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Cycle indices of an automaton
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A. A. Letunovskii
Published/Copyright:
May 1, 2014
Abstract
The notion of cycle indices of an automaton is introduced as a pair of positive parameters (b, q) effectively evaluated by the automaton. It is shown that the totality of periods of constant automata which may be represented as superpositions of a given automaton, Boolean functions, and the delay element, coincides with the variety of divisors of the members of the geometric progression b, bq, bq2,... This suggests an algorithm for checking the expressibility of constant automata, as well as a theorem on the verification of the expressibility of the totality of all automata with a limited number of states.
Published Online: 2014-5-1
Published in Print: 2013-12-1
© 2014 by Walter de Gruyter Berlin/Boston
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Articles in the same Issue
- Front matter
- Criterion for propositional calculi to be finitely generated
- Fast Catalan constant computation via the approximations obtained by the Kummer’s type transformations
- Cycle indices of an automaton
- Definability in the language of functional equations of a countable-valued logic
- On bigram languages
- The diagnosis of states of contacts
- Finite systems of generators of infinite subgroups of the Golod group
- On the number of cyclic points of random A-mapping
Articles in the same Issue
- Front matter
- Criterion for propositional calculi to be finitely generated
- Fast Catalan constant computation via the approximations obtained by the Kummer’s type transformations
- Cycle indices of an automaton
- Definability in the language of functional equations of a countable-valued logic
- On bigram languages
- The diagnosis of states of contacts
- Finite systems of generators of infinite subgroups of the Golod group
- On the number of cyclic points of random A-mapping
