On the Confluence of Trace Rewriting Systems

Complexity Results for Confluence Problems

We study the complexity of the confluence problem for restricted kinds of semi–Thue systems, vector replacement systems and general trace rewriting systems. We prove that confluence for length– reducing semi–Thue systems is P–complete and that this complexity reduces to NC in the monadic case. For length–reducing vector replacement systems we prove that the confluence problem is PSPACE– complet...

On the Theory of One-Step Rewriting in Trace Monoids

We prove that the first-order theory of the one-step rewriting relation associated with a trace rewriting system is decidable and give a nonelementary lower bound for the complexity. The decidability extends known results on semi-Thue systems but our proofs use new methods; these new methods yield the decidability of local properties expressed in first-order logic augmented by modulo-counting q...

Confluence Problems for Trace Rewriting

Ground Confluence Prover based on Rewriting Induction

Ground confluence of term rewriting systems guarantees that all ground terms are confluent. Recently, interests in proving confluence of term rewriting systems automatically has grown, and confluence provers have been developed. But they mainly focus on confluence and not ground confluence. In fact, little interest has been paid to developing tools for proving ground confluence automatically. W...

Confluence of nearly orthogonal infinitary term rewriting systems

We give a relatively simple coinductive proof of confluence, modulo equivalence of root-active terms, of nearly orthogonal infinitary term rewriting systems. Nearly orthogonal systems allow certain root overlaps, but no non-root overlaps. Using a slightly more complicated method we also show confluence modulo equivalence of hypercollapsing terms. The condition we impose on root overlaps is simi...