88,295 research outputs found

    Symmetry reduction and heuristic search for error detection in model checking

    Get PDF
    The state explosion problem is the main limitation of model checking. Symmetries in the system being verified can be exploited in order to avoid this problem by defining an equivalence (symmetry) relation on the states of the system, which induces a semantically equivalent quotient system of smaller size. On the other hand, heuristic search algorithms can be applied to improve the bug finding capabilities of model checking. Such algorithms use heuristic functions to guide the exploration. Bestfirst is used for accelerating the search, while A* guarantees optimal error trails if combined with admissible estimates. We analyze some aspects of combining both approaches, concentrating on the problem of finding the optimal path to the equivalence class of a given error state. Experimental results evaluate our approach

    Matching Subsequences in Trees

    Full text link
    Given two rooted, labeled trees PP and TT the tree path subsequence problem is to determine which paths in PP are subsequences of which paths in TT. Here a path begins at the root and ends at a leaf. In this paper we propose this problem as a useful query primitive for XML data, and provide new algorithms improving the previously best known time and space bounds.Comment: Minor correction of typos, et

    Deterministic and Probabilistic Binary Search in Graphs

    Full text link
    We consider the following natural generalization of Binary Search: in a given undirected, positively weighted graph, one vertex is a target. The algorithm's task is to identify the target by adaptively querying vertices. In response to querying a node qq, the algorithm learns either that qq is the target, or is given an edge out of qq that lies on a shortest path from qq to the target. We study this problem in a general noisy model in which each query independently receives a correct answer with probability p>12p > \frac{1}{2} (a known constant), and an (adversarial) incorrect one with probability 1p1-p. Our main positive result is that when p=1p = 1 (i.e., all answers are correct), log2n\log_2 n queries are always sufficient. For general pp, we give an (almost information-theoretically optimal) algorithm that uses, in expectation, no more than (1δ)log2n1H(p)+o(logn)+O(log2(1/δ))(1 - \delta)\frac{\log_2 n}{1 - H(p)} + o(\log n) + O(\log^2 (1/\delta)) queries, and identifies the target correctly with probability at leas 1δ1-\delta. Here, H(p)=(plogp+(1p)log(1p))H(p) = -(p \log p + (1-p) \log(1-p)) denotes the entropy. The first bound is achieved by the algorithm that iteratively queries a 1-median of the nodes not ruled out yet; the second bound by careful repeated invocations of a multiplicative weights algorithm. Even for p=1p = 1, we show several hardness results for the problem of determining whether a target can be found using KK queries. Our upper bound of log2n\log_2 n implies a quasipolynomial-time algorithm for undirected connected graphs; we show that this is best-possible under the Strong Exponential Time Hypothesis (SETH). Furthermore, for directed graphs, or for undirected graphs with non-uniform node querying costs, the problem is PSPACE-complete. For a semi-adaptive version, in which one may query rr nodes each in kk rounds, we show membership in Σ2k1\Sigma_{2k-1} in the polynomial hierarchy, and hardness for Σ2k5\Sigma_{2k-5}

    Hierarchical path-finding for Navigation Meshes (HNA*)

    Get PDF
    Path-finding can become an important bottleneck as both the size of the virtual environments and the number of agents navigating them increase. It is important to develop techniques that can be efficiently applied to any environment independently of its abstract representation. In this paper we present a hierarchical NavMesh representation to speed up path-finding. Hierarchical path-finding (HPA*) has been successfully applied to regular grids, but there is a need to extend the benefits of this method to polygonal navigation meshes. As opposed to regular grids, navigation meshes offer representations with higher accuracy regarding the underlying geometry, while containing a smaller number of cells. Therefore, we present a bottom-up method to create a hierarchical representation based on a multilevel k-way partitioning algorithm (MLkP), annotated with sub-paths that can be accessed online by our Hierarchical NavMesh Path-finding algorithm (HNA*). The algorithm benefits from searching in graphs with a much smaller number of cells, thus performing up to 7.7 times faster than traditional A¿ over the initial NavMesh. We present results of HNA* over a variety of scenarios and discuss the benefits of the algorithm together with areas for improvement.Peer ReviewedPostprint (author's final draft
    corecore