Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
A proof theory for general unification
A proof theory for general unification
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The complexity of solving equations over finite groups
Information and Computation
Unification and Matching in Process Algebras
RTA '98 Proceedings of the 9th International Conference on Rewriting Techniques and Applications
Nominal logic, a first order theory of names and binding
Information and Computation - TACS 2001
Inapproximability results for equations over finite groups
Theoretical Computer Science - Special issue on automata, languages and programming
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Theoretical Computer Science
Nominal logic programming
Electronic Notes in Theoretical Computer Science (ENTCS)
Information and Computation
Nominal Techniques in Isabelle/HOL
Journal of Automated Reasoning
ACM Transactions on Programming Languages and Systems (TOPLAS)
A polynomial nominal unification algorithm
Theoretical Computer Science
Nominal Unification from a Higher-Order Perspective
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Resolving Inductive Definitions with Binders in Higher-Order Typed Functional Programming
ESOP '09 Proceedings of the 18th European Symposium on Programming Languages and Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
Journal of Logic and Computation
Avoiding equivariance in alpha-prolog
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Information and Computation
| Hi-index | 0.00 |
Nominal logic is a variant of first-order logic with special facilities for reasoning about names and binding based on the underlying concepts of swapping and freshness. It serves as the basis of logic programming, term rewriting, and automated theorem proving techniques that support reasoning about languages with name-binding. These applications often require nominal unification, or equational reasoning and constraint solving in nominal logic. Urban, Pitts and Gabbay developed an algorithm for a broadly applicable class of nominal unification problems. However, because of nominal logic's equivariance property, these applications also require a different form of unification, which we call equivariant unification. In this article, we first study the complexity of the decision problem for equivariant unification and equivariant matching. We show that these problems are NP-hard in general, as is nominal unification without the ground-name restrictions employed in previous work on nominal unification. Moreover, we present an exponential-time algorithm for equivariant unification that can be used to decide satisfiability, or produce a complete finite set of solutions. We also study special cases that can be solved efficiently. In particular, we present a polynomial time algorithm for swapping-free equivariant matching, that is, for matching problems in which the swapping operation does not appear.