Journal of Formalized Mathematics
Volume 6, 1994
University of Bialystok
Copyright (c) 1994 Association of Mizar Users

## Introduction to Circuits, I

Yatsuka Nakamura
Shinshu University, Nagano
Piotr Rudnicki
University of Alberta, Edmonton
Andrzej Trybulec
Warsaw University, Bialystok
Pauline N. Kawamoto
Shinshu University, Nagano

### Summary.

This article is the third in a series of four articles (preceded by [20],[21] and continued in [22]) about modelling circuits by many sorted algebras.\par A circuit is defined as a locally-finite algebra over a circuit-like many sorted signature. For circuits we define notions of input function and of circuit state which are later used (see [22]) to define circuit computations. For circuits over monotonic signatures we introduce notions of vertex size and vertex depth that characterize certain graph properties of circuit's signature in terms of elements of its free envelope algebra. The depth of a finite circuit is defined as the maximal depth over its vertices.

Partial funding for this work has been provided by: Shinshu Endowment Fund for Information Science, NSERC Grant OGP9207, JSTF award 651-93-S009.

#### MML Identifier: CIRCUIT1

The terminology and notation used in this paper have been introduced in the following articles [25] [15] [32] [5] [4] [29] [2] [28] [33] [14] [11] [34] [18] [30] [1] [23] [6] [31] [16] [7] [3] [8] [9] [10] [17] [12] [26] [27] [13] [19] [24] [20] [21]

#### Contents (PDF format)

1. Circuit State
2. Vertex Size
3. Vertex and Circuit Depth

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