Probabilistic Bisimulation for Parameterized Systems (Technical Report)
This work addresses a critical gap in formal verification for parameterized probabilistic systems, which are important in security and communication protocols but previously lacked automated verification methods.
The paper tackles the undecidable problem of verifying probabilistic bisimulation for parameterized systems by introducing a generic framework that encodes proof rules and uses a decidable first-order theory for automatic checking, enabling fully automated verification of anonymity properties for protocols like the dining cryptographers and grades protocols.
Probabilistic bisimulation is a fundamental notion of process equivalence for probabilistic systems. Among others, it has important applications including formalizing the anonymity property of several communication protocols. There is a lot of work on verifying probabilistic bisimulation for finite systems. This is however not the case for parameterized systems, where the problem is in general undecidable. In this paper we provide a generic framework for reasoning about probabilistic bisimulation for parameterized systems. Our approach is in the spirit of software verification, wherein we encode proof rules for probabilistic bisimulation and use a decidable first-order theory to specify systems and candidate bisimulation relations, which can then be checked automatically against the proof rules. As a case study, we show that our framework is sufficiently expressive for proving the anonymity property of the parameterized dining cryptographers protocol and the parameterized grades protocol, when supplied with a candidate regular bisimulation relation. Both of these protocols hitherto could not be verified by existing automatic methods. Moreover, with the help of standard automata learning algorithms, we show that the candidate relations can be synthesized fully automatically, making the verification fully automated.