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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| Format: | Article |
| Published: |
2003
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| Series: | Acta cybernetica
16 No. 1 |
| Kulcsszavak: | Számítástechnika, Kibernetika, Automaták |
| Subjects: | |
| Online Access: | http://acta.bibl.u-szeged.hu/12705 |
| Summary: | 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. |
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| Physical Description: | 1-28 |
| ISSN: | 0324-721X |