Solving equations over small unary algebras

We consider the problem of solving a system of polynomial equations over fixed algebra $A$ which we call MPolSat($A$). We restrict ourselves to unary algebras and give a partial characterization of complexity of MPolSat($A$). We isolate a preorder $P(A)$ to show that when $A$ has at most 3 elements...

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Bibliographic Details
Published in:Discrete mathematics and theoretical computer science Vol. DMTCS Proceedings vol. AF,...; no. Proceedings; pp. 49 - 60
Main Author: Broniek, Przemyslaw
Format: Journal Article Conference Proceeding
Language:English
Published: DMTCS 01.01.2005
Discrete Mathematics and Theoretical Computer Science
Discrete Mathematics & Theoretical Computer Science
Series:DMTCS Proceedings
Subjects:
[info.info-lo] computer science [cs]/logic in computer science [cs.lo]
[info.info-sc] computer science [cs]/symbolic computation [cs.sc]
algebra
computational complexity
Computer Science
dichotomy
Logic in Computer Science
sat
Symbolic Computation
algebra
dichotomy
SAT
computational complexity
ISSN:1365-8050, 1462-7264, 1365-8050
Online Access:Get full text
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Summary:We consider the problem of solving a system of polynomial equations over fixed algebra $A$ which we call MPolSat($A$). We restrict ourselves to unary algebras and give a partial characterization of complexity of MPolSat($A$). We isolate a preorder $P(A)$ to show that when $A$ has at most 3 elements then MPolSat($A$) is in $P$ when width of $P(A)$ is at most 2 and is NP-complete otherwise. We show also that if $P ≠ NP$ then the class of unary algebras solvable in polynomial time is not closed under homomorphic images.
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.3474