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Superpositions of bounded-deterministic functions. (English. Russian original) Zbl 0795.68137
Math. Notes 47, No. 3, 231-235 (1990); translation from Mat. Zametki 47, No. 3, 3-10 (1990).
Summary: We consider the problem of completeness of systems of bounded- deterministic functions under superposition. It is known that finite complete systems of b-d. functions do not exist. The known complete systems contain functions with (jointly) unbounded number of variables. We show that any b.-d. function is representable as a superposition of b.-d. functions of two variables. More precisely, any b.-d. function is generated by one-place b.-d. functions and Boolean functions.

MSC:
68Q45 Formal languages and automata
03D05 Automata and formal grammars in connection with logical questions
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References:
[1] V. B. Kudryavtsev, S. V. Aleshin, and A. S. Podkolzin, An Introduction to Automata Theory [in Russian], Nauka, Moscow (1985), pp. 151-174. · Zbl 0604.68058
[2] S. S. Marchenkov, ?On one method of analysis of superpositions of continuous functions,? Probl. Kibern., No. 37, 5-17 (1980). · Zbl 0472.26006
[3] V. B. Kudryavtsev, ?On cardinality of sets of some function system associated with automata,? Probl. Kibern., No. 13, 45-57 (1965).
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