Generating and Solving Symbolic Parity Games

TL;DR

This paper introduces a symbolic parity game-based tool for modal mu-calculus verification, improving efficiency and scalability through structure-preserving translation, symbolic representation with MDDs, and recursive solving algorithms.

Contribution

It enhances existing PBES-based methods by structural preservation, extends LTSmin for symbolic parity games, and implements Zielonka's recursive algorithm for large systems.

Findings

Better time performance than existing PBES tools

Comparable speed to NuSMV with slightly higher memory use

Able to handle larger systems due to symbolic representation

Abstract

We present a new tool for verification of modal mu-calculus formulae for process specifications, based on symbolic parity games. It enhances an existing method, that first encodes the problem to a Parameterised Boolean Equation System (PBES) and then instantiates the PBES to a parity game. We improved the translation from specification to PBES to preserve the structure of the specification in the PBES, we extended LTSmin to instantiate PBESs to symbolic parity games, and implemented the recursive parity game solving algorithm by Zielonka for symbolic parity games. We use Multi-valued Decision Diagrams (MDDs) to represent sets and relations, thus enabling the tools to deal with very large systems. The transition relation is partitioned based on the structure of the specification, which allows for efficient manipulation of the MDDs. We performed two case studies on modular specifications, that demonstrate that the new method has better time and memory performance than existing PBES based tools and can be faster (but slightly less memory efficient) than the symbolic model checker NuSMV.