Variable automata over infinite alphabets

Orna Grumberg*, Orna Kupferman, Sarai Sheinvald

*Corresponding author for this work

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

59 Scopus citations


Automated reasoning about systems with infinite domains requires an extension of regular automata to infinite alphabets. Existing formalisms of such automata cope with the infiniteness of the alphabet by adding to the automaton a set of registers or pebbles, or by attributing the alphabet by labels from an auxiliary finite alphabet that is read by an intermediate transducer. These formalisms involve a complicated mechanism on top of the transition function of automata over finite alphabets and are therefore difficult to understand and to work with. We introduce and study variable finite automata over infinite alphabets (VFA). VFA form a natural and simple extension of regular (and ω-regular) automata, in which the alphabet consists of letters as well as variables that range over the infinite alphabet domain. Thus, VFAs have the same structure as regular automata, only that some of the transitions are labeled by variables. We compare VFA with existing formalisms, and study their closure properties and classical decision problems. We consider the settings of both finite and infinite words. In addition, we identify and study the deterministic fragment of VFA. We show that while this fragment is sufficiently strong to express many interesting properties, it is closed under union, intersection, and complementation, and its nonemptiness and containment problems are decidable. Finally, we describe a determinization process for a determinizable subset of VFA.

Original languageAmerican English
Title of host publicationLanguage and Automata Theory and Applications - 4th International Conference, LATA 2010, Proceedings
Number of pages12
StatePublished - 2010
Event4th International Conference on Language and Automata Theory and Applications, LATA 2010 - Trier, Germany
Duration: 24 May 201028 May 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6031 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference4th International Conference on Language and Automata Theory and Applications, LATA 2010


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