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  • 1.
    Abdulla, Parosh
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Datorteknik.
    Aronis, Stavros
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Datalogi.
    Jonsson, Bengt
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Datalogi.
    Sagonas, Konstantinos
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Datalogi.
    Source Sets: A Foundation for Optimal Dynamic Partial Order Reduction2017Inngår i: Journal of the ACM, ISSN 0004-5411, E-ISSN 1557-735X, Vol. 64, nr 4, artikkel-id 25Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Stateless model checking is a powerful method for program verification that, however, suffers from an exponential growth in the number of explored executions. A successful technique for reducing this number, while still maintaining complete coverage, is Dynamic Partial Order Reduction (DPOR), an algorithm originally introduced by Flanagan and Godefroid in 2005 and since then not only used as a point of reference but also extended by various researchers. In this article, we present a new DPOR algorithm, which is the first to be provably optimal in that it always explores the minimal number of executions. It is based on a novel class of sets, called source sets, that replace the role of persistent sets in previous algorithms. We begin by showing how to modify the original DPOR algorithm to work with source sets, resulting in an efficient and simple-to-implement algorithm, called source-DPOR. Subsequently, we enhance this algorithm with a novel mechanism, called wakeup trees, that allows the resulting algorithm, called optimal-DPOR, to achieve optimality. Both algorithms are then extended to computational models where processes may disable each other, for example, via locks. Finally, we discuss tradeoffs of the source-and optimal-DPOR algorithm and present programs that illustrate significant time and space performance differences between them. We have implemented both algorithms in a publicly available stateless model checking tool for Erlang programs, while the source-DPOR algorithm is at the core of a publicly available stateless model checking tool for C/pthread programs running on machines with relaxed memory models. Experiments show that source sets significantly increase the performance of stateless model checking compared to using the original DPOR algorithm and that wakeup trees incur only a small overhead in both time and space in practice.

  • 2.
    Andersson, Arne
    et al.
    Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Datalogi.
    Thorup, Mikkel
    Dynamic Ordered Sets with Exponential Search Trees2007Inngår i: Journal of the ACM, ISSN 0004-5411, E-ISSN 1557-735X, Vol. 54, nr 3, s. 1236460-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We introduce exponential search trees as a novel technique for converting static polynomial space search structures for ordered sets into fully-dynamic linear space data structures. This leads to an optimal bound of O(log n/log log n) for searching and updating a dynamic set X of n integer keys in linear space. Searching X for an integer y means finding the maximum key in X which is smaller than or equal to y. This problem is equivalent to the standard text book problem of maintaining an ordered set. The best previous deterministic linear space bound was O(log n/log log n) due to Fredman and Willard from STOC 1990. No better deterministic search bound was known using polynomial space. We also get the following worst-case linear space trade-offs between the number n, the word length W, and the maximal key U < 2W: O(min log log n + log n/logW, log log n log log U/log log log U). These trade-offs are, however, not likely to be optimal. Our results are generalized to finger searching and string searching, providing optimal results for both in terms of n.

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