Generation of the path to counter-examples by backward state space traversal in symbolic model checking based on term rewriting

Abstract

Model checking has proved to be a very useful formal verification technique in the design of communication and security protocols. Researches have used it to validate the communications protocols from the point of view of their functional and security specifications. Over the years, model checking has evolved from explicit encoding of the state space to symbolic encoding, thus overcoming the state space explosion problem and being able to handle almost infinite state spaces. Research has indicated that another means of improving the symbolic encoding of the state space is to encode only the states of the system, but not the transition relations. But this raises the problem of how to compute the path to the counter-examples. This paper address the issue and proposes the use of a backward traversal of the state space. The idea is to start from the counter-example state and compute its predecessor(s), then take each of the predecessors and apply recursively the same inversing operation until the initial state is reached, thus obtaining the sought path. The new approach was formally defined and exemplified.