Handling Left-Quadratic Rules When Completing Tree Automata

This paper addresses the following general problem of tree regular model-checking: decide whether R∗(L)∩Lp=∅ where R∗ is the reflexive and transitive closure of a successor relation induced by a term rewriting system R, and L and Lp are both regular tree languages. We develop an automatic approximation-based technique to handle this – undecidable in general – problem in the case when term rewriting system rules are left-quadratic. The most common practical case is handled this way.