Information and Computation
Simple second-order languages for which unification is undecidable
Theoretical Computer Science
Bottom-up tree pushdown automata: classification and connection with rewrite systems
Theoretical Computer Science
Simultaneous rigid E-unification and other decision problems related to the Herbrand theorem
Theoretical Computer Science
Journal of the ACM (JACM)
Theoretical Computer Science
ASIAN '98 Proceedings of the 4th Asian Computing Science Conference on Advances in Computing Science
Monadic Simultaneous Rigid E-Unification and Related Problems
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Makanin's Algorithm for Word Equations - Two Improvements and a Generalization
IWWERT '90 Proceedings of the First International Workshop on Word Equations and Related Topics
Decidable and Undecidable Second-Order Unification Problems
RTA '98 Proceedings of the 9th International Conference on Rewriting Techniques and Applications
The Decidability of Simultaneous Rigid E-Unification with One Variable
RTA '98 Proceedings of the 9th International Conference on Rewriting Techniques and Applications
Term Rewriting, French Spring School of Theoretical Computer Science, Advanced Course
Simultaneous Rigid E-Unification and Related Algorithmic Problems
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Decidability Problems for the Prenex Fragment of Intuitionistic Logic
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
The Relation Between Second-Order Unification and Simultaneous Rigid E-Unification
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
Lower bounds for natural proof systems
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Tree acceptors and some of their applications
Journal of Computer and System Sciences
Hi-index | 0.00 |
In this paper we prove decidability results of restricted fragments of simultaneous rigid reachability or SRR, that is the nonsymmetrical form of simultaneous rigid E-unification or SREU. The absence of symmetry enforces us to use different methods, than the ones that have been successful in the context of SREU (for example word equations). The methods that we use instead, involve finite (tree) automata techniques, and the decidability proofs provide precise computational complexity bounds. The main results are 1) monadic SRR with ground rules is PSPACE-complete, and 2) balanced SRR with ground rules is EXPTIME-complete. These upper bounds have been open already for corresponding fragments of SREU, for which only the hardness results have been known. The first result indicates the difference in computational power between fragments of SREU with ground rules and nonground rules, respectively, due to a straightforward encoding of word equations in monadic SREU (with nonground rules). The second result establishes the decidability and precise complexity of the largest known subfragment of nonmonadic SREU.