Equational approximations for tree automata completion

Equational Abstraction Refinement for Certified Tree Regular Model Checking

“…Our approximation framework and methodology are close to the equational abstractions of [33]. In [27], it has been shown that, under some assumptions, the widening operator may be exact, i.e., does not add terms that are not reachable.…”

Termination criteria for tree automata completion

“…When approximations are used, they are defined using a set of equations E and a theorem of [7] guarantees that completion introduces no more approximation than what E defines. The second termination condition is on the set of equations E. This condition is essentially syntactic and simple to check.…”

“…Tree Automata Completion algorithms were proposed in [16,17,12,7,18]. Tree automata completion is very similar to a Knuth-Bendix completion except that it runs on two distinct sets of rules: a TRS R and a set of transitions ∆ of a tree automaton A.…”

“…This definition is simpler and equivalent to top-down definitions [7]. In the recursive call, the choice of the context C[ ] may be non deterministic but all the possible results are the equivalent modulo state renaming.…”

“…A strength of the completion algorithm, and at the same time a weakness, is that its precision is parameterized by a function [6] or a set of equations [7]. It is a strength because tuning the approximation function (or equations) permits to adapt the precision of completion to a specific goal to tackle.…”