Temporal logic with cyclic counting and the degree of aperiodicity of finite automata

Ésik, Zoltán and Ito, Masami: Temporal logic with cyclic counting and the degree of aperiodicity of finite automata. Acta cybernetica, (16) 1. pp. 1-28. (2003)

[img] Cikk, tanulmány, mű
cybernetica_016_numb_001_001-028.pdf

Download (1MB)

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
Page Range: pp. 1-28
ISSN: 0324-721X
Language: angol
Uncontrolled Keywords: Természettudomány
Additional Information: Bibliogr.: p. 27-28.; Abstract
Date Deposited: 2016. Oct. 15. 12:25
Last Modified: 2018. Apr. 11. 17:12
URI: http://acta.bibl.u-szeged.hu/id/eprint/12705

Actions (login required)

View Item View Item