ON THE DEPTH OF COMBINATIONAL CIRCUITS REQUIRED TO COMPUTE SWITCHING FUNCTIONS.

Hiroto Yasuura, Shuzo Yajima

Research output: Contribution to journalArticle

Abstract

The properties of the O(log n)-depth realizable set of functions is discussed. It is shown that the necessary and sufficient condition for a set of functions A to be O(log n)-depth realizable is that there exist a Boolean expression for any n-variable function in A such that its literal number is bounded by a certain polynomial of n. It is shown that the family of linear functions, family of symmetrical functions and the family of threshold functions are O(log n)-depth realizable. Then, as a special case of the set of functions, a sequence of functions is introduced wherein exactly one n-variable function is contained for any n. The sequence of functions is in one-to-one correspondence to the formal language on right brace 0, 1 left brace and it is shown that the sequence of functions corresponding to the regular set is O (log n)-depth realizable.

Original languageEnglish
Pages (from-to)1-10
Number of pages10
JournalSystems, computers, controls
Volume10
Issue number5
Publication statusPublished - Sep 1979
Externally publishedYes

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Switching functions
Combinatorial circuits
Formal languages
Polynomials

All Science Journal Classification (ASJC) codes

  • Engineering(all)

Cite this

ON THE DEPTH OF COMBINATIONAL CIRCUITS REQUIRED TO COMPUTE SWITCHING FUNCTIONS. / Yasuura, Hiroto; Yajima, Shuzo.

In: Systems, computers, controls, Vol. 10, No. 5, 09.1979, p. 1-10.

Research output: Contribution to journalArticle

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