Petri Nets Based Verification of Epistemic Logic and Its Application on Protocols of Privacy and Security

Abstract

Epistemic logic can specify many design requirements of privacy and security of multi-agent systems (MAS). The existing model checkers of epistemic logic use some programming languages to describe MAS, induce Kripke models as the behavioral representation of MAS, apply Ordered Binary Decision Diagrams (OBDD) to encode Kripke models to solve their state explosion problem and verify epistemic logic based on the encoded Kripke models. However, these programming languages are usually non-intuitive. More seriously, their OBDD-based model checking processes are often time-consuming due to their dynamic variable ordering for OBDD. Therefore, we define Knowledge-oriented Petri Nets (KPN) to intuitively describe MAS, induce similar reachability graphs as the behavioral representation of KPN, apply OBDD to encode all reachable states, and finally verify epistemic logic. Although we also use OBDD, we adopt a heuristic method for the computation of a static variable order instead of dynamic variable ordering. More importantly, while verifying an epistemic formula, we dynamically generate its needed similar relations, which makes our model checking process much more efficient. In this paper, we introduce our work.