Journal of Formalized Mathematics
Volume 7, 1995
University of Bialystok
Copyright (c) 1995 Association of Mizar Users

## Introduction to Circuits, II

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 last in a series of four articles (preceded by [22], [23], [21]) about modelling circuits by many sorted algebras.\par The notion of a circuit computation is defined as a sequence of circuit states. For a state of a circuit the next state is given by executing operations at circuit vertices in the current state, according to denotations of the operations. The values at input vertices at each state of a computation are provided by an external sequence of input values. The process of how input values propagate through a circuit is described in terms of a homomorphism of the free envelope algebra of the circuit into itself. We prove that every computation of a circuit over a finite monotonic signature and with constant input values stabilizes after executing the number of steps equal to the depth of the circuit.

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: CIRCUIT2

The terminology and notation used in this paper have been introduced in the following articles [25] [13] [32] [29] [33] [28] [11] [12] [18] [14] [2] [8] [16] [5] [6] [7] [30] [1] [3] [31] [4] [15] [9] [26] [19] [27] [10] [20] [17] [24] [22] [23] [21]

#### Contents (PDF format)

1. Circuit Inputs
2. Circuit Computations

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