Equational Abstraction Refinement for Certified Tree Regular Model Checking

Tree Regular Model Checking (TRMC) is the name of a family of techniques for analyzing in nite-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 nite time. This paper proposes a new CounterExample Guided Abstraction Re- nement (CEGAR) algorithm for TRMC. Our approach relies on a new equational-abstraction based completion algorithm to compute a regular overapproximation of the set of reachable states in nite 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 e cient manner. Our approach has been implemented in TimbukCEGAR, a new toolset that is capable of analyzing Java programs by exploiting an elegant translation from the Java byte code to term rewriting systems. Experiments show that TimbukCEGAR outperforms existing CEGAR-based completion algorithms. Contrary to existing TRMC toolsets, the answers provided by TimbukCEGAR are certi- ed by Coq, which means that they are formally proved correct.