A game-theoretic approach to simulation of data-parameterized systems

Abstract

This work focuses on data-parameterized abstract systems that extend standard modelling by allowing atomic propositions to be parameterized by variables that range over some infinite domain. These variables may range over process ids, message numbers, etc. Thus, abstract systems enable simple modelling of infinite-state systems whose source of infinity is the data. We define and study a simulation pre-order between abstract systems. The definition extends the definition of standard simulation by referring also to variable assignments. We define VCTL* – an extension of CTL* by variables, which is capable of specifying properties of abstract systems. We show that VCTL* logically characterizes the simulation pre-order between abstract systems. That is, that satisfaction of VACTL*, namely the universal fragment of VCTL*, is preserved in simulating abstract systems. For the second direction, we show that if an abstract system A2 does not simulate an abstract system A1, then there exists a VACTL formula that distinguishes A1 from A2. Finally, we present a game-theoretic approach to simulation of abstract systems and show that the prover wins the game iff A2 simulates A1. Further, if A2 does not simulate A1, then the refuter wins the game and his winning strategy corresponds to a VACTL formula that distinguishes A1 from A2. Thus, the many appealing practical advantages of simulation are lifted to the setting of data-parameterized abstract systems.