Results 1  10
of
61
PRISM: Probabilistic symbolic model checker
, 2002
"... Abstract. In this paper we describe PRISM, a tool being developed at the University of Birmingham for the analysis of probabilistic systems. PRISM supports two probabilistic models: continuoustime Markov chains and Markov decision processes. Analysis is performed through model checking such systems ..."
Abstract

Cited by 235 (14 self)
 Add to MetaCart
Abstract. In this paper we describe PRISM, a tool being developed at the University of Birmingham for the analysis of probabilistic systems. PRISM supports two probabilistic models: continuoustime Markov chains and Markov decision processes. Analysis is performed through model checking such systems against specifications written in the probabilistic temporal logics PCTL and CSL. The tool features three model checking engines: one symbolic, using BDDs (binary decision diagrams) and MTBDDs (multiterminal BDDs); one based on sparse matrices; and one which combines both symbolic and sparse matrix methods. PRISM has been successfully used to analyse probabilistic termination, performance, dependability and quality of service properties for a range of systems, including randomized distributed algorithms, polling systems, workstation cluster and wireless cell communication. 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 231 (45 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.
Probabilistic Symbolic Model Checking with PRISM: A Hybrid Approach
 International Journal on Software Tools for Technology Transfer (STTT
, 2002
"... In this paper we introduce PRISM, a probabilistic model checker, and describe the ecient symbolic techniques we have developed during its implementation. PRISM is a tool for analysing probabilistic systems. It supports three models: discretetime Markov chains, continuoustime Markov chains and ..."
Abstract

Cited by 201 (32 self)
 Add to MetaCart
In this paper we introduce PRISM, a probabilistic model checker, and describe the ecient symbolic techniques we have developed during its implementation. PRISM is a tool for analysing probabilistic systems. It supports three models: discretetime Markov chains, continuoustime Markov chains and Markov decision processes. Analysis is performed through model checking speci cations in the probabilistic temporal logics PCTL and CSL. Motivated by the success of model checkers such as SMV, which use BDDs (binary decision diagrams), we have developed an implementation of PCTL and CSL model checking based on MTBDDs (multiterminal BDDs) and BDDs. Existing work in this direction has been hindered by the generally poor performance of MTBDDbased numerical computation, which is often substantially slower than explicit methods using sparse matrices. We present a novel hybrid technique which combines aspects of symbolic and explicit approaches to overcome these performance problems. For typical examples, we achieve orders of magnitude speedup compared to MTBDDs and are able to almost match the speed of sparse matrices whilst maintaining considerable space savings.
Approximate symbolic model checking of continuoustime Markov chains (Extended Abstract)
, 1999
"... . This paper presents a symbolic model checking algorithm for continuoustime Markov chains for an extension of the continuous stochastic logic CSL of Aziz et al [1]. The considered logic contains a timebounded untiloperator and a novel operator to express steadystate probabilities. We show that t ..."
Abstract

Cited by 156 (25 self)
 Add to MetaCart
. This paper presents a symbolic model checking algorithm for continuoustime Markov chains for an extension of the continuous stochastic logic CSL of Aziz et al [1]. The considered logic contains a timebounded untiloperator and a novel 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 steady stateoperator) and a Volterra integral equation system for timebounded until. We propose a symbolic approximate method for solving the integrals using MTDDs (multiterminal decision diagrams), a generalisation of MTBDDs. These new structures are suitable for numerical integration using quadrature formulas based on equallyspaced abscissas, like trapezoidal, Simpson and Romberg integration schemes. 1 Introduction The mechanised verification of a given (usually) finitestate model against a property expressed in some temporal logic is known as model checking. For probabilistic...
Process Algebra for Performance Evaluation
, 2000
"... This paper surveys the theoretical developments in the field of stochastic process algebras, process algebras where action occurrences may be subject to a delay that is determined by a random variable. A huge class of resourcesharing systems  like largescale computers, clientserver architectur ..."
Abstract

Cited by 72 (13 self)
 Add to MetaCart
This paper surveys the theoretical developments in the field of stochastic process algebras, process algebras where action occurrences may be subject to a delay that is determined by a random variable. A huge class of resourcesharing systems  like largescale computers, clientserver architectures, networks  can accurately be described using such stochastic specification formalisms.
Better quality in synthesis through quantitative objectives
 In CoRR, abs/0904.2638
, 2009
"... Abstract. Most specification languages express only qualitative constraints. However, among two implementations that satisfy a given specification, one may be preferred to another. For example, if a specification asks that every request is followed by a response, one may prefer an implementation tha ..."
Abstract

