Equational Abstraction Refinement for Certified Tree Regular Model Checking

International audienceTree Regular Model Checking (TRMC) is the name of a fam- ily of techniques for analyzing infinite-state systems in which states are represented by trees and sets of states by tree automata. The central problem is to decide whether a set of bad states belongs to the set of reachable states. An obstacle is that this set is in general neither regular nor computable in finite time. This paper proposes a new CounterExample Guided Abstraction Re- finement (CEGAR) algorithm for TRMC. Our approach relies on a new equational-abstraction based completion algorithm to compute a regu- lar overapproximation of the set of reachable states in finite time. This set is represented by R/E-automata, a new extended tree automaton formalism whose structure can be exploited to detect and remove false positives in an efficient manner. Our approach has been implemented in TimbukCEGAR, a new toolset that is capable of analyzing Java pro- grams by exploiting an elegant translation from the Java byte code to term rewriting systems. Experiments show that TimbukCEGAR outper- forms existing CEGAR-based completion algorithms. Contrary to exist- ing TRMC toolsets, the answers provided by TimbukCEGAR are certi- fied by Coq, which means that they are formally proved correct