Saturation-Based Symbolic Reachability Analysis Using Conjunctive and Disjunctive Partitioning

Ciardo, Gianfranco; Yu, Andy Jinqing

doi:10.1007/11560548_13

Cited by 34 publications

(36 citation statements)

References 26 publications

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“…When this happens, the Kronecker encoding of event e has R (k) e = I n k , while the quasi-reduced or the fully-reduced forms alone cannot take advantage of these common patterns. To exploit these patterns, a combination of the fully-reduced form, for unprimed level X k , and a new identity-reduced form (Ciardo & Yu, 2005) for primed level X k , is needed. This allows us to encode R e in an EV * MDD which has nodes only at (unprimed and primed) levels corresponding to state variables in S e .…”

Section: Adopting Ideas From Kronecker Encodings: Identity Patternsmentioning

confidence: 99%

“…This idea was first introduced for logic analysis (Ciardo & Yu, 2005) but it is also related to Equation 76, which expresses R as a sum of products. This is particularly appropriate for globally-asynchronous locally-synchronous systems, where not only each state change is due to an (asynchronous) event e ∈ E, but the occurrence of e de-pends on and (synchronously) changes only a few state variables.…”

Section: Beyond Kronecker: Disjunctive-then-conjunctive Partition Encmentioning

confidence: 99%

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Tutorial on Structured Continuous-Time Markov Processes

Shelton¹,

Ciardo²

2014

jair

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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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Section: Adopting Ideas From Kronecker Encodings: Identity Patternsmentioning

confidence: 99%

Section: Beyond Kronecker: Disjunctive-then-conjunctive Partition Encmentioning

confidence: 99%

Tutorial on Structured Continuous-Time Markov Processes

Shelton¹,

Ciardo²

2014

jair

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“…In several studies, Saturation has been shown superior to BFS-style iterations when symbolically computing least fixpoints for asynchronous models [8,9,10]. The challenge in adapting Saturation to bounded model checking lies in the need to bound the symbolic traversal in the nested fixpoint computations.…”

Section: Bounded Reachability Checking Using Decision Diagramsmentioning

confidence: 99%

“…A version of Saturation using ADDs can be obtained by extending the MDD-based Saturation algorithm of [10], so that it uses an ADD to store the states and their distances, instead of a simple MDD. The ADD has B + 1 terminal nodes corresponding to the distances of interest, {0, 1, .…”

Section: Bounded Reachability Checking Using Decision Diagramsmentioning

confidence: 99%

“…The Saturation algorithm for computing the reachable state spaces of asynchronous systems was originally proposed in [7] for models in Kronecker-product form; it has since been extended to general models [10] and applied to shortest path computations and CTL model-checking [9]. Saturation has been shown to reduce memory and runtime requirements by several orders of magnitude with respect to BFS-based algorithms, when applied to asynchronous systems.…”

Section: Introductionmentioning

confidence: 99%

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Bounded Reachability Checking of Asynchronous Systems Using Decision Diagrams

Ciardo

Lüttgen

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. Bounded reachability or model checking is widely believed to work poorly when using decision diagrams instead of SAT procedures. Recent research suggests this to be untrue with regards to synchronous systems, particularly digital circuits. This paper shows that the belief is also a myth for asynchronous systems, such as models specified by Petri nets. We propose Bounded Saturation, a new algorithm to compute bounded state spaces using Multi-way Decision Diagrams (MDDs). This is based on the established Saturation algorithm which benefits from a non-standard search strategy that is very different from breadth-first search. To bound Saturation, we employ Edge-Valued MDDs and rework its search strategy. Experimental results show that our algorithm often, but not always, compares favorably against two SAT-based approaches advocated in the literature for deadlock checking in Petri nets.

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Decision diagrams for the approximate analysis of Markov models

Ciardo

2007

Proc Appl Math and Mech

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Decision diagrams of various types can be used to encode the exact state space and transition rate matrix of large Markov models. However, the exact solution of such models still requires to store at least one real vector with one entry per reachable state, a formidable limitation to the practical use of these encodings. Thus, we discuss automatic techniques for the approximate computation of performance measures when the Markov model can be compactly encoded but not exactly solved.

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Saturation-Based Symbolic Reachability Analysis Using Conjunctive and Disjunctive Partitioning

Cited by 34 publications

References 26 publications

Tutorial on Structured Continuous-Time Markov Processes

Tutorial on Structured Continuous-Time Markov Processes

Bounded Reachability Checking of Asynchronous Systems Using Decision Diagrams

Decision diagrams for the approximate analysis of Markov models

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