346 research outputs found

    An extensive English language bibliography on graph theory and its applications

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    Bibliography on graph theory and its application

    Generating a checking sequence with a minimum number of reset transitions

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    Given a finite state machine M, a checking sequence is an input sequence that is guaranteed to lead to a failure if the implementation under test is faulty and has no more states than M. There has been much interest in the automated generation of a short checking sequence from a finite state machine. However, such sequences can contain reset transitions whose use can adversely affect both the cost of applying the checking sequence and the effectiveness of the checking sequence. Thus, we sometimes want a checking sequence with a minimum number of reset transitions rather than a shortest checking sequence. This paper describes a new algorithm for generating a checking sequence, based on a distinguishing sequence, that minimises the number of reset transitions used.This work was supported in part by Leverhulme Trust grant number F/00275/D, Testing State Based Systems, Natural Sciences and Engineering Research Council (NSERC) of Canada grant number RGPIN 976, and Engineering and Physical Sciences Research Council grant number GR/R43150, Formal Methods and Testing (FORTEST)

    Incremental Dead State Detection in Logarithmic Time

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    Identifying live and dead states in an abstract transition system is a recurring problem in formal verification; for example, it arises in our recent work on efficiently deciding regex constraints in SMT. However, state-of-the-art graph algorithms for maintaining reachability information incrementally (that is, as states are visited and before the entire state space is explored) assume that new edges can be added from any state at any time, whereas in many applications, outgoing edges are added from each state as it is explored. To formalize the latter situation, we propose guided incremental digraphs (GIDs), incremental graphs which support labeling closed states (states which will not receive further outgoing edges). Our main result is that dead state detection in GIDs is solvable in O(logā”m)O(\log m) amortized time per edge for mm edges, improving upon O(m)O(\sqrt{m}) per edge due to Bender, Fineman, Gilbert, and Tarjan (BFGT) for general incremental directed graphs. We introduce two algorithms for GIDs: one establishing the logarithmic time bound, and a second algorithm to explore a lazy heuristics-based approach. To enable an apples-to-apples experimental comparison, we implemented both algorithms, two simpler baselines, and the state-of-the-art BFGT baseline using a common directed graph interface in Rust. Our evaluation shows 110110-530530x speedups over BFGT for the largest input graphs over a range of graph classes, random graphs, and graphs arising from regex benchmarks.Comment: 22 pages + reference

    Testing from a finite state machine: Extending invertibility to sequences

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    When testing a system modelled as a finite state machine it is desirable to minimize the effort required. It has been demonstrated that it is possible to utilize test sequence overlap in order to reduce the test effort and this overlap has been represented by using invertible transitions. In this paper invertibility will be extended to sequences in order to reduce the test effort further and encapsulate a more general type of test sequence overlap. It will also be shown that certain properties of invertible sequences can be used in the generation of state identification sequences

    Global approaches to solving recognition problems of noisy images, 1989

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    An important problem in the area of pattern recognition is automatic detection of certain pre-assigned elements of an image distorted by noise. In this research, a global ap proach will be used. One such approach is to use an optimal smoothing algorithm which depends on efficient dynamic programming computational techniques. The basic purpose of this research is to make this dynamic programming process efficient in terms of storage requirement and computational effort. Our goal, using the objective function, is to find an optimal order of optimization and then design an effi cient computational technique. Two global techniques will be presented in this paper. Included is a graph-searching technique and the above men tioned technique using dynamic programming. Emphasis will be on the development of an algorithm using dynamic program ming. I wish to express ray deepest appreciation and sincere gratitude to those who have contributed their time, energy, and support to make this study possible. Thanks are especially due Dr. Warsi, Nazir A. , my thesis advisor. His instruction, suggestions, and patience were essential to the completion of this thesi s. Further thanks are also due Nasa Langley for providing financial, technical, and general support to help make this study possible. Special thanks are offered to Mr. Micheal Goode, Technical Monitor, for his technical support and to Dr. Samuel E. Massenberg, University Affairs Officer, for his general support

    SDP-based bounds for the Quadratic Cycle Cover Problem via cutting plane augmented Lagrangian methods and reinforcement learning

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    We study the Quadratic Cycle Cover Problem (QCCP), which aims to find a node-disjoint cycle cover in a directed graph with minimum interaction cost between successive arcs. We derive several semidefinite programming (SDP) relaxations and use facial reduction to make these strictly feasible. We investigate a nontrivial relationship between the transformation matrix used in the reduction and the structure of the graph, which is exploited in an efficient algorithm that constructs this matrix for any instance of the problem. To solve our relaxations, we propose an algorithm that incorporates an augmented Lagrangian method into a cutting plane framework by utilizing Dykstra's projection algorithm. Our algorithm is suitable for solving SDP relaxations with a large number of cutting planes. Computational results show that our SDP bounds and our efficient cutting plane algorithm outperform other QCCP bounding approaches from the literature. Finally, we provide several SDP-based upper bounding techniques, among which a sequential Q-learning method that exploits a solution of our SDP relaxation within a reinforcement learning environment

    Parallel local search

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