509 research outputs found

    Many-Body Density Matrices for Free Fermions

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    Building upon an analytical technique introduced by Chung and Peschel [M. Chung and I. Peschel, Phys. Rev. B 64, art. 064412 (2001)], we calculated the density matrix rho_B of a finite block of B sites within an infinite system of free spinless fermions. In terms of the block Green function matrix G (whose elements are G_ij = , where c_i^+ and c_j are fermion creation and annihilation operators acting on sites i and j within the block respectively), the density matrix can be written as rho_B = det(1 - G) exp[ sum_ij (log G(1 - G^{-1})_ij c_i^+ c_j]. Implications of such a result to Hilbert space truncation for real-space renormalization schemes is discussed.Comment: 12 pages in RevTeX4 format. Uses amsmath, bbold, dcolumn and mathrsfs package

    Linear Compressed Pattern Matching for Polynomial Rewriting (Extended Abstract)

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    This paper is an extended abstract of an analysis of term rewriting where the terms in the rewrite rules as well as the term to be rewritten are compressed by a singleton tree grammar (STG). This form of compression is more general than node sharing or representing terms as dags since also partial trees (contexts) can be shared in the compression. In the first part efficient but complex algorithms for detecting applicability of a rewrite rule under STG-compression are constructed and analyzed. The second part applies these results to term rewriting sequences. The main result for submatching is that finding a redex of a left-linear rule can be performed in polynomial time under STG-compression. The main implications for rewriting and (single-position or parallel) rewriting steps are: (i) under STG-compression, n rewriting steps can be performed in nondeterministic polynomial time. (ii) under STG-compression and for left-linear rewrite rules a sequence of n rewriting steps can be performed in polynomial time, and (iii) for compressed rewrite rules where the left hand sides are either DAG-compressed or ground and STG-compressed, and an STG-compressed target term, n rewriting steps can be performed in polynomial time.Comment: In Proceedings TERMGRAPH 2013, arXiv:1302.599

    Pattern matching of compressed terms and contexts and polynomial rewriting

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    A generalization of the compressed string pattern match that applies to terms with variables is investigated: Given terms s and t compressed by singleton tree grammars, the task is to find an instance of s that occurs as a subterm in t. We show that this problem is in NP and that the task can be performed in time O(ncjVar(s)j), including the construction of the compressed substitution, and a representation of all occurrences. We show that the special case where s is uncompressed can be performed in polynomial time. As a nice application we show that for an equational deduction of t to t0 by an equality axiom l = r (a rewrite) a single step can be performed in polynomial time in the size of compression of t and l; r if the number of variables is fixed in l. We also show that n rewriting steps can be performed in polynomial time, if the equational axioms are compressed and assumed to be constant for the rewriting sequence. Another potential application are querying mechanisms on compressed XML-data bases

    Extracting and Verifying Cryptographic Models from C Protocol Code by Symbolic Execution

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    Consider the problem of verifying security properties of a cryptographic protocol coded in C. We propose an automatic solution that needs neither a pre-existing protocol description nor manual annotation of source code. First, symbolically execute the C program to obtain symbolic descriptions for the network messages sent by the protocol. Second, apply algebraic rewriting to obtain a process calculus description. Third, run an existing protocol analyser (ProVerif) to prove security properties or find attacks. We formalise our algorithm and appeal to existing results for ProVerif to establish computational soundness under suitable circumstances. We analyse only a single execution path, so our results are limited to protocols with no significant branching. The results in this paper provide the first computationally sound verification of weak secrecy and authentication for (single execution paths of) C code

    Detecting Zero-day Polymorphic Worms with Jaccard Similarity Algorithm

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    Zero-day polymorphic worms pose a serious threat to the security of Mobile systems and Internet infrastructure. In many cases, it is difficult to detect worm attacks at an early stage. There is typically little or no time to develop a well-constructed solution during such a worm outbreak. This is because the worms act only to spread from node to node and they bring security concerns to everyone using Internet via any static or mobile node. No system is safe from an aggressive worm crisis. However, many of the characteristics of a worm can be used to defeat it, including its predictable behavior and shared signatures. In this paper, we propose an efficient signature generation method based on string similarity algorithms to generate signatures for Zero-day polymorphic worms. Then, these signatures are practically applied to an Intrusion Detection System (IDS) to prevent the network from such attacks. The experimental results show the efficiency of the proposed approach compared to other existing mechanisms
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