Geodesic
Properties of systems of defining relations for automata
Diskretnaya Matematika, Tome 16 (2004) no. 4, pp. 79-87.

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We suggest a canonical system of defining relations for finite everywhere defined outputless automata. We construct a procedure to pass from an arbitrary finite system of defining relations to a canonical one and, as a corollary, a procedure to check whether a finite system of pairs of words is a defining system for a given automaton or not. We also suggest a procedure to pass from a traversal of all arcs of the automaton graph to a system of defining relations and vice versa. 
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I. S. Grunskii; A. S. Senchenko. Properties of systems of defining relations for automata. Diskretnaya Matematika, Tome 16 (2004) no. 4, pp. 79-87. http://geodesic.mathdoc.fr/item/DM_2004_16_4_a7/

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