Logical and Stochastic Modeling with Smart

Ciardo, Gianfranco; Jones, Ryan M.; Miner, Andrew S.; Siminiceanu, Radu

doi:10.1007/978-3-540-45232-4_6

Cited by 56 publications

(56 citation statements)

References 21 publications

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“…Related topic include: probabilistic generalisations of bisimulation and simulation relations for DTMCs [49,57] and for CTMCs [17,11]; and approximate methods for stochastic model checking based on discrete event simulation [33,63]. Stochastic model checkers SMART [19], E T MC 2 [34] and MRMC [39] have similarities with the PRISM model checker described here. Finally, we mention a challenging direction of research is into the verification of models which allow more general probability distributions.…”

Section: Discussionmentioning

confidence: 99%

Stochastic Model Checking

Kwiatkowska

Norman

Parker

Lecture Notes in Computer Science

460

353

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Abstract. This tutorial presents an overview of model checking for both discrete and continuous-time 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 real-world case studies: a probabilistic security protocol, dynamic power management and a biological pathway.

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Section: Discussionmentioning

confidence: 99%

Stochastic Model Checking

Kwiatkowska

Norman

Parker

Lecture Notes in Computer Science

460

353

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“…In SR-Sym, each transition rate is set to 1.0, while in SR-Asym, different rates were chosen for the transitions. -The KanBan SPN models from [11] describe the kanban manufacturing system with various resource pool sizes. -Members of the Cloud family are SPN performability models of a cloud architecture [17].…”

Section: Discussionmentioning

confidence: 99%

“…Recall that x (j) ∼ (j) y (j) is defined as env x (j) = env y (j) in Eq. (11). Let X and Y be the environments of x (j) and y (j) , respectively, so that x (j) ∼ (j) y (j) holds if and only if X = Y .…”

Section: Propositionmentioning

confidence: 99%

Efficient Decomposition Algorithm for Stationary Analysis of Complex Stochastic Petri Net Models

Marussy

Klenik

Molnár³

et al. 2016

Application and Theory of Petri Nets and Concurrency

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Abstract. Stochastic Petri nets are widely used for the modeling and analysis of non-functional properties of critical systems. The state space explosion problem often inhibits the numerical analysis of such models. Symbolic techniques exist to explore the discrete behavior of even complex models, while block Kronecker decomposition provides memoryefficient representation of the stochastic behavior. However, the combination of these techniques into a stochastic analysis approach is not straightforward. In this paper we integrate saturation-based symbolic techniques and decomposition-based stochastic analysis methods. Saturation-based exploration is used to build the state space representation and a new algorithm is introduced to efficiently build block Kronecker matrix representation to be used by the stochastic analysis algorithms. Measurements confirm that the presented combination of the two representations can expand the limits of previous approaches.

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“…Decision diagrams have long been used in computer science to compactly encode functions over discrete domains. Here we show how they have been used in CTMPs and how they can be seen as an alternative to Kronecker algebra encodings, in the case of the MTBDDs used in PRISM (Kwiatkowska, Norman, & Parker, 2011), or even as an extension of Kronecker algebra encodings, in the case of the Matrix Diagrams used in Möbius (Deavours, Clark, Courtney, Daly, Derisavi, Doyle, Sanders, & Webster, 2002) or the EV * MDDs used in SMART (Ciardo, Jones, Miner, & Siminiceanu, 2006).…”

Section: Decision Diagram Representationsmentioning

confidence: 99%

Tutorial on Structured Continuous-Time Markov Processes

Shelton¹,

Ciardo²

2014

jair

Self Cite

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A continuous-time Markov process (CTMP) is a collection of variables indexed by a continuous quantity, time. It obeys the Markov property that the distribution over a future variable is independent of past variables given the state at the present time. We introduce continuous-time Markov process representations and algorithms for filtering, smoothing, expected sufficient statistics calculations, and model estimation, assuming no prior knowledge of continuous-time processes but some basic knowledge of probability and statistics. We begin by describing "flat" or unstructured Markov processes and then move to structured Markov processes (those arising from state spaces consisting of assignments to variables) including Kronecker, decision-diagram, and continuous-time Bayesian network representations. We provide the first connection between decision-diagrams and continuoustime Bayesian networks. Tutorial GoalsThis tutorial is intended for readers interested in learning about continuous-time Markov processes, and in particular compact or structured representations of them. It is assumed that the reader is familiar with general probability and statistics and has some knowledge of discrete-time Markov chains and perhaps hidden Markov model algorithms.While this tutorial deals only with Markovian systems, we do not require that all variables be observed. Thus, hidden variables can be used to model long-range interactions among observations. In these models, at any given instant the assignment to all state variables is sufficient to describe the future evolution of the system. The variables themselves real-valued (continuous) times. We consider evidence or observations that can be regularly spaced, irregularly spaced, or continuous over intervals. These evidence patterns can change by model variable and time.We deal exclusively with discrete-state continuous-time systems. Real-valued variables are important in many situations, but to keep the scope manageable, we will not treat them here. We refer to the work of Särkkä (2006) for a machine-learning-oriented treatment of filtering and smoothing in such models. The literature on parameter estimation is more scattered. We will further constrain our discussion to systems with finite states, although many of the concepts can be extended to countably infinite state systems.We will be concerned with two main problems: inference and learning (parameter estimation). These were chosen as those most familiar to and applicable for researchers in artificial intelligence. At points we will also discuss the computation of steady-state properties, especially for model for which most research concentrates on this computation.

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Logical and Stochastic Modeling with Smart

Cited by 56 publications

References 21 publications

Stochastic Model Checking

Stochastic Model Checking

Efficient Decomposition Algorithm for Stationary Analysis of Complex Stochastic Petri Net Models

Tutorial on Structured Continuous-Time Markov Processes

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