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

Z. Ésik, M. Ito

Research output: Contribution to journalArticle

27 Citations (Scopus)


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 QAM 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.

Original languageEnglish
Pages (from-to)1-28
Number of pages28
JournalActa Cybernetica
Issue number1
Publication statusPublished - Jan 1 2003


ASJC Scopus subject areas

  • Software
  • Computer Science (miscellaneous)
  • Computer Vision and Pattern Recognition
  • Management Science and Operations Research
  • Information Systems and Management
  • Electrical and Electronic Engineering

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