Automated proof for equivalence of telephone systems

An extended telephone system to avoid a phone fraud was introduced by Yamamoto et al. In this study, we prove that the extended telephone system is equivalent to the original telephone system at a level of abstraction. We conduct an automatic proof with the Alloy analyzer. After describing specifications of telephone systems in I/O-automaton, we translate the specifications into Alloy. We finally prove the existence of forward simulations by SAT solving.