Higher-order unification revisited: Complete sets of transformations
Journal of Symbolic Computation
Simple second-order languages for which unification is undecidable
Theoretical Computer Science
The clausal theory of types
Handbook of logic in artificial intelligence and logic programming
Completion of rewrite systems with membership constraints. Part I: deduction rules
Journal of Symbolic Computation - Special issue: order-sorted rewriting
Completion of rewrite systems with membership constraints. Part II: constraint solving
Journal of Symbolic Computation - Special issue: order-sorted rewriting
Term rewriting and all that
A decision algorithm for distributive unification
Theoretical Computer Science - Special issue on rewriting techniques and applications
Satisfiability of word equations with constants is in NEXPTIME
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
On the undecidability of second-order unification
Information and Computation - Special issue on RTA-98
Proving termination with multiset orderings
Communications of the ACM
Solvability of context equations with two context variable is decidable
Journal of Symbolic Computation
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the Exponent of Periodicity of Minimal Solutions of Context Equation
RTA '98 Proceedings of the 9th International Conference on Rewriting Techniques and Applications
Decidable and Undecidable Second-Order Unification Problems
RTA '98 Proceedings of the 9th International Conference on Rewriting Techniques and Applications
Linear Second-Order Unification
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
The Security of Individual RSA Bits
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Satisfiability of Word Equations with Constants is in PSPACE
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Parameterized Complexity
On the building of affine retractions
Mathematical Structures in Computer Science
Decidability of bounded higher-order unification
Journal of Symbolic Computation
Bounded second-order unification is NP-complete
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
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It is well-known that first order unification is decidable, whereas second order (and higher order) unification is undecidable. Bounded second order unification is second order unification under the restriction that only a bounded number of bound variables in the instantiating terms for second order variables is permitted, however, the size of the instantiation is not restricted. In this paper, a decision algorithm for bounded second order unification is described. This is the first nontrivial decidability result for second order unification, where the signature is not restricted and there are no restrictions on the occurrences of variables. This supports the claim that bounded second order unification is easier than context unification, whose decidability is currently an open question.