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316,436
E.: Counterexample generation for Markov chains using SMTbased bounded model checking
 In: Proc. of FMOODS/FORTE’11. Volume 6722 of LNCS, SpringerVerlag
, 2011
"... Abstract. Generation of counterexamples is a highly important task in the model checking process. In contrast to, e. g., digital circuits where counterexamples typically consist of a single path leading to a critical state of the system, in the probabilistic setting counterexamples may consist of a ..."
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Cited by 1 (1 self)
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large number of paths. In order to be able to handle large systems and to use the capabilities of modern SATsolvers, bounded model checking (BMC) for discretetime Markov chains was established. In this paper we introduce the usage of SMTsolving over linear real arithmetic for the BMC procedure. SMT
SMTbased Model Checking
"... Software or hardware systems can be often represented as a state transition system M = (S,I,T,L) where • S is a set of states • I ⊆ S is a set of initial states • T ⊆ S ×S is a (righttotal) transition relation • L: S → 2 Pr is a labeling function where Pr is a set of base predicates in some logic T ..."
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Typically, the base predicates denote variablevalue pairs x = v Atherton, CA, May 2011 – p.2/44Model Checking Software or hardware systems can be often represented as a state transition system, or model, M = (S,I,T,L) M is a model both in
Counterexampleguided Abstraction Refinement
, 2000
"... We present an automatic iterative abstractionrefinement methodology in which the initial abstract model is generated by an automatic analysis of the control structures in the program to be verified. Abstract models may admit erroneous (or "spurious") counterexamples. We devise new symb ..."
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Cited by 848 (71 self)
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We present an automatic iterative abstractionrefinement methodology in which the initial abstract model is generated by an automatic analysis of the control structures in the program to be verified. Abstract models may admit erroneous (or "spurious") counterexamples. We devise new
Symbolic Model Checking without BDDs
, 1999
"... Symbolic Model Checking [3, 14] has proven to be a powerful technique for the verification of reactive systems. BDDs [2] have traditionally been used as a symbolic representation of the system. In this paper we show how boolean decision procedures, like Stalmarck's Method [16] or the Davis ..."
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Cited by 910 (74 self)
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& Putnam Procedure [7], can replace BDDs. This new technique avoids the space blow up of BDDs, generates counterexamples much faster, and sometimes speeds up the verification. In addition, it produces counterexamples of minimal length. We introduce a bounded model checking procedure for LTL
Exact Sampling with Coupled Markov Chains and Applications to Statistical Mechanics
, 1996
"... For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has ..."
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Cited by 548 (13 self)
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For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain
SMTbased bisimulation minimisation of markov models
 In VMCAI, volume 7737 of LNCS
, 2013
"... Abstract. Probabilistic model checking is an increasingly widely used formal verification technique. However, its dependence on computationally expensive numerical operations makes it particularly susceptible to the statespace explosion problem. Among other abstraction techniques, bisimulation min ..."
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Cited by 4 (1 self)
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Abstract. Probabilistic model checking is an increasingly widely used formal verification technique. However, its dependence on computationally expensive numerical operations makes it particularly susceptible to the statespace explosion problem. Among other abstraction techniques, bisimulation
Finite state Markovchain approximations to univariate and vector autoregressions
 Economics Letters
, 1986
"... The paper develops a procedure for finding a discretevalued Markov chain whose sample paths approximate well those of a vector autoregression. The procedure has applications in those areas of economics, finance, and econometrics where approximate solutions to integral equations are required. 1. ..."
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Cited by 472 (0 self)
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The paper develops a procedure for finding a discretevalued Markov chain whose sample paths approximate well those of a vector autoregression. The procedure has applications in those areas of economics, finance, and econometrics where approximate solutions to integral equations are required. 1.
Analysis, Modeling and Generation of SelfSimilar VBR Video Traffic
, 1994
"... We present a detailed statistical analysis of a 2hour long empirical sample of VBR video. The sample was obtained by applying a simple intraframe video compression code to an action movie. The main findings of our analysis are (1) the tail behavior of the marginal bandwidth distribution can be accu ..."
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Cited by 546 (6 self)
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be accurately described using "heavytailed" distributions (e.g., Pareto); (2) the autocorrelation of the VBR video sequence decays hyperbolically (equivalent to longrange dependence) and can be modeled using selfsimilar processes. We combine our findings in a new (nonMarkovian) source model
Results 1  10
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316,436