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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| Vydáno v: | Discrete mathematics and theoretical computer science Ročník DMTCS Proceedings vol. AF,...; číslo Proceedings; s. 49 - 60 |
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| Médium: | Journal Article Konferenční příspěvek |
| Jazyk: | angličtina |
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DMTCS
01.01.2005
Discrete Mathematics and Theoretical Computer Science Discrete Mathematics & Theoretical Computer Science |
| Edice: | DMTCS Proceedings |
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| ISSN: | 1365-8050, 1462-7264, 1365-8050 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Broniek, Przemyslaw |
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| Snippet | 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... |
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| SubjectTerms | [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 |
| Title | Solving equations over small unary algebras |
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