Generation of Constants and Synchronization of Finite Automata

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Generation of Constants and Synchronization of Finite Automata
: The problem about the synchronization of a finite deterministic automaton is not yet properly understood. The present paper investigates this and related problems within the general framework of a composition theory for functions over a finite domain N with n elements. The notion of depth introduced in this connection is a good indication of the complexity of a given function, namely, the complexity with respect to the length of composition sequences in terms of functions belonging to a basic set. The depth may vary considerably with the target function. Not much is known about the reachability of some target functions, notably constants. Synchronizability of a finite automaton amounts to the representability of some constant as a composition of the functions defined by the input letters. Properties of n such as primality or being a power of 2 turn out to be important, independently of the semantic interpretation. We present some necessary, as well as some sufficient, conditions for ...
Arto Salomaa
Added 22 Dec 2010
Updated 22 Dec 2010
Type Journal
Year 2002
Where JUCS
Authors Arto Salomaa
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