Temporal logic with cyclic counting and the degree of aperiodicity of finite automata
We define the degree of aperiodicity of finite automata and show that for every set M of positive integers, the class QAM of finite automata whose degree of aperiodicity belongs to the division ideal generated by M is closed with respect to direct products, disjoint unions, subautomata, homomorphic...
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Dokumentumtípus: | Cikk |
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2003
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Sorozat: | Acta cybernetica
16 No. 1 |
Kulcsszavak: | Számítástechnika, Kibernetika, Automaták |
Tárgyszavak: | |
Online Access: | http://acta.bibl.u-szeged.hu/12705 |
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001 | acta12705 | ||
005 | 20220615084838.0 | ||
008 | 161015s2003 hu o 0|| eng d | ||
022 | |a 0324-721X | ||
040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
041 | |a eng | ||
100 | 1 | |a Ésik Zoltán | |
245 | 1 | 0 | |a Temporal logic with cyclic counting and the degree of aperiodicity of finite automata |h [elektronikus dokumentum] / |c Ésik Zoltán |
260 | |c 2003 | ||
300 | |a 1-28 | ||
490 | 0 | |a Acta cybernetica |v 16 No. 1 | |
520 | 3 | |a We define the degree of aperiodicity of finite automata and show that for every set M of positive integers, the class QAM of finite automata whose degree of aperiodicity belongs to the division ideal generated by M is closed with respect to direct products, disjoint unions, subautomata, homomorphic images and renamings. These closure conditions define q-varieties of finite automata. We show that q-varieties are in a one-to-one correspondence with literal varieties of regular languages. We also characterize QA M as the cascade product of a variety of counters with the variety of aperiodic (or counter-free) automata. We then use the notion of degree of aperiodicity to characterize the expressive power of first-order logic and temporal logic with cyclic counting with respect to any given set M of moduli. It follows that when M is finite, then it is decidable whether a regular language is definable in first-order or temporal logic with cyclic counting with respect to moduli in M. | |
650 | 4 | |a Természettudományok | |
650 | 4 | |a Számítás- és információtudomány | |
695 | |a Számítástechnika, Kibernetika, Automaták | ||
700 | 0 | 1 | |a Ito Masami |e aut |
710 | |a Conference for PhD Students in Computer Science (3.) (2002) (Szeged) | ||
856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/12705/1/cybernetica_016_numb_001_001-028.pdf |z Dokumentum-elérés |