Preliminaries 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 second in a series of four articles (started with [19] and continued in [18], [20]) about modelling circuits by many sorted algebras.\par First, we introduce some additional terminology for many sorted signatures. The vertices of such signatures are divided into input vertices and inner vertices. A many sorted signature is called {\em circuit like} if each sort is a result sort of at most one operation. Next, we introduce some notions for many sorted algebras and many sorted free algebras. Free envelope of an algebra is a free algebra generated by the sorts of the algebra. Evaluation of an algebra is defined as a homomorphism from the free envelope of the algebra into the algebra. We define depth of elements of free many sorted algebras.\par A many sorted signature is said to be monotonic if every finitely generated algebra over it is locally finite (finite in each sort). Monotonic signatures are used (see [18],[20]) in modelling backbones of circuits without directed cycles.

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: MSAFREE2

Contents (PDF format)

1. Many Sorted Signatures
2. Free Many Sorted Algebras

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