TY - GEN

T1 - Variable automata over infinite alphabets

AU - Grumberg, Orna

AU - Kupferman, Orna

AU - Sheinvald, Sarai

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77953773956&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-13089-2_47

DO - 10.1007/978-3-642-13089-2_47

M3 - Conference contribution

AN - SCOPUS:77953773956

SN - 3642130887

SN - 9783642130885

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

SP - 561

EP - 572

BT - Language and Automata Theory and Applications - 4th International Conference, LATA 2010, Proceedings

T2 - 4th International Conference on Language and Automata Theory and Applications, LATA 2010

Y2 - 24 May 2010 through 28 May 2010

ER -