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Prikl. Diskr. Mat., 2010, Number 2(8), Pages 104–116 (Mi pdm169)  

Applied Automata Theory

On constructing minimal deterministic finite automaton recognizing a prefix-code of a given cardinality

I. R. Akishev, M. E. Dvorkin

St. Petersburg State University of Information Technologies, Mechanics and Optics, St. Petersburg, Russia

Abstract: The article considers constructing minimal deterministic finite automaton recognizing a prefix-code of a given cardinality over the alphabet $\{0,1\}$. The considered problem is proved to be equivalent to the problem of finding the shortest addition-chain ending with a given number. Several interesting properties of the desired minimal finite automaton are proved, and the identical problem concerning Moore automata is discussed.

Keywords: prefix code, finite-state machine, Moore automaton, addition chain.

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UDC: 519.713+519.766

Citation: I. R. Akishev, M. E. Dvorkin, “On constructing minimal deterministic finite automaton recognizing a prefix-code of a given cardinality”, Prikl. Diskr. Mat., 2010, no. 2(8), 104–116

Citation in format AMSBIB
\Bibitem{AkiDvo10}
\by I.~R.~Akishev, M.~E.~Dvorkin
\paper On constructing minimal deterministic finite automaton recognizing a~prefix-code of a~given cardinality
\jour Prikl. Diskr. Mat.
\yr 2010
\issue 2(8)
\pages 104--116
\mathnet{http://mi.mathnet.ru/pdm169}


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