文章基本信息

标题：Temporal Logic with Cyclic Counting and the Degree of Aperiodicity of Finite Automata
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作者：Zoltán Ésik ; Masami Ito
期刊名称：BRICS Report Series
印刷版ISSN：0909-0878
出版年度：2001
卷号：8
期号：53
出版社：Aarhus University
摘要：We define the degree of aperiodicity of finite automata and show that for every set M of positive integers, the class QA_M 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.