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Counterexample Generation for Markov Chains Using SMT-Based Bounded Model Checking [chapter]

Bettina Braitling, Ralf Wimmer, Bernd Becker, Nils Jansen, Erika Ábrahám
2011 Lecture Notes in Computer Science  
In order to be able to handle large systems and to use the capabilities of modern SAT-solvers, bounded model checking (BMC) for discrete-time Markov chains was established.  ...  Generation of counterexamples is a highly important task in the model checking process.  ...  For instance, properties can be formulated in probabilistic computation tree logic (PCTL) [4] for models called discrete-time Markov chains (DTMCs).  ... 
doi:10.1007/978-3-642-21461-5_5 fatcat:ozokqknl5ffu3mz5srud2f4wnq

A Study of Complex Property Counterexample Generation Method for Markov Model

Mingyu Ji, Zhiyuan Chen, Yanmei Li
2014 International Journal of Control and Automation  
The literature [12] shows the counterexample algorithm of reachability probability of until formula under transition step constraint for discrete time Markov chain.  ...  With the wide application of probabilistic systems, the research of counterexample generation for probabilistic system with model checking has attracted wide attention.  ...  Acknowledgements The authors would like to thank the anonymous reviewers of this paper for their carefully reading of the manuscript as well as their many constructive comments.  ... 
doi:10.14257/ijca.2014.7.2.24 fatcat:uq6j7fsp4fhmtontqek67wozoe

DiPro - A Tool for Probabilistic Counterexample Generation [chapter]

Husain Aljazzar, Florian Leitner-Fischer, Stefan Leue, Dimitar Simeonov
2011 Lecture Notes in Computer Science  
It allows for the computation of probabilistic counterexamples for discrete time Markov chains (DTMCs), continuous time Markov chains (CTMCs) and Markov decision processes (MDPs).  ...  The computation of counterexamples for probabilistic model checking has been an area of active research over the past years.  ...  Introduction Due to the numerical nature of the used model checking algorithm stochastic model checkers are unable to derive a counterexample witnessing a property violation directly from the model checking  ... 
doi:10.1007/978-3-642-22306-8_13 fatcat:us5n7iedhneu7n3h4x26xokrfu

Perspectives in Probabilistic Verification

Joost-Pieter Katoen
2008 2008 2nd IFIP/IEEE International Symposium on Theoretical Aspects of Software Engineering  
Model checking of probabilistic models received quite some attention in the late nineties, and this popularity lasts until today.  ...  Soon after the birth of the flourishing research area of model checking in the early eighties, researchers started to apply this technique to finite automata equipped with probabilities.  ...  In case all states in an MDP just have a single outgoing transition, one obtains a discrete-time Markov chain (DTMC).  ... 
doi:10.1109/tase.2008.44 dblp:conf/tase/Katoen08 fatcat:34t7l56fwfep3psrn42cqe2m4m

Directed Explicit State-Space Search in the Generation of Counterexamples for Stochastic Model Checking

H. Aljazzar, S. Leue
2010 IEEE Transactions on Software Engineering  
In this paper we apply directed explicit state space search to discrete-and continuous-time Markov chains in order to compute counterexamples for the violation of PCTL or CSL properties.  ...  Current stochastic model checkers do not make counterexamples for property violations readily available.  ...  The authors wish to thank Holger Hermanns for inspiring discussions that lead to the precursory work as documented in the paper [23] .  ... 
doi:10.1109/tse.2009.57 fatcat:5nylchyx4jdl7g3opwcyruviti

Linear Inequality LTL (iLTL): A Model Checker for Discrete Time Markov Chains [chapter]

YoungMin Kwon, Gul Agha
2004 Lecture Notes in Computer Science  
We develop a way of analyzing the behavior of systems modeled using Discrete Time Markov Chains (DTMC).  ...  Continuous-time Stochastic Logic (CSL) is a logic for Continuous Time Markov Chains (CTMC) which has an operator to reason about the steady-state probabilities of a system [13].  ...  Conclusions We have developed an LTL model checking algorithm for discrete time Markov chain models.  ... 
doi:10.1007/978-3-540-30482-1_21 fatcat:6m2wuh3dznbo7nbm7ldzbnpxzm

$$2^5$$ Years of Model Checking [chapter]

Edmund M. Clarke, Qinsi Wang
2015 Lecture Notes in Computer Science  
Model Checking is an automatic verification technique for large state transition systems. It was originally developed for reasoning about finite-state concurrent systems.  ...  Model Checking and State Explosion Problem Model Checking, as a framework consisting of powerful techniques for verifying finite-state systems, was independently developed by Clarke and Emerson [22] and  ...  Compared to former method, the latter approach exploits the grid to construct a discrete-time Markov chain (DTMC), and then employs standard model checking procedures for it.  ... 
doi:10.1007/978-3-662-46823-4_2 fatcat:g4tbd7fribgothf2bfgajkywfe

PRISM 4.0: Verification of Probabilistic Real-Time Systems [chapter]

