Bisimulations for Verifying Strategic Abilities with an Application to the ThreeBallot Voting Protocol

TL;DR

This paper introduces a new bisimulation concept for verifying strategic abilities in multi-agent systems with imperfect information, and applies it to prove coercion-resistance in the ThreeBallot voting protocol, enabling more scalable model checking.

Contribution

It develops an alternating bisimulation for ATL* under imperfect information and demonstrates its application to simplify models of the ThreeBallot voting system for verification.

Findings

Bisimulation preserves ATL* formulas for objective and subjective semantics.

Simplified models are bisimulations of original models, maintaining properties.

Model checking becomes feasible for larger voting systems with the new approach.

Abstract

We propose a notion of alternating bisimulation for strategic abilities under imperfect information. The bisimulation preserves formulas of ATL$^*$ for both the {\em objective} and {\em subjective} variants of the state-based semantics with imperfect information, which are commonly used in the modeling and verification of multi-agent systems. Furthermore, we apply the theoretical result to the verification of coercion-resistance in the ThreeBallot voting system, a voting protocol that does not use cryptography. In particular, we show that natural simplifications of an initial model of the protocol are in fact bisimulations of the original model, and therefore satisfy the same ATL$^*$ properties, including coercion-resistance. These simplifications allow the model-checking tool MCMAS to terminate on models with a larger number of voters and candidates, compared with the initial model.