### 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 language | English |
---|---|

Pages (from-to) | 1-10 |

Number of pages | 10 |

Journal | Systems, computers, controls |

Volume | 10 |

Issue number | 5 |

Publication status | Published - Sep 1979 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Engineering(all)

### Cite this

*Systems, computers, controls*,

*10*(5), 1-10.

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

Research output: Contribution to journal › Article

*Systems, computers, controls*, vol. 10, no. 5, pp. 1-10.

}

TY - JOUR

T1 - ON THE DEPTH OF COMBINATIONAL CIRCUITS REQUIRED TO COMPUTE SWITCHING FUNCTIONS.

AU - Yasuura, Hiroto

AU - Yajima, Shuzo

PY - 1979/9

Y1 - 1979/9

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=0018510470&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0018510470

VL - 10

SP - 1

EP - 10

JO - Systems, computers, controls

JF - Systems, computers, controls

SN - 0096-8765

IS - 5

ER -