Cited by 61 (18 self)
 Add to MetaCart
(Show Context)
Abstract. Most specification languages express only qualitative constraints. However, among two implementations that satisfy a given specification, one may be preferred to another. For example, if a specification asks that every request is followed by a response, one may prefer an implementation that generates responses quickly but does not generate unnecessary responses. We use quantitative properties to measure the “goodness ” of an implementation. Using games with corresponding quantitative objectives, we can synthesize “optimal ” implementations, which are preferred among the set of possible implementations that satisfy a given specification. In particular, we show how automata with lexicographic meanpayoff conditions can be used to express many interesting quantitative properties for reactive systems. In this framework, the synthesis of optimal implementations requires the solution of lexicographic meanpayoff games (for safety requirements), and the solution of games with both lexicographic meanpayoff and parity objectives (for liveness requirements). We present algorithms for solving both kinds of novel graph games. 1
Verifying quantitative properties of continuous probabilistic timed automata
, 2000
"... Abstract. We consider the problem of automatically verifying realtime systems with continuously distributed random delays. We generalise probabilistic timed automata introduced in [19], an extension of the timed automata model of [4], with clock resets made according to continuous probability distri ..."
Abstract

Cited by 46 (10 self)
 Add to MetaCart
Abstract. We consider the problem of automatically verifying realtime systems with continuously distributed random delays. We generalise probabilistic timed automata introduced in [19], an extension of the timed automata model of [4], with clock resets made according to continuous probability distributions. Thus, our model exhibits nondeterministic and probabilistic choice, the latter being made according to both discrete and continuous probability distributions. To facilitate algorithmic verification, we modify the standard region graph construction by subdividing the unit intervals in order to approximate the probability to within an interval. We then develop a model checking method for continuous probabilistic timed automata, taking as our specification language Probabilistic Timed Computation Tree Logic (PTCTL). Our method improves on the previously known techniques in that it allows the verification of quantitative probability bounds, as opposed to qualitative properties which can only refer to bounds of probability 0 or 1. 1
Probabilistic Model Checking of Deadline Properties in the IEEE1394 FireWire Root Contention Protocol
 in the IEEE 1394 FireWire root contention protocol. Special Issue of Formal Aspects of Computing
"... The increasing dependence of businesses on distributed architectures and computer networking places heavy demands on the speed and reliability of data exchange, leading to the emergence of sophisticated protocols which involve both realtime and randomization, for example FireWire IEEE1394. Automati ..."
Abstract

Cited by 44 (26 self)
 Add to MetaCart
The increasing dependence of businesses on distributed architectures and computer networking places heavy demands on the speed and reliability of data exchange, leading to the emergence of sophisticated protocols which involve both realtime and randomization, for example FireWire IEEE1394. Automatic verification techniques such as model checking have been adapted to this class of probabilistic, timed systems [1, 9, 3, 14]. This abstract considers an application of such techniques to the IEEE1394 (FireWire) root contention protocol, in which the interplay between timed and probabilistic aspects is used to break the symmetry which may arise during the leader election process. Here, the properties of interest concern the election of a leader within a certain deadline, with a certain probability or greater. Our specification formalism is that of probabilistic timed automata [14], a variant of timed automa...
Quantitative analysis of probabilistic pushdown automata: . . .
, 2005
"... Probabilistic pushdown automata (pPDA) have been identified as a natural model for probabilistic programs with rcursive procedure calls. Previous works considered the decidability and complexity of the modelchecking problem for pPDA and various probabilistic temporal logics. In this paper we concen ..."
Abstract

Cited by 40 (15 self)
 Add to MetaCart
Probabilistic pushdown automata (pPDA) have been identified as a natural model for probabilistic programs with rcursive procedure calls. Previous works considered the decidability and complexity of the modelchecking problem for pPDA and various probabilistic temporal logics. In this paper we concentrate on computing the expected values and variances of various random variables defined over runs of a given probabilistic pushdown automaton. In particular, we show how to compute the expected accumulated reward and the expected gain for certain classes of reward functions. Using these results, we show how to analyze various quantitative properties of pPDA that are not expressible in conventional probabilistic temporal logics.
Stochastic Transition Systems
, 1998
"... . Traditional methods for the analysis of system performance and reliability generally assume a precise knowledge of the system and its workload. Here, we present methods that are suited for the analysis of systems that contain partly unknown or unspecified components, such as systems in their early ..."
Abstract

Cited by 39 (4 self)
 Add to MetaCart
(Show Context)
. Traditional methods for the analysis of system performance and reliability generally assume a precise knowledge of the system and its workload. Here, we present methods that are suited for the analysis of systems that contain partly unknown or unspecified components, such as systems in their early design stages. We introduce stochastic transition systems, a highlevel formalism for the modeling of timed probabilistic systems. Stochastic transition systems extend current modeling capabilities by enabling the representation of transitions having unknown delay distributions, alongside transitions with zero or exponentiallydistributed delay. We show how these various types of transitions can be uniformly represented in terms of nondeterminism, probability, fairness and time, yielding efficient algorithms for system analysis. Finally, we present methods for the specification and verification of longrun average properties of STSs. These properties include many relevant performance and re...