An introduction to mathematical logic and type theory: to truth through proof
An introduction to mathematical logic and type theory: to truth through proof
Simple second-order languages for which unification is undecidable
Theoretical Computer Science
Complexity of Makanin's algorithm
Journal of the ACM (JACM)
A decision algorithm for distributive unification
Theoretical Computer Science - Special issue on rewriting techniques and applications
On the undecidability of second-order unification
Information and Computation - Special issue on RTA-98
On rewrite constraints and context unification
Information Processing Letters - Special issue analytical theory of fuzzy control with applications
Dominance Constraints in Context Unification
LACL '98 Selected papers from the Third International Conference, on Logical Aspects of Computational Linguistics
On the Exponent of Periodicity of Minimal Solutions of Context Equation
RTA '98 Proceedings of the 9th International Conference on Rewriting Techniques and Applications
RTA '00 Proceedings of the 11th International Conference on Rewriting Techniques and Applications
Currying Second-Order Unification Problems
RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
Linear Second-Order Unification
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
Testing Equivalence of Morphisms on Context-Free Languages
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
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
System Description: Twelf - A Meta-Logical Framework for Deductive Systems
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
Dominance Constraints: Algorithms and Complexity
LACL '98 Selected papers from the Third International Conference, on Logical Aspects of Computational Linguistics
Higher-order unification and matching
Handbook of automated reasoning
A uniform approach to underspecification and parallelism
ACL '98 Proceedings of the 35th Annual Meeting of the Association for Computational Linguistics and Eighth Conference of the European Chapter of the Association for Computational Linguistics
Satisfiability of word equations with constants is in PSPACE
Journal of the ACM (JACM)
Efficient memory representation of XML documents
DBPL'05 Proceedings of the 10th international conference on Database Programming Languages
Well-nested context unification
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
Bounded second-order unification is NP-complete
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
Dominance constraints in stratified context unification
Information Processing Letters
Unification with Singleton Tree Grammars
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
Context unification with one context variable
Journal of Symbolic Computation
Unification and matching on compressed terms
ACM Transactions on Computational Logic (TOCL)
Congruence closure of compressed terms in polynomial time
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
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Context Unification is the problem to decide for a given set of second-order equations E where all second-order variables are unary, whether there exists a unifier, such that for every second-order variable X, the abstraction λx. r instantiated for X has exactly one occurrence of the bound variable x in r. Stratified Context Unification is a specialization where the nesting of second-order variables in E is restricted. It is already known that Stratified Context Unification is decidable, NP-hard, and in PSPACE, whereas the decidability and the complexity of Context Unification is unknown. We prove that Stratified Context Unification is in NP by proving that a size-minimal solution can be represented in a singleton tree grammar of polynomial size, and then applying a generalization of Plandowski's polynomial algorithm that compares compacted terms in polynomial time. This also demonstrates the high potential of singleton tree grammars for optimizing programs maintaining large terms. A corollary of our result is that solvability of rewrite constraints is NP-complete.