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LICS
2000
IEEE

Computational Complexity of Some Problems Involving Congruences on Algebras

14 years 2 months ago
Computational Complexity of Some Problems Involving Congruences on Algebras
We prove that several problems concerning congruences on algebras are complete for nondeterministic log-space. These problems are: determining the congruence on a given algebra generated by a set of pairs, and determining whether a given algebra is simple or subdirectly irreducible. We also consider the problem of determining the smallest fully invariant congruence on a given algebra containing a given set of pairs. We prove that this problem is complete for nondeterministic polynomial time. Key words and phrases. congruence, simple algebra, nondeterministic log-space, graph accessibility One of the fundamental constructions in algebra is the formation of quotient structures. Every quotient of an algebra A is a homomorphic image of A, and conversely, every homomorphic image is isomorphic to a quotient of A. For familiar sorts of algebraic structures such as groups or rings, a quotient is often determined by a special subset, i.e., a normal subgroup or an ideal. But for an arbitrary alg...
Clifford Bergman, Giora Slutzki
Added 31 Jul 2010
Updated 31 Jul 2010
Type Conference
Year 2000
Where LICS
Authors Clifford Bergman, Giora Slutzki
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