists a bound k such that r visits an accepting state every at most k transitions. We study the expressive power of nondeterministic and deterministic prompt-Büchi automata, their properties, and decision problems for them. In particular, we show that regular nondeterministic prompt Büchi automata are exactly as expressive as nondeterministic co-Büchi automata.

Original languageEnglish
Title of host publicationAutomated Technology for Verification and Analysis - 8th International Symposium, ATVA 2010, Proceedings
Number of pages15
StatePublished - 2010
Event8th International Symposium on Automated Technology for Verification and Analysis, ATVA 2010 - Singapore, Singapore
Duration: 21 Sep 201024 Sep 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6252 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference8th International Symposium on Automated Technology for Verification and Analysis, ATVA 2010


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