Marta Kwiatkowska, Gethin Norman, David Parker
2011 Lecture Notes in Computer Science  
for statistical model checking; support for generation of optimal adversaries/strategies; and a benchmark suite.  ...  These include: an extensible toolkit for building, verifying and refining abstractions of probabilistic models; an explicit-state probabilistic model checking library; a discrete-event simulation engine  ...  For a full list of PRISM contributors, see [16].  ... 
doi:10.1007/978-3-642-22110-1_47 fatcat:y6aqczsj3fhtrcwwwljw5iqqki

Significant Diagnostic Counterexamples in Probabilistic Model Checking [article]

Miguel E. Andres, Pedro D'Argenio, Peter van Rossum
2008 arXiv   pre-print
This paper presents a novel technique for counterexample generation in probabilistic model checking of Markov Chains and Markov Decision Processes.  ...  counterexamples for reachability properties over acyclic Markov Chains.  ...  We use this result to generate counterexamples for the acyclic Markov Chains.  ... 
arXiv:0806.1139v1 fatcat:k4qndmplpvdpnhdlcegwsolxb4

Significant Diagnostic Counterexamples in Probabilistic Model Checking [chapter]

Miguel E. Andrés, Pedro D'Argenio, Peter van Rossum
2009 Lecture Notes in Computer Science  
This paper presents a novel technique for counterexample generation in probabilistic model checking of Markov Chains and Markov Decision Processes.  ...  This papers shows how to compute these witnesses by reducing the problem of generating counterexamples for general properties over Markov Decision Processes, in several steps, to the easy problem of generating  ...  We use this result to generate counterexamples for the acyclic Markov Chains.  ... 
doi:10.1007/978-3-642-01702-5_15 fatcat:gemuf4ph7zbpppkpda5vznwxum

Debugging of Dependability Models Using Interactive Visualization of Counterexamples

Husain Aljazzar, Stefan Leue
2008 2008 Fifth International Conference on Quantitative Evaluation of Systems  
The goal of this work is to facilitate the identification of causal factors in the potentially very large sets of execution traces that form counterexamples in stochastic model checking.  ...  We present an approach to support the debugging of stochastic system models using interactive visualization.  ...  STOCHASTIC MODEL CHECKING A. Markov Chains System dependability and performance models are often represented by variants of Markov chains.  ... 
doi:10.1109/qest.2008.40 dblp:conf/qest/AljazzarL08 fatcat:cqdxgxlcejcnrexcgpbniuqnxa

Generating Diagnoses for Probabilistic Model Checking Using Causality

Hichem Debbi, Mustapha Bourahla
2013 Journal of Computing and Information Technology  
Given a counterexample for a probabilistic CTL (PCTL) formula that does not hold over Discrete Time Markov Chain (DTMC) model, this method guides the user to the most responsible causes in the counterexample  ...  We call this trace a counterexample. In probabilistic model checking (PMC), counterexample generation has a quantitative aspect.  ...  These systems are described usually using Discrete-Time Markov Chains (DTMC), Continuous-Time Markov Chains (CTMC) or Markov Decision Processes (MDP), and verified against properties specified in Probabilistic  ... 
doi:10.2498/cit.1002115 fatcat:r3rcse7o5veczkji6gesuphhty

Verifying Pufferfish Privacy in Hidden Markov Models [article]

Depeng Liu, Bow-yaw Wang, Lijun Zhang
2021 arXiv   pre-print
In this paper, we propose an automatic verification technique for Pufferfish privacy. We use hidden Markov models to specify and analyze discretized Pufferfish privacy mechanisms.  ...  certifying counterexamples and (ii) obtaining a better lower bound for the privacy budget ϵ.  ...  Our modeling formalism is inspired by the work [Liu et al. 2018] , where Markov chains are used to model differential privacy with discretized mechanisms.  ... 
arXiv:2008.01704v2 fatcat:ekgg4vglxng4jdjwkedqosyjgi

Counterexample Generation for Infinite-State Chemical Reaction Networks [article]

Mohammad Ahmadi
2022 arXiv   pre-print
A method based on bounded model checking using SMT solving is developed for counterexample generation for CRNs.  ...  Counterexample generation is an indispensable part of model checking process.  ...  For performance and dependability analysis, the target systems often show stochastic behavior, and are usually modeled using probabilistic formalisms such as discrete-time Markov chains (DTMCs) or continuous-time  ... 
arXiv:2207.05207v1 fatcat:s4sfixziazhkzmn354pnnnczqm

Counterexamples for Timed Probabilistic Reachability [chapter]

Husain Aljazzar, Holger Hermanns, Stefan Leue
2005 Lecture Notes in Computer Science  
The inability to provide counterexamples for the violation of timed probabilistic reachability properties constrains the practical use of CSL model checking for continuous time Markov chains (CTMCs).  ...  We propose the use of explicit state model checking to determine runs leading into property offending states.  ...  In particular, we use explicit state model checking to explain why probabilistic timed reachability properties are not satisfied by a stochastic model given in the form of a Continuous-Time Markov Chain  ... 
doi:10.1007/11603009_15 fatcat:he2qx2vwrvdz5ivljzlnfan3ge
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