3,350 research outputs found

    Solving satisfiability problems by fluctuations: The dynamics of stochastic local search algorithms

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    Stochastic local search algorithms are frequently used to numerically solve hard combinatorial optimization or decision problems. We give numerical and approximate analytical descriptions of the dynamics of such algorithms applied to random satisfiability problems. We find two different dynamical regimes, depending on the number of constraints per variable: For low constraintness, the problems are solved efficiently, i.e. in linear time. For higher constraintness, the solution times become exponential. We observe that the dynamical behavior is characterized by a fast equilibration and fluctuations around this equilibrium. If the algorithm runs long enough, an exponentially rare fluctuation towards a solution appears.Comment: 21 pages, 18 figures, revised version, to app. in PRE (2003

    Bit-Vector Model Counting using Statistical Estimation

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    Approximate model counting for bit-vector SMT formulas (generalizing \#SAT) has many applications such as probabilistic inference and quantitative information-flow security, but it is computationally difficult. Adding random parity constraints (XOR streamlining) and then checking satisfiability is an effective approximation technique, but it requires a prior hypothesis about the model count to produce useful results. We propose an approach inspired by statistical estimation to continually refine a probabilistic estimate of the model count for a formula, so that each XOR-streamlined query yields as much information as possible. We implement this approach, with an approximate probability model, as a wrapper around an off-the-shelf SMT solver or SAT solver. Experimental results show that the implementation is faster than the most similar previous approaches which used simpler refinement strategies. The technique also lets us model count formulas over floating-point constraints, which we demonstrate with an application to a vulnerability in differential privacy mechanisms

    Hamiltonian Oracles

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    Hamiltonian oracles are the continuum limit of the standard unitary quantum oracles. In this limit, the problem of finding the optimal query algorithm can be mapped into the problem of finding shortest paths on a manifold. The study of these shortest paths leads to lower bounds of the original unitary oracle problem. A number of example Hamiltonian oracles are studied in this paper, including oracle interrogation and the problem of computing the XOR of the hidden bits. Both of these problems are related to the study of geodesics on spheres with non-round metrics. For the case of two hidden bits a complete description of the geodesics is given. For n hidden bits a simple lower bound is proven that shows the problems require a query time proportional to n, even in the continuum limit. Finally, the problem of continuous Grover search is reexamined leading to a modest improvement to the protocol of Farhi and Gutmann.Comment: 16 pages, REVTeX 4 (minor corrections in v2

    A Meaningful MD5 Hash Collision Attack

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    It is now proved by Wang et al., that MD5 hash is no more secure, after they proposed an attack that would generate two different messages that gives the same MD5 sum. Many conditions need to be satisfied to attain this collision. Vlastimil Klima then proposed a more efficient and faster technique to implement this attack. We use these techniques to first create a collision attack and then use these collisions to implement meaningful collisions by creating two different packages that give identical MD5 hash, but when extracted, each gives out different files with contents specified by the atacker

    On the cavity method for decimated random constraint satisfaction problems and the analysis of belief propagation guided decimation algorithms

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    We introduce a version of the cavity method for diluted mean-field spin models that allows the computation of thermodynamic quantities similar to the Franz-Parisi quenched potential in sparse random graph models. This method is developed in the particular case of partially decimated random constraint satisfaction problems. This allows to develop a theoretical understanding of a class of algorithms for solving constraint satisfaction problems, in which elementary degrees of freedom are sequentially assigned according to the results of a message passing procedure (belief-propagation). We confront this theoretical analysis to the results of extensive numerical simulations.Comment: 32 pages, 24 figure

    Computational core and fixed-point organisation in Boolean networks

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    In this paper, we analyse large random Boolean networks in terms of a constraint satisfaction problem. We first develop an algorithmic scheme which allows to prune simple logical cascades and under-determined variables, returning thereby the computational core of the network. Second we apply the cavity method to analyse number and organisation of fixed points. We find in particular a phase transition between an easy and a complex regulatory phase, the latter one being characterised by the existence of an exponential number of macroscopically separated fixed-point clusters. The different techniques developed are reinterpreted as algorithms for the analysis of single Boolean networks, and they are applied to analysis and in silico experiments on the gene-regulatory networks of baker's yeast (saccaromices cerevisiae) and the segment-polarity genes of the fruit-fly drosophila melanogaster.Comment: 29 pages, 18 figures, version accepted for publication in JSTA
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