Matching, unification and complexity
ACM SIGSAM Bulletin
Journal of Symbolic Computation
Theorem proving using equational matings and rigid E-unification
Journal of the ACM (JACM)
An algorithm for finding canonical sets of ground rewrite rules in polynomial time
Journal of the ACM (JACM)
Optimal implementation of conjunctive queries in relational data bases
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Complexity of finitely presented algebras
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Constructing rewrite-based decision procedures for embeddings and termination
MPC'06 Proceedings of the 8th international conference on Mathematics of Program Construction
Hi-index | 0.00 |
An algebra $\cal A$ is finitely presented if there is a finite set G of generator symbols, a finite set O of operator symbols, and a finite set $\Gamma$ of defining relations $x \equiv y$ where $x$ and $y$ are well-formed terms over G and O, such that $\cal A$ is isomorphic to the free algebra on G and O modulo the congruence induced by $\Gamma$. The uniform word problem, the finiteness problem, the triviality problem (whether $\cal A$ is the one element algebra), and the subalgebra membership problem (whether a given element of $\cal A$ is contained in a finitely generated subalgebra of $\cal A$) for finitely presented algebras are shown to be $\leq^{m}_{\log}$-complete for P. The schema satisfiability problem and schema validity problem are shown to be $\leq^{m}_{\log}$-complete for NP and co-NP, respectively, Finally, the problem of isomorphism of finitely presented algebras is shown to be polynomial time many-one equivalent to the problem of graph isomorphism.