Automatic proofs by induction in theories without constructors
Information and Computation
Sufficient-completeness, ground-reducibility and their complexity
Acta Informatica
Handbook of theoretical computer science (vol. B)
Testing for the ground (co-)reducibility property in term-rewriting systems
CAAP '90 Selected papers of the conference on Fifteenth colloquium on trees in algebra and programming
Haskell overloading is DEXPTIME-complete
Information Processing Letters
Automata for reduction properties solving
Journal of Symbolic Computation
Pumping, Cleaning and Symbolic Constraints Solving
ICALP '94 Proceedings of the 21st International Colloquium on Automata, Languages and Programming
Ground Reducibility and Automata with Disequality Constraints
STACS '94 Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science
Encompassment Properties and Automata with Constraints
RTA '93 Proceedings of the 5th International Conference on Rewriting Techniques and Applications
An Effective Method for Handling Initial Algebras
Proceedings of the International Workshop on Algebraic and Logic Programming
Languages Modulo Normalization
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
Combining Equational Tree Automata over AC and ACI Theories
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Automated Induction with Constrained Tree Automata
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Unique Normalization for Shallow TRS
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
Journal of Symbolic Computation
Tree automata with memory, visibility and structural constraints
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
Constructors, sufficient completeness, and deadlock freedom of rewrite theories
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
A sufficient completeness checker for linear order-sorted specifications modulo axioms
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
The HOM Problem is EXPTIME-Complete
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Non-Linear Rewrite Closure and Weak Normalization
Journal of Automated Reasoning
Hi-index | 0.00 |
We prove that ground reducibility is EXPTIME-complete in the general case. EXPTIME-hardness is proved by encoding the emptiness problem for the intersection of recognisable tree languages. It is more difficult to show that ground reducibility belongs to DEXPTIME. We associate first an automaton with disequality constraints AR,t to a rewrite system R and a term t. This automaton is deterministic and accepts at least one term iff t is not ground reducible by R. The number of states of AR,t is O(2||R||×||t||) and the size of its constraints is polynomial in the size of R, t. Then we prove some new pumping lemmas, using a total ordering on the computations of the automaton. Thanks to these lemmas, we can show that emptiness for an automaton with disequality constraints can be decided in a time which is polynomial in the number of states and exponential in the size of the constraints. Altogether, we get a simply exponential time deterministic algorithm for ground reducibility decision.