Solving linear equations over polynomial semirings

Authors:
P. Narendran
Affiliations:
-
Venue:
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Year:
1996

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Abstract

We consider the problem of solving linear equations over various semirings. In particular, solving of linear equations over polynomial rings with the additional restriction that the solutions must have only non-negative coefficients is shown to be undecidable. Applications to undecidability proofs of several unification problems are illustrated, one of which, unification modulo one associative-commutative function and one endomorphism, has been a long-standing open problem. The problem of solving multiset constraints is also shown to be undecidable.