Ésik Zoltán and Ito Masami: Temporal logic with cyclic counting and the degree of aperiodicity of finite automata. In: Acta cybernetica, (16) 1. pp. 1-28. (2003)
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Abstract
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.
| Item Type: | Article |
|---|---|
| Journal or Publication Title: | Acta cybernetica |
| Date: | 2003 |
| Volume: | 16 |
| Number: | 1 |
| ISSN: | 0324-721X |
| Page Range: | pp. 1-28 |
| Language: | English |
| Place of Publication: | Szeged |
| Event Title: | Conference for PhD Students in Computer Science (3.) (2002) (Szeged) |
| Related URLs: | http://acta.bibl.u-szeged.hu/38515/ |
| Uncontrolled Keywords: | Számítástechnika, Kibernetika, Automaták |
| Additional Information: | Bibliogr.: p. 27-28. ; összefoglalás angol nyelven |
| Subjects: | 01. Natural sciences 01. Natural sciences > 01.02. Computer and information sciences |
| Date Deposited: | 2016. Oct. 15. 12:25 |
| Last Modified: | 2022. Jun. 15. 08:48 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/12705 |
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