Probabilistic symmetry reduction

Power, Christopher (2012) Probabilistic symmetry reduction. PhD thesis, University of Glasgow.

Abstract

Model checking is a technique used for the formal verification of concurrent systems. A major hindrance to model checking is the so-called state space explosion problem where the number of states in a model grows exponentially as variables are added. This means even trivial systems can require millions of states to define and are often too large to feasibly verify. Fortunately, models often exhibit underlying replication which can be exploited to aid in verification. Exploiting this replication is known as symmetry reduction and has yielded considerable success in non probabilistic verification.

The main contribution of this thesis is to show how symmetry reduction techniques can be applied to explicit state probabilistic model checking. In probabilistic model checking the need for such techniques is particularly acute since it requires not only an exhaustive state-space exploration, but also a numerical solution phase to compute probabilities or other quantitative values.

The approach we take enables the automated detection of arbitrary data and component symmetries from a probabilistic specification. We define new techniques to exploit the identified symmetry and provide efficient generation of the quotient model. We prove the correctness of our approach, and demonstrate its viability by implementing a tool to apply symmetry reduction to an explicit state model checker.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Keywords: Formal Methods, Model Checking, Probabilistic, Symmetry Reduction
• Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
• Colleges/Schools: College of Science and Engineering > School of Computing Science
• Supervisor's Name: Miller, Dr. Alice
• Date of Award: 2012
• Depositing User: Mr Christopher Power
• Unique ID: glathesis:2012-3493
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 29 Jun 2012
• Last Modified: 10 Dec 2012 14:07
• URI: https://theses.gla.ac.uk/id/eprint/3493