Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Minimal and complete word unification
Journal of the ACM (JACM)
Simple second-order languages for which unification is undecidable
Theoretical Computer Science
Word unification and transformation of generalized equations
Journal of Automated Reasoning
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
Studying Algorithmic Problems for Free Semi-groups and Groups
LFCS '97 Proceedings of the 4th International Symposium on Logical Foundations of Computer Science
forall exists*-Equational Theory of Context Unification is Pi10-Hard
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
On the Exponent of Periodicity of Minimal Solutions of Context Equation
RTA '98 Proceedings of the 9th 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
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
| Hi-index | 5.23 |
Context unification is a particular case of second-order unification in which all second-order variables are unary and only linear functions are sought for as solutions. Its decidability is an intriguing open problem, with only a very weak known NP-lower bound. We present the simplest (currently known) undecidable quantified fragment of the theory of context unification by showing that the set of 5-quantified context equations (i.e., sentences of the form WU,V,S,G,Hs=t) is undecidable and, in fact, is co-recursively enumerable hard (i.e., every set with recursively enumerable complement is many-one reducible to it).