Formalization of finite-state discrete-time Markov chains in HOL

Authors:
Liya Liu;Osman Hasan;Sofiène Tahar
Affiliations:
Dept. of Electrical & Computer Engineering, Concordia University, Montreal, Quebec, Canada;Dept. of Electrical & Computer Engineering, Concordia University, Montreal, Quebec, Canada;Dept. of Electrical & Computer Engineering, Concordia University, Montreal, Quebec, Canada
Venue:
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
Year:
2011

Citing 11
Cited 2

Mechanizing programming logics in higher order logic

Current trends in hardware verification and automated theorem proving
Introduction to Monte Carlo methods

Proceedings of the NATO Advanced Study Institute on Learning in graphical models
Probability and statistics with reliability, queuing and computer science applications

Probability and statistics with reliability, queuing and computer science applications
SPNP: Stochastic Petri Net Package

PNPM '89 The Proceedings of the Third International Workshop on Petri Nets and Performance Models
Model-Checking Algorithms for Continuous-Time Markov Chains

IEEE Transactions on Software Engineering
VESTA: A Statistical Model-checker and Analyzer for Probabilistic Systems

QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
Principles of Model Checking (Representation and Mind Series)

Principles of Model Checking (Representation and Mind Series)
Formal probabilistic analysis using theorem proving

Formal probabilistic analysis using theorem proving
Formal Reasoning about Expectation Properties for Continuous Random Variables

FM '09 Proceedings of the 2nd World Congress on Formal Methods
Stochastic Petri Nets: Modelling, Stability, Simulation

Stochastic Petri Nets: Modelling, Stability, Simulation
On the formalization of the lebesgue integration theory in HOL

ITP'10 Proceedings of the First international conference on Interactive Theorem Proving

Verifying pCTL model checking

TACAS'12 Proceedings of the 18th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Formal reasoning about classified markov chains in HOL

ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving

Quantified Score

Hi-index	0.00

Visualization

Abstract

The mathematical concept of Markov chains is widely used to model and analyze many engineering and scientific problems. Markovian models are usually analyzed using computer simulation, and more recently using probabilistic model-checking but these methods either do not guarantee accurate analysis or are not scalable. As an alternative, we propose to use higher-order-logic theorem proving to reason about properties of systems that can be described as Markov chains. As the first step towards this goal, this paper presents a formalization of time homogeneous finite-state Discrete-time Markov chains and the formal verification of some of their fundamental properties, such as Joint probabilities, Chapman-Kolmogorov equation and steady state probabilities, using the HOL theorem prover. For illustration purposes, we utilize our formalization to analyze a simplified binary communication channel.