543 research outputs found
Lex-Partitioning: A New Option for BDD Search
For the exploration of large state spaces, symbolic search using binary
decision diagrams (BDDs) can save huge amounts of memory and computation time.
State sets are represented and modified by accessing and manipulating their
characteristic functions. BDD partitioning is used to compute the image as the
disjunction of smaller subimages.
In this paper, we propose a novel BDD partitioning option. The partitioning
is lexicographical in the binary representation of the states contained in the
set that is represented by a BDD and uniform with respect to the number of
states represented. The motivation of controlling the state set sizes in the
partitioning is to eventually bridge the gap between explicit and symbolic
search.
Let n be the size of the binary state vector. We propose an O(n) ranking and
unranking scheme that supports negated edges and operates on top of precomputed
satcount values. For the uniform split of a BDD, we then use unranking to
provide paths along which we partition the BDDs. In a shared BDD representation
the efforts are O(n). The algorithms are fully integrated in the CUDD library
and evaluated in strongly solving general game playing benchmarks.Comment: In Proceedings GRAPHITE 2012, arXiv:1210.611
Efficient parallel binary decision diagram construction using Cilk
Thesis (S.B. and M.Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2000.Includes bibliographical references (leaves 44-45).by David B. Berman.S.B.and M.Eng
Symbolic analysis of bounded Petri nets
This paper presents a symbolic approach for the analysis of bounded Petri nets. The structure and behavior of the Petri net is symbolically modeled by using Boolean functions, thus reducing reasoning about Petri nets to Boolean calculation. The set of reachable markings is calculated by symbolically firing the transitions in the Petri net. Highly concurrent systems suffer from the state explosion problem produced by an exponential increase of the number of reachable states. This state explosion is handled by using Binary Decision Diagrams (BDDs) which are capable of representing large sets of markings with small data structures. Petri nets have the ability to model a large variety of systems and the flexibility to describe causality, concurrency, and conditional relations. The manipulation of vast state spaces generated by Petri nets enables the efficient analysis of a wide range of problems, e.g., deadlock freeness, liveness, and concurrency. A number of examples are presented in order to show how large reachability sets can be generated, represented, and analyzed with moderate BDD sizes. By using this symbolic framework, properties requiring an exhaustive analysis of the reachability graph can be efficiently verified.Peer ReviewedPostprint (published version
Applying Formal Methods to Networking: Theory, Techniques and Applications
Despite its great importance, modern network infrastructure is remarkable for
the lack of rigor in its engineering. The Internet which began as a research
experiment was never designed to handle the users and applications it hosts
today. The lack of formalization of the Internet architecture meant limited
abstractions and modularity, especially for the control and management planes,
thus requiring for every new need a new protocol built from scratch. This led
to an unwieldy ossified Internet architecture resistant to any attempts at
formal verification, and an Internet culture where expediency and pragmatism
are favored over formal correctness. Fortunately, recent work in the space of
clean slate Internet design---especially, the software defined networking (SDN)
paradigm---offers the Internet community another chance to develop the right
kind of architecture and abstractions. This has also led to a great resurgence
in interest of applying formal methods to specification, verification, and
synthesis of networking protocols and applications. In this paper, we present a
self-contained tutorial of the formidable amount of work that has been done in
formal methods, and present a survey of its applications to networking.Comment: 30 pages, submitted to IEEE Communications Surveys and Tutorial
Multi-core Decision Diagrams
Decision diagrams are fundamental data structures that revolutionized fields such as model checking, automated reasoning and decision processes. As performance gains in the current era mostly come from parallel processing, an ongoing challenge is to develop data structures and algorithms for modern multicore architectures. This chapter describes the parallelization of decision diagram operations as implemented in the parallel decision diagram package Sylvan, which allows sequential algorithms that use decision diagrams to exploit the power of multi-core machines
