Results 1  10
of
372
Verification by abstract interpretation
 In Verification: Theory and Practice
, 2003
"... Dedicated to Zohar Manna, for his 2 6 th birthday. Abstract. Abstract interpretation theory formalizes the idea of abstraction of mathematical structures, in particular those involved in the specification of properties and proof methods of computer systems. Verification by abstract interpretation is ..."
Abstract

Cited by 237 (16 self)
 Add to MetaCart
Dedicated to Zohar Manna, for his 2 6 th birthday. Abstract. Abstract interpretation theory formalizes the idea of abstraction of mathematical structures, in particular those involved in the specification of properties and proof methods of computer systems. Verification by abstract interpretation is illustrated on the particular cases of predicate abstraction, which is revisited to handle infinitary abstractions, and on the new parametric predicate abstraction. 1
Modelchecking algorithms for continuoustime Markov chains
 IEEE TRANSACTIONS ON SOFTWARE ENGINEERING
, 2003
"... Continuoustime Markov chains (CTMCs) have been widely used to determine system performance and dependability characteristics. Their analysis most often concerns the computation of steadystate and transientstate probabilities. This paper introduces a branching temporal logic for expressing realt ..."
Abstract

Cited by 235 (48 self)
 Add to MetaCart
(Show Context)
Continuoustime Markov chains (CTMCs) have been widely used to determine system performance and dependability characteristics. Their analysis most often concerns the computation of steadystate and transientstate probabilities. This paper introduces a branching temporal logic for expressing realtime probabilistic properties on CTMCs and presents approximate model checking algorithms for this logic. The logic, an extension of the continuous stochastic logic CSL of Aziz et al., contains a timebounded until operator to express probabilistic timing properties over paths as well as an operator to express steadystate probabilities. We show that the model checking problem for this logic reduces to a system of linear equations (for unbounded until and the steadystate operator) and a Volterra integral equation system (for timebounded until). We then show that the problem of modelchecking timebounded until properties can be reduced to the problem of computing transient state probabilities for CTMCs. This allows the verification of probabilistic timing properties by efficient techniques for transient analysis for CTMCs such as uniformization. Finally, we show that a variant of lumping equivalence (bisimulation), a wellknown notion for aggregating CTMCs, preserves the validity of all formulas in the logic.
Verifying Continuous Time Markov Chains
, 1996
"... . We present a logical formalism for expressing properties of continuous time Markov chains. The semantics for such properties arise as a natural extension of previous work on discrete time Markov chains to continuous time. The major result is that the verification problem is decidable; this is show ..."
Abstract

Cited by 125 (1 self)
 Add to MetaCart
(Show Context)
. We present a logical formalism for expressing properties of continuous time Markov chains. The semantics for such properties arise as a natural extension of previous work on discrete time Markov chains to continuous time. The major result is that the verification problem is decidable; this is shown using results in algebraic and transcendental number theory. Introduction Recent work on formal verification has addressed systems with stochastic dynamics. Certain models for discrete time Markov chains have been investigated in [6, 3]. However, a large class of stochastic systems operate in continuous time. In a generalized decision and control framework, continuous time Markov chains form a useful extension [9]. In this paper we propose a logic for specifying properties of such systems, and describe a decision procedure for the model checking problem. Our result differs from past work in this area [2] in that quantitative bounds on the probability of events can be expressed in the logi...
Probabilistic Verification of Discrete Event Systems using Acceptance Sampling
 In Proc. 14th International Conference on Computer Aided Verification, volume 2404 of LNCS
, 2002
"... We propose a model independent procedure for verifying properties of discrete event systems. The dynamics of such systems can be very complex, making them hard to analyze, so we resort to methods based on Monte Carlo simulation and statistical hypothesis testing. The verification is probabilistic in ..."
Abstract

Cited by 124 (9 self)
 Add to MetaCart
(Show Context)
We propose a model independent procedure for verifying properties of discrete event systems. The dynamics of such systems can be very complex, making them hard to analyze, so we resort to methods based on Monte Carlo simulation and statistical hypothesis testing. The verification is probabilistic in two senses. First, the properties, expressed as CSL formulas, can be probabilistic. Second, the result of the verification is probabilistic, and the probability of error is bounded by two parameters passed to the verification procedure. The verification of properties can be carried out in an anytime manner by starting off with loose error bounds, and gradually tightening these bounds.
Automatic verification of realtime systems with discrete probability distributions
 Theoretical Computer Science
, 1999
"... Abstract. We consider the timed automata model of [3], which allows the analysis of realtime systems expressed in terms of quantitative timing constraints. Traditional approaches to realtime system description express the model purely in terms of nondeterminism; however, we may wish to express the ..."
Abstract

