Journal of Formalized Mathematics
Volume 13, 2001
University of Bialystok
Copyright (c) 2001 Association of Mizar Users

## Circuit Generated by Terms and Circuit Calculating Terms

Grzegorz Bancerek
University of Bialystok, Shinshu University, Nagano

### Summary.

In the paper we investigate the dependence between the structure of circuits and sets of terms. Circuits in our terminology (see [19]) are treated as locally-finite many sorted algebras over special signatures. Such approach enables to formalize every real circuit. The goal of this investigation is to specify circuits by terms and, enentualy, to have methods of formal verification of real circuits. The following notation is introduced in this paper: \begin{itemize} \item structural equivalence of circuits, i.e. equivalence of many sorted signatures, \item embedding of a circuit into another one, \item similarity of circuits (a concept narrower than isomorphism of many sorted algebras over equivalent signatures), \item calculation of terms by a circuit according to an algebra, \item specification of circuits by terms and an algebra. \end{itemize}

#### MML Identifier: CIRCTRM1

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

#### Contents (PDF format)

1. Circuit Structure Generated by Terms
2. Circuit Generated by Terms
3. Correctness of a Term Circuit
4. Circuit Similarity
5. Term Specification

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