Algorithms and Data Structures in VLSI Design

Meinel, Christoph; Theobald, Thorsten

doi:10.1007/978-3-642-58940-9

Cited by 183 publications

(139 citation statements)

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“…Such languages allow for several equivalent representations of a formula but with an exponential gap between their sizes. Finding a minimal representation in any of these languages is NP-hard [37]. D-trees generalize ws-trees [35] with independent-and decompositions, which are crucial for the treatment of tractable queries because they capture 1OF formulas [38].…”

Section: Related Workmentioning

confidence: 99%

Anytime approximation in probabilistic databases

2013

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This article describes an approximation algorithm for computing the probability of propositional formulas over discrete random variables. It incrementally refines lower and upper bounds on the probability of the formulas until the desired absolute or relative error guarantee is reached. This algorithm is used by the SPROUT query engine to approximate the probabilities of results to relational algebra queries on expressive probabilistic databases.

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Section: Related Workmentioning

confidence: 99%

Anytime approximation in probabilistic databases

2013

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“…To encode the set sharing domain using ZBDDs, we define the primitive elements to be the variables in the program being analyzed. ZBDDs have been demostrated to perform better [15,14] than standard BDDs when encoding sets of combinations that are sparse in the sense that a) the set contains just a small fraction of all the possible combinations, and b) each combination contains just a few literals. A ZBDD is a rooted directed acyclic graph (DAG) of non-terminal and terminal nodes.…”

Section: Semantics As Zbdd Operationsmentioning

confidence: 99%

Efficient Set Sharing Using ZBDDs

Méndez-Lojo

Lhoták

Hermenegildo

2008

Languages and Compilers for Parallel Computing

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Abstract. Set sharing is an abstract domain in which each concrete object is represented by the set of local variables from which it might be reachable. It is a useful abstraction to detect parallelism opportunities, since it contains definite information about which variables do not share in memory, i.e., about when the memory regions reachable from those variables are disjoint. Set sharing is a more precise alternative to pair sharing, in which each domain element is a set of all pairs of local variables from which a common object may be reachable. However, the exponential complexity of some set sharing operations has limited its wider application. This work introduces an efficient implementation of the set sharing domain using Zero-supressed Binary Decision Diagrams (ZBDDs). Because ZBDDs were designed to represent sets of combinations (i.e., sets of sets), they naturally represent elements of the set sharing domain. We show how to synthesize the operations needed in the set sharing transfer functions from basic ZBDD operations. For some of the operations, we devise custom ZBDD algorithms that perform better in practice. We also compare our implementation of the abstract domain with an efficient, compact, bitset-based alternative, and show that the ZBDD version scales better in terms of both memory usage and running time.

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“…(Details can be found, e.g., in [16,23].) It is well-known that the size of an (MT)BDD for a discrete function can crucially depend on the underlying variable ordering and that the problem of finding the optimal variable ordering is NPcomplete.…”

Section: Optimizations Of the Mtbdd Representationmentioning

confidence: 99%

Generating Compact MTBDD-Representations from Probmela Specifications

Ciesinski

Baier

Größer

et al.

Model Checking Software

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Abstract. The purpose of the paper is to provide an automatic transformation of parallel programs of an imperative probabilistic guarded command language (called Probmela) into probabilistic reactive module specifications. The latter serve as basis for the input language of the symbolic MTBDD-based probabilistic model checker PRISM, while Probmela is the modeling language of the model checker LiQuor which relies on an enumerative approach and supports partial order reduction and other reduction techniques. By providing the link between the model checkers PRISM and LiQuor, our translation supports comparative studies of different verification paradigms and can serve to use the (more comfortable) guarded command language for a MTBDD-based quantitative analysis. The challenges were (1) to ensure that the translation preserves the Markov decision process semantics, (2) the efficiency of the translation and (3) the compactness of the symbolic BDD-representation of the generated PRISM-language specifications.

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Algorithms and Data Structures in VLSI Design

Cited by 183 publications

References 0 publications

Anytime approximation in probabilistic databases

Anytime approximation in probabilistic databases

Efficient Set Sharing Using ZBDDs

Generating Compact MTBDD-Representations from Probmela Specifications

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