Volume 6, 1994

University of Bialystok

Copyright (c) 1994 Association of Mizar Users

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

- 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.

- Circuit State
- Vertex Size
- Vertex and Circuit Depth

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*Journal of Formalized Mathematics*, 6, 1994. - [20]
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Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec, and Pauline N. Kawamoto.
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Many-sorted sets.
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Many sorted algebras.
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Andrzej Trybulec.
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Edmund Woronowicz.
Relations defined on sets.
*Journal of Formalized Mathematics*, 1, 1989.

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