Simple second-order languages for which unification is undecidable
Theoretical Computer Science
Complexity of Makanin's algorithm
Journal of the ACM (JACM)
Second-order unification and type inference for Church-style polymorphism
POPL '98 Proceedings of the 25th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
On the undecidability of second-order unification
Information and Computation - Special issue on RTA-98
An Efficient Unification Algorithm
ACM Transactions on Programming Languages and Systems (TOPLAS)
On the Exponent of Periodicity of Minimal Solutions of Context Equation
RTA '98 Proceedings of the 9th 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
Stratified Context Unification Is in PSPACE
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
Testing Equivalence of Morphisms on Context-Free Languages
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
Higher-order unification and matching
Handbook of automated reasoning
Decidability of bounded second order unification
Information and Computation
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
On the building of affine retractions
Mathematical Structures in Computer Science
Parameter Reduction in Grammar-Compressed Trees
FOSSACS '09 Proceedings of the 12th International Conference on Foundations of Software Science and Computational Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
Unification with Singleton Tree Grammars
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
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
Stratified context unification is NP-complete
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Parameter reduction and automata evaluation for grammar-compressed trees
Journal of Computer and System Sciences
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Bounded Second-Order Unification is the problem of deciding, for a given second-order equation ${t {\stackrel{_?}=} u}$ and a positive integer m, whether there exists a unifier σ such that, for every second-order variable F, the terms instantiated for F have at most m occurrences of every bound variable. It is already known that Bounded Second-Order Unification is decidable and NP-hard, whereas general Second-Order Unification is undecidable. We prove that Bounded Second-Order Unification is NP-complete, provided that m is given in unary encoding, by proving that a size-minimal solution can be represented in polynomial space, and then applying a generalization of Plandowski's polynomial algorithm that compares compacted terms in polynomial time.