Draft:Probabilistic Model Checking
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Comment: Good first draft. :) 1. I have marked several paragraphs with no inline citations. Existing citations might cover those paragraphs, or new ones might be necessary. Can you provide them? 2. Please add categories (Help:Category) and a "see also" section. Thank you! :) CopyleftEverything (talk) 02:07, 11 June 2026 (UTC)
In computer science, Probabilistic Model Checking is a technique for the formal verification of systems that exhibit probabilistic behavior. It extends traditional model checking approaches to verify probabilistic notions of correctness in Markov Automata such as Markov decision processes, discrete-time Markov chains, and continuous-time Markov chains.[1] This technique is commonly used to analyze systems where uncertainty is inherent, such as communication protocols, randomized algorithms, and engineered biological systems. It provides proofs of exact solutions to a specification.[citation needed]
Specification
[edit]Algorithmic solutions rely on the formulation of the probabilistic system's specification in a precise mathematical language. Probabilistic Model Checking enables the automated verification of properties specified in probabilistic temporal logics. By rigorously analyzing these models, one can determine whether a model satisfies given conditions with a specified probability.[citation needed]
Models
[edit]The foundational model structures for Probabilistic Model Checking are Markov Automata, including Markov chains (discrete-time and continuous-time) and Markov decision processes.[citation needed]
Properties
[edit]Probabilistic Model Checking relies on logics including PCTL (Probabilistic Computation Tree Logic) for property specifications on discrete-time models and CSL (Continuous Stochastic Logic) for property specification on continuous-time models.[citation needed]
Algorithms and Tools
[edit]Probabilistic model checking relies on several algorithms that enable the analysis of probabilistic computational systems.
Symbolic Approaches
[edit]For applications that are suited to it, symbolic representations such as Binary Decision Diagrams (BDDs) are used to efficiently represent large or infinite state spaces.[2] Symbolic representations apply to many models, but transient reachability analysis for continuous-time models requires an explicit state space representation.[3] Once a BDD is constructed for the state space, a Breadth-first or Depth-first Search is used to traverse the state space and evaluate a specification.[4]
Approximate Solutions
[edit]Monte Carlo methods leverage random sampling to estimate probabilities across state spaces. These algorithms are particularly useful in scenarios where the state space is too large for exhaustive enumeration. These approaches can include weighted ensemble,[5] the weighted Stochastic Simulation Algorithm,[6] Importance Sampling,[7] and Importance Splitting.[8]
Numeric Methods
[edit]Numeric techniques involve the direct computation of probability distributions over states. These methods include Linear Programming techniques for Markov decision processes and matrix exponentiation for continuous-time Markov chains.[9]
Tools
[edit]Publicly-available tools for Probabilistic Model Checking include PRISM,[10] Storm,[3] and Modest.[11]
References
[edit]- ↑ Kwiatkowska, Marta; Norman, Gethin; Parker, David (2007), "Stochastic Model Checking", in Bernardo, Marco; Hillston, Jane (eds.), Formal Methods for Performance Evaluation, vol. 4486, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 220–270, doi:10.1007/978-3-540-72522-0_6, ISBN 978-3-540-72482-7, retrieved 2026-03-06
- ↑ de Alfaro, Luca; Kwiatkowska, Marta; Norman, Gethin; Parker, David; Segala, Roberto (2000), "Symbolic Model Checking of Probabilistic Processes Using MTBDDs and the Kronecker Representation", in Graf, Susanne; Schwartzbach, Michael (eds.), Tools and Algorithms for the Construction and Analysis of Systems, vol. 1785, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 395–410, doi:10.1007/3-540-46419-0_27, ISBN 978-3-540-67282-1, retrieved 2026-03-17
- 1 2 Hensel, Christian; Junges, Sebastian; Katoen, Joost-Pieter; Quatmann, Tim; Volk, Matthias (August 2022). "The probabilistic model checker Storm". International Journal on Software Tools for Technology Transfer. 24 (4): 589–610. doi:10.1007/s10009-021-00633-z. ISSN 1433-2779.
- ↑ Hermanns, Holger; Kwiatkowska, Marta; Norman, Gethin; Parker, David; Siegle, Markus (May 2003). "On the use of MTBDDs for performability analysis and verification of stochastic systems". The Journal of Logic and Algebraic Programming. 56 (1–2): 23–67. doi:10.1016/S1567-8326(02)00066-8.
- ↑ Donovan, Rory M.; Sedgewick, Andrew J.; Faeder, James R.; Zuckerman, Daniel M. (2013-09-21). "Efficient stochastic simulation of chemical kinetics networks using a weighted ensemble of trajectories". The Journal of Chemical Physics. 139 (11). doi:10.1063/1.4821167. ISSN 0021-9606. PMC 3790806. PMID 24070313.
- ↑ Gillespie, Dan T.; Roh, Min; Petzold, Linda R. (2009-05-07). "Refining the weighted stochastic simulation algorithm". The Journal of Chemical Physics. 130 (17). doi:10.1063/1.3116791. ISSN 0021-9606. PMC 2832048. PMID 19425765.
- ↑ Kahn, H.; Marshall, A. W. (November 1953). "Methods of Reducing Sample Size in Monte Carlo Computations". Journal of the Operations Research Society of America. 1 (5): 263–278. doi:10.1287/opre.1.5.263. ISSN 0096-3984.
- ↑ Rosenbluth, Marshall N.; Rosenbluth, Arianna W. (1955-02-01). "Monte Carlo Calculation of the Average Extension of Molecular Chains". The Journal of Chemical Physics. 23 (2): 356–359. doi:10.1063/1.1741967. ISSN 0021-9606.
- ↑ Stewart, William J. (1994). Introduction to the numerical solution of Markov chains. Princeton: Princeton university press. ISBN 978-0-691-03699-1.
- ↑ Kwiatkowska, Marta; Norman, Gethin; Parker, David (2011), "PRISM 4.0: Verification of Probabilistic Real-Time Systems", in Gopalakrishnan, Ganesh; Qadeer, Shaz (eds.), Computer Aided Verification, vol. 6806, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 585–591, doi:10.1007/978-3-642-22110-1_47, ISBN 978-3-642-22109-5, retrieved 2026-03-06
- ↑ Hartmanns, Arnd; Hermanns, Holger (2014), "The Modest Toolset: An Integrated Environment for Quantitative Modelling and Verification", in Ábrahám, Erika; Havelund, Klaus (eds.), Tools and Algorithms for the Construction and Analysis of Systems, vol. 8413, Berlin, Heidelberg: Springer Berlin Heidelberg, pp. 593–598, doi:10.1007/978-3-642-54862-8_51, ISBN 978-3-642-54861-1, retrieved 2026-03-06
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