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
Fast equality test for straight-line compressed strings
Information Processing Letters
Parameter reduction and automata evaluation for grammar-compressed trees
Journal of Computer and System Sciences
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This paper is an investigation of the matching problem for term equations s = t where s contains context variables and first-order variables, and both terms s and t are given using some kind of compressed representation. The main result is a polynomial time algorithm for context matching with dags, when the number of different context variables is fixed for the problem. NP-completeness is obtained when the terms are represented using the more general formalism of singleton tree grammars. As an ingredient of this proof, we also show that the special case of first-order matching with singleton tree grammars is decidable in polynomial time.