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Author Nipkow, Tobias
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©1990
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Abstract This paper examines the unification problem in the class of primal algebras and the varieties they generate. An algebra is called primal if every function on its carrier can be expressed just in terms of the basic operations of the algebra. The two-element Boolean algebra is the simplest nontrivial example: Every truth-function can be realized in terms of the basic connectives, for example, negation and conjunction.It is shown that unification in primal algebras is unitary, that is, if an equation has a solution, it has a single most general one. Two unification algorithms, based on equation-solving techniques for Boolean algebras due to Boole and Lo¨wenheim, are studied in detail. Applications include certain finite Post algebras and matrix rings over finite fields. The former are algebraic models for many-valued logics, the latter cover in particular modular arithmetic.Then unification is extended from primal algebras to their direct powers, which leads to unitary unification algorithms covering finite Post algebras, finite, semisimple Artinian rings, and finite, semisimple nonabelian groups.Finally the fact that the variety generated by a primal algebra coincides with the class of its subdirect powers is used. This yields unitary unification algorithms for the equational theories of Post algebras and $\textit{p}-rings.$
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 1990-10-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 37
Issue Number 4
Page Count 35
Starting Page 742
Ending Page 776


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Source: ACM Digital Library