Handling Non Left-Linear Rules When Completing Tree Automata

Abstract

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 thisundecidable in general -problem in the case when term rewriting system rules are non left-linear.

Termination criteria for tree automata completion

“…However, some of the aforementioned completion techniques can [19,18]. An interesting research direction would be to extend the coverage results of section 5 to completion techniques of [19,18] with the non left-linear TRS classes preserving regularity. In the same way, completion fails with non left-linear TRSs when the tree automaton to complete is non deterministic (see Example 25).…”

“…Note that, in the literature, there exists some solutions to remove or weaken the left-linearity condition on R [12,6,19]. If we are interested in the precision of the approximation, it can be estimated using the R/E-coherence notion.…”

“…With regards to most papers about completion [17,12,10,6,19,7], our contribution is to give the first criterion on the approximation for the completion to terminate. Note that it is possible to guarantee termination of the completion by inferring an approximation adapted to the TRS under consideration, like in [36].…”

Towards Static Analysis of Functional Programs Using Tree Automata Completion

“…Tree automata completion. With regards to most papers about completion [9,23,8,4,14,20], our contribution is to give the first criterion on the approximation for the completion to terminate. Note that it is possible to guarantee termination of the completion by inferring an approximation adapted to the TRS under concern, like in [21].…”

“…Most of them also rely on a Knuth-Bendix completion-like algorithm completing a tree automaton A recognizing L 0 into an automaton A * recognizing exactly, or over-approximating, the set R * (L 0 ). As a result, these techniques can be refered as tree automata completion techniques [9,23,8,4,14,20]. A strength of this algorithm, and at the same time a weakness, is that its precision is parameterized by a function [8] or a set of equations [14].…”