The Church-Rosser property for ground term-rewriting systems is decidable
Theoretical Computer Science
Information and Computation
A fast algorithm for generating reduced ground rewriting systems from a set of ground equations
Journal of Symbolic Computation
A fast algorithm for constructing a tree automaton recognizing a congruential tree language
Theoretical Computer Science
Proof lengths for equational completion
Information and Computation - special issue: symposium on theoretical aspects of computer software TACS '94
Derivation trees of ground term rewriting systems
Information and Computation
Congruential complements of ground term rewrite systems
Theoretical Computer Science
Restricted ground tree transducers
Theoretical Computer Science
Shostak's Congruence Closure as Completion
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
Complexity of finitely presented algebras
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
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For a tree automaton A over a ranked alphabet Σ, we study the ground tree transformation π(A) induced by A and the restriction θ(A) of the congruence ↔A* to terms over Σ. We define a congruence relation ρ ⊆ A × A on A, called the determiner of A, and the quotient tree automaton A/ρ. We show the following results. It is decidable if θ(A) = π(A). If A is deterministic, then θ(A) = π(A). The determiner ρ of A can be effectively constructed, A/ρ is deterministic, and θ(A) = θ(A/ρ). For a connected tree automaton A, π(A) = π(A/ρ) if and only if π(A) = π(B) for some deterministic tree automaton B if and only if θ(A) = π(A).