A contribution to the evaluation and optimization of networks reliability
LâĂ©valuation de la fiabilitĂ© des rĂ©seaux est un problĂšme combinatoire trĂšs complexe qui nĂ©cessite des moyens de calcul trĂšs puissants. Plusieurs mĂ©thodes ont Ă©tĂ© proposĂ©es dans la littĂ©rature pour apporter des solutions. Certaines ont Ă©tĂ© programmĂ©es dont notamment les mĂ©thodes dâĂ©numĂ©ration des ensembles minimaux et la factorisation, et dâautres sont restĂ©es Ă lâĂ©tat de simples thĂ©ories. Cette thĂšse traite le cas de lâĂ©valuation et lâoptimisation de la fiabilitĂ© des rĂ©seaux. Plusieurs problĂšmes ont Ă©tĂ© abordĂ©s dont notamment la mise au point dâune mĂ©thodologie pour la modĂ©lisation des rĂ©seaux en vue de lâĂ©valuation de leur fiabilitĂ©s. Cette mĂ©thodologie a Ă©tĂ© validĂ©e dans le cadre dâun rĂ©seau de radio communication Ă©tendu implantĂ© rĂ©cemment pour couvrir les besoins de toute la province quĂ©bĂ©coise. Plusieurs algorithmes ont aussi Ă©tĂ© Ă©tablis pour gĂ©nĂ©rer les chemins et les coupes minimales pour un rĂ©seau donnĂ©. La gĂ©nĂ©ration des chemins et des coupes constitue une contribution importante dans le processus dâĂ©valuation et dâoptimisation de la fiabilitĂ©. Ces algorithmes ont permis de traiter de maniĂšre rapide et efficace plusieurs rĂ©seaux tests ainsi que le rĂ©seau de radio communication provincial. Ils ont Ă©tĂ© par la suite exploitĂ©s pour Ă©valuer la fiabilitĂ© grĂące Ă une mĂ©thode basĂ©e sur les diagrammes de dĂ©cision binaire. Plusieurs contributions thĂ©oriques ont aussi permis de mettre en place une solution exacte de la fiabilitĂ© des rĂ©seaux stochastiques imparfaits dans le cadre des mĂ©thodes de factorisation. A partir de cette recherche plusieurs outils ont Ă©tĂ© programmĂ©s pour Ă©valuer et optimiser la fiabilitĂ© des rĂ©seaux. Les rĂ©sultats obtenus montrent clairement un gain significatif en temps dâexĂ©cution et en espace de mĂ©moire utilisĂ© par rapport Ă beaucoup dâautres implĂ©mentations. Mots-clĂ©s: FiabilitĂ©, rĂ©seaux, optimisation, diagrammes de dĂ©cision binaire, ensembles des chemins et coupes minimales, algorithmes, indicateur de Birnbaum, systĂšmes de radio tĂ©lĂ©communication, programmes.Efficient computation of systems reliability is required in many sensitive networks. Despite the increased efficiency of computers and the proliferation of algorithms, the problem of finding good and quickly solutions in the case of large systems remains open. Recently, efficient computation techniques have been recognized as significant advances to solve the problem during a reasonable period of time. However, they are applicable to a special category of networks and more efforts still necessary to generalize a unified method giving exact solution. Assessing the reliability of networks is a very complex combinatorial problem which requires powerful computing resources. Several methods have been proposed in the literature. Some have been implemented including minimal sets enumeration and factoring methods, and others remained as simple theories. This thesis treats the case of networks reliability evaluation and optimization. Several issues were discussed including the development of a methodology for modeling networks and evaluating their reliabilities. This methodology was validated as part of a radio communication network project. In this work, some algorithms have been developed to generate minimal paths and cuts for a given network. The generation of paths and cuts is an important contribution in the process of networks reliability and optimization. These algorithms have been subsequently used to assess reliability by a method based on binary decision diagrams. Several theoretical contributions have been proposed and helped to establish an exact solution of the stochastic networks reliability in which edges and nodes are subject to failure using factoring decomposition theorem. From this research activity, several tools have been implemented and results clearly show a significant gain in time execution and memory space used by comparison to many other implementations. Key-words: Reliability, Networks, optimization, binary decision diagrams, minimal paths set and cuts set, algorithms, Birnbaum performance index, Networks, radio-telecommunication systems, programs
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