Probabilistic Bisimulation for Parameterized Systems (Technical Report)

TL;DR

This paper introduces a generic, automated framework for verifying probabilistic bisimulation in parameterized systems, enabling the proof of properties like anonymity in protocols previously unverifiable by existing methods.

Contribution

It presents a novel approach encoding proof rules within a decidable first-order theory, allowing automatic verification and synthesis of bisimulation relations for complex parameterized protocols.

Findings

Successfully verified anonymity in dining cryptographers and grades protocols.

Automated synthesis of bisimulation relations using automata learning algorithms.

Framework extends verification capabilities to previously intractable parameterized systems.

Abstract

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.