Cited by 118 (33 self)
 Add to MetaCart
Abstract. We consider the timed automata model of [3], which allows the analysis of realtime systems expressed in terms of quantitative timing constraints. Traditional approaches to realtime system description express the model purely in terms of nondeterminism; however, we may wish to express the likelihood of the system making certain transitions. In this paper, we present a model for realtime systems augmented with discrete probability distributions. Furthermore, using the algorithm of [5] with fairness, we develop a model checking method for such models against temporal logic properties which can refer both to timing properties and probabilities, such as, “with probability 0.6 or greater, the clock x remains below 5 until clock y exceeds 2”. 1
On probabilistic model checking
, 1996
"... Abstract. This tutorial presents an overview of model checking for both discrete and continuoustime Markov chains (DTMCs and CTMCs). Model checking algorithms are given for verifying DTMCs and CTMCs against specifications written in probabilistic extensions of temporal logic, including quantitative ..."
Abstract

Cited by 107 (25 self)
 Add to MetaCart
(Show Context)
Abstract. This tutorial presents an overview of model checking for both discrete and continuoustime Markov chains (DTMCs and CTMCs). Model checking algorithms are given for verifying DTMCs and CTMCs against specifications written in probabilistic extensions of temporal logic, including quantitative properties with rewards. Example properties include the probability that a fault occurs and the expected number of faults in a given time period. We also describe the practical application of stochastic model checking with the probabilistic model checker PRISM by outlining the main features supported by PRISM and three realworld case studies: a probabilistic security protocol, dynamic power management and a biological pathway. 1
It Usually Works: The Temporal Logic of Stochastic Systems
, 1995
"... . In this paper the branching time logic pCTL is defined. pCTL expresses quantitative bounds on the probabilities of correct behavior; it can be interpreted over discrete Markov processes. A bisimulation relation is defined on finite Markov processes, and shown to be sound and complete with re ..."
Abstract

Cited by 103 (0 self)
 Add to MetaCart
(Show Context)
. In this paper the branching time logic pCTL is defined. pCTL expresses quantitative bounds on the probabilities of correct behavior; it can be interpreted over discrete Markov processes. A bisimulation relation is defined on finite Markov processes, and shown to be sound and complete with respect to pCTL . We extend the universe of models to generalized Markov processes in order to support notions of refinement, abstraction, and parametrization. Model checking pCTL over generalized Markov processes is shown to be elementary by a reduction to RCF. We conclude by describing practical and theoretical avenues for further work. 1 Introduction The study of formal methods to specify and prove properties of finite state systems has been the subject of intense research. Various methodologies have been proposed; some of the most fruitful, in both theory and practise, have been based on temporal logic [10]. Properties are expressed using formulae which are built out of operators ...
Model checking continuoustime Markov chains by transient analysis
, 2000
"... . The verification of continuoustime Markov chains (CTMCs) against continuous stochastic logic (CSL) [3, 6], a stochastic branchingtime temporal logic, is considered. CSL facilitates among others the specification of steadystate properties and the specification of probabilistic timing properties o ..."
Abstract

Cited by 91 (21 self)
 Add to MetaCart
. The verification of continuoustime Markov chains (CTMCs) against continuous stochastic logic (CSL) [3, 6], a stochastic branchingtime temporal logic, is considered. CSL facilitates among others the specification of steadystate properties and the specification of probabilistic timing properties of the form P# #p(#1 U I #2 ), for state formulas #1 and #2 , comparison operator ##, probability p, and real interval I. The main result of this paper is that model checking probabilistic timing properties can be reduced to the problem of computing transient state probabilities for CTMCs. This allows us to verify such properties by using e#cient techniques for transient analysis of CTMCs such as uniformisation. A second result is that a variant of ordinary lumping equivalence (i.e., bisimulation), a wellknown notion for aggregating CTMCs, preserves the validity of all CSLformulas. In 12th Annual Symposium on Computer Aided Verification, CAV 2000, c # SpringerVerlag 2000 Chicago,...
Model Checking Continuous Time Markov Chains
, 2000
"... This paper is an expanded and revised version of an eponymous paper presented by the authors at the ComputerAided Verification Conference held at Rutgers, NJ in 1996. Support from IBM, NSF, SRC, and The State of Texas is gratefully acknowledged ..."
Abstract

Cited by 83 (0 self)
 Add to MetaCart
This paper is an expanded and revised version of an eponymous paper presented by the authors at the ComputerAided Verification Conference held at Rutgers, NJ in 1996. Support from IBM, NSF, SRC, and The State of Texas is gratefully acknowledged
Symbolic Model Checking of Probabilistic Timed Automata Using Backwards Reachability
, 2000
"... We consider probabilistic timed automata of [13], an extension of the timed automata model of [2] with discrete probability distributions. In contrast to timed automata, which model realtime systems purely in terms of nondeterminism, our model allows to express the likelihood of the system makin ..."
Abstract

Cited by 82 (26 self)
 Add to MetaCart
We consider probabilistic timed automata of [13], an extension of the timed automata model of [2] with discrete probability distributions. In contrast to timed automata, which model realtime systems purely in terms of nondeterminism, our model allows to express the likelihood of the system making certain transitions, and is thus appropriate for modelling faulttolerance and probabilistic failures. We present a symbolic model checking algorithm for the existential fragment of the logic PTCTL of [13] based on backward reachability as in [12]. The logic allows us to specify properties such as \with probability 0.99 or greater, it is possible to correctly deliver a data packet within 5 time units", or \with probability 0.87 or greater, the system never enters an error state".