Symmetries of automata
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Symmetries of automata
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| Creator |
Egri-Nagy, A.
Nehaniv, C.L. |
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| Description |
For a given reachable automaton A, we prove that the (state-) endomorphism monoid End(A) divides its characteristic monoid M(A). Hence so does its (state-)automorphism group Aut(A), and, for finite A, Aut(A) is a homomorphic image of a subgroup of the characteristic monoid. It follows that in the presence of a (state-) automorphism group G of A, a finite automaton A (and its transformation monoid) always has a decomposition as a divisor of the wreath product of two transformation semigroups whose semigroups are divisors of M(A), namely the symmetry group G and the quotient of M(A) induced by the action of G. Moreover, this division is an embedding if M(A) is transitive on states of A. For more general automorphisms, which may be non-trivial on input letters, counterexamples show that they need not be induced by any corresponding characteristic monoid element.
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| Date |
2019-06-12T20:52:55Z
2019-06-12T20:52:55Z 2015 |
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| Type |
Article
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| Identifier |
Symmetries of automata / A. Egri-Nagy, C.L. Nehaniv // Algebra and Discrete Mathematics. — 2015. — Vol. 19, № 1. — С. 48-57. — Бібліогр.: 7 назв. — англ.
1726-3255 2010 MSC:20B25, 20E22, 20M20, 20M35, 68Q70. http://dspace.nbuv.gov.ua/handle/123456789/152786 |
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| Language |
en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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