Decidability of unification in the theory of one-sided distributivity and a multiplicative unit
Journal of Symbolic Computation
Grid structures and undecidable constraint theories
Theoretical Computer Science
Proceedings of the 7th International Conference on Rewriting Techniques and Applications
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
Proceedings of the 8th International Conference on Rewriting Techniques and Applications
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
Equality and Disequality Constraints on Direct Subterms in Tree Automata
STACS '92 Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science
Grid Structure and Undecidable Constraint Theories
TAPSOFT '97 Proceedings of the 7th International Joint Conference CAAP/FASE on Theory and Practice of Software Development
Linear Second-Order Unification
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
The First-Order Theory of One-Step Rewriting is Undecidable
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
An Algorithm for Distributive Unification
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
The First-Order Theory of One Step Rewriting in Linear Noetherian Systems is Undecidable
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
Undecidability of the First Order Theory of One-Step Right Ground Rewriting
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
On Equality Up-to Constraints over Finite Trees, Context Unification, and One-Step Rewriting
CADE-14 Proceedings of the 14th International Conference on Automated Deduction
Weakly Regular Relations and Applications
RTA '01 Proceedings of the 12th International Conference on Rewriting Techniques and Applications
The Existential Fragment of the One-Step Parallel Rewriting Theory
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
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We consider quantifier free formulae of a first order theory without functions and with predicates x rewrites to y in one step with given rewrite systems. Variables are interpreted in the set of finite trees. The full theory is undecidable [Tre96] and recent results [STT97], [Mar97], [Vor97] have strengthened the undecidability result to formulae with small prefixes (∃*∀*) and very restricted classes of rewriting systems (e.g. linear, shallow and convergent in [STTT98]). Decidability of the positive existential fragment has been shown in [NPR97]. We give a decision procedure for positive and negative existential formulae in the case when the rewrite systems are quasi-shallow, that is all variables in the rewrite rules occur at depth one. Our result extends to formulae with equalities and memberships relations of the form x ∈ L where L is a recognizable set of terms.