Quantitative Probabilistic Verification in Distributed Environment

Bc. Jiří Appl

Master's thesis

Abstract:

The goal of this thesis is to contribute to the practical probabilistic verification by implementing a reliable, distributed model checking tool for quantitative analysis. We focus on systems modeled by Markov decision processes which combine the best of both nondeterministic and probabilistic models. The checked properties are expressed with use of linear temporal logic. The tool is able to determine the minimum and maximum probability that the given Markov decision process satisfies the desired temporal logic formula. The designed and implemented tool called ProbDiVinE 2.0 is built on DiVinE 2.x series. It uses power of several computers to speed up the verification process and to cope with so-called state space explosion problem, which is even more critical for probabilistic systems then for non-probabilistic ones. The model checking method implemented in the new tool is based on automata-theoretic approach to verification. The given temporal logic specification is translated into a deterministic Rabin automaton. A product of the system model and the Rabin automaton is then constructed and interpreted as a graph. Finally, modifications of standard graph algorithms together with solving a linear programming problem are used to obtain the answer to the quantitative analysis problem.

Abstract:

The goal of this thesis is to contribute to the practical probabilistic verification by implementing a reliable, distributed model checking tool for quantitative analysis. We focus on systems modeled by Markov decision processes which combine the best of both nondeterministic and probabilistic models. The checked properties are expressed with use of linear temporal logic. The tool is able to determine the minimum and maximum probability that the given Markov decision process satisfies the desired temporal logic formula. The designed and implemented tool called ProbDiVinE 2.0 is built on DiVinE 2.x series. It uses power of several computers to speed up the verification process and to cope with so-called state space explosion problem, which is even more critical for probabilistic systems then for non-probabilistic ones. The model checking method implemented in the new tool is based on automata-theoretic approach to verification. The given temporal logic specification is translated into a deterministic Rabin automaton. A product of the system model and the Rabin automaton is then constructed and interpreted as a graph. Finally, modifications of standard graph algorithms together with solving a linear programming problem are used to obtain the answer to the quantitative analysis problem.

Keywords

Probabilistic Verification, Model Checking, Linear Temporal Logic, Parallel and Distributed Environment, Distributed Memory, DiVinE Verification Framework, Strongly Connected Components, Accepting End Components

Language used: English

Date on which the thesis was submitted / produced: 30. 5. 2011

Thesis defence

• Date of defence: 30. 6. 2011
• Supervisor: prof. RNDr. Jiří Barnat, Ph.D.
• Reader: prof. RNDr. Ivana Černá, CSc.

Masaryk University

Faculty of Informatics

Master programme / field:
Informatics / Parallel and Distributed Systems