Abstract
This chapter provides a survey of algorithms that have been used to solve decision problems (mainly word problems) in various varieties of algebras, e.g., lattices, commutative semigroups, and quasigroups. The interest is in the algebraic properties that imply the existence of such algorithms. The chapter discusses the connection between embedding of partial algebras in a variety and the solvability of the word problem for finitely presented (f.p.) algebras in the variety. It considers algorithms based on the finite separability properties. The chapter discusses the aspects of normal form theorems. The work is limited to finitely presented variety V— that is, a variety defined by a finite number of finitary operations and a finite set of identities, and by algebra.
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