Ground Reducibility is EXPTIME-complete

Hubert Comon Florent Jacquemard 1
1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : 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 recognizable tree languages. It is more difficult to show that ground reducibility belongs to DEXPTIME. We associate first a tree automaton with disequality constraints to a rewrite system and a term. This automaton is deterministic and accepts a non-empty tree language iff the given term is not ground reducible by the system. The number of states of the automaton is exponential in the size of the term and the system, and the size of its constraints is polynomial in the size of the term and the system. 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 a tree 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.
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Submitted on : Wednesday, May 24, 2006 - 11:07:06 AM
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Hubert Comon, Florent Jacquemard. Ground Reducibility is EXPTIME-complete. [Research Report] RR-3800, INRIA. 1999, pp.26. ⟨inria-00072859⟩

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