矩形代数

[1992] Proceedings The Twenty-Second International Symposium on Multiple-Valued Logic Pub Date : 1900-01-01 DOI:10.1109/ISMVL.1992.186804

R. Pöschel, M. Reichel

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引用次数: 1

摘要

由投影代数(类型为tau)生成的RA/sub /类型的代数称为矩形代数。事实证明代数(A;F)是矩形的，当且仅当A可以分解为(即由)分量来编码，使得每个项函数F:A/sup n/ to A可以并行执行，并且是每个分量上的投影(从代数上讲，它同构于投影代数的直积)。给出了一个完整表征矩形代数的恒等式列表。RA/中的每一项都有一个正规形式。给出了有限型有限代数的一些算法(分解算法和范式算法)和实例。

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Rectangular algebras

Algebras of the variety RA/sub tau / generated by projection algebras (of type tau ) are called rectangular algebras. It turns out that an algebra (A; F) is rectangular if and only if A can be decomposed in (i.e., encoded by) components in such a way that every term function f:A/sup n/ to A can be performed in parallel and is a projection on each component (algebraically speaking, if is isomorphic to a direct product of projection algebras). A list Sigma /sub tau / of identities that completely characterize rectangular algebras is given. Every term in RA/sub tau / has a normal form. Some algorithms (for decomposition and normal form) and examples for finite algebras of finite type are given.<>

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[1992] Proceedings The Twenty-Second International Symposium on Multiple-Valued Logic

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