19,893 research outputs found

    Simulation of Two-Way Pushdown Automata Revisited

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    The linear-time simulation of 2-way deterministic pushdown automata (2DPDA) by the Cook and Jones constructions is revisited. Following the semantics-based approach by Jones, an interpreter is given which, when extended with random-access memory, performs a linear-time simulation of 2DPDA. The recursive interpreter works without the dump list of the original constructions, which makes Cook's insight into linear-time simulation of exponential-time automata more intuitive and the complexity argument clearer. The simulation is then extended to 2-way nondeterministic pushdown automata (2NPDA) to provide for a cubic-time recognition of context-free languages. The time required to run the final construction depends on the degree of nondeterminism. The key mechanism that enables the polynomial-time simulations is the sharing of computations by memoization.Comment: In Proceedings Festschrift for Dave Schmidt, arXiv:1309.455

    Tabular Parsing

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    This is a tutorial on tabular parsing, on the basis of tabulation of nondeterministic push-down automata. Discussed are Earley's algorithm, the Cocke-Kasami-Younger algorithm, tabular LR parsing, the construction of parse trees, and further issues.Comment: 21 pages, 14 figure

    Probabilistic parsing

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    Postprin

    If the Current Clique Algorithms are Optimal, so is Valiant's Parser

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    The CFG recognition problem is: given a context-free grammar G\mathcal{G} and a string ww of length nn, decide if ww can be obtained from G\mathcal{G}. This is the most basic parsing question and is a core computer science problem. Valiant's parser from 1975 solves the problem in O(nĻ‰)O(n^{\omega}) time, where Ļ‰<2.373\omega<2.373 is the matrix multiplication exponent. Dozens of parsing algorithms have been proposed over the years, yet Valiant's upper bound remains unbeaten. The best combinatorial algorithms have mildly subcubic O(n3/logā”3n)O(n^3/\log^3{n}) complexity. Lee (JACM'01) provided evidence that fast matrix multiplication is needed for CFG parsing, and that very efficient and practical algorithms might be hard or even impossible to obtain. Lee showed that any algorithm for a more general parsing problem with running time O(āˆ£Gāˆ£ā‹…n3āˆ’Īµ)O(|\mathcal{G}|\cdot n^{3-\varepsilon}) can be converted into a surprising subcubic algorithm for Boolean Matrix Multiplication. Unfortunately, Lee's hardness result required that the grammar size be āˆ£Gāˆ£=Ī©(n6)|\mathcal{G}|=\Omega(n^6). Nothing was known for the more relevant case of constant size grammars. In this work, we prove that any improvement on Valiant's algorithm, even for constant size grammars, either in terms of runtime or by avoiding the inefficiencies of fast matrix multiplication, would imply a breakthrough algorithm for the kk-Clique problem: given a graph on nn nodes, decide if there are kk that form a clique. Besides classifying the complexity of a fundamental problem, our reduction has led us to similar lower bounds for more modern and well-studied cubic time problems for which faster algorithms are highly desirable in practice: RNA Folding, a central problem in computational biology, and Dyck Language Edit Distance, answering an open question of Saha (FOCS'14)

    A Robust Parsing Algorithm For Link Grammars

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    In this paper we present a robust parsing algorithm based on the link grammar formalism for parsing natural languages. Our algorithm is a natural extension of the original dynamic programming recognition algorithm which recursively counts the number of linkages between two words in the input sentence. The modified algorithm uses the notion of a null link in order to allow a connection between any pair of adjacent words, regardless of their dictionary definitions. The algorithm proceeds by making three dynamic programming passes. In the first pass, the input is parsed using the original algorithm which enforces the constraints on links to ensure grammaticality. In the second pass, the total cost of each substring of words is computed, where cost is determined by the number of null links necessary to parse the substring. The final pass counts the total number of parses with minimal cost. All of the original pruning techniques have natural counterparts in the robust algorithm. When used together with memoization, these techniques enable the algorithm to run efficiently with cubic worst-case complexity. We have implemented these ideas and tested them by parsing the Switchboard corpus of conversational English. This corpus is comprised of approximately three million words of text, corresponding to more than 150 hours of transcribed speech collected from telephone conversations restricted to 70 different topics. Although only a small fraction of the sentences in this corpus are "grammatical" by standard criteria, the robust link grammar parser is able to extract relevant structure for a large portion of the sentences. We present the results of our experiments using this system, including the analyses of selected and random sentences from the corpus.Comment: 17 pages, compressed postscrip

    Synchronous Context-Free Grammars and Optimal Linear Parsing Strategies

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    Synchronous Context-Free Grammars (SCFGs), also known as syntax-directed translation schemata, are unlike context-free grammars in that they do not have a binary normal form. In general, parsing with SCFGs takes space and time polynomial in the length of the input strings, but with the degree of the polynomial depending on the permutations of the SCFG rules. We consider linear parsing strategies, which add one nonterminal at a time. We show that for a given input permutation, the problems of finding the linear parsing strategy with the minimum space and time complexity are both NP-hard

    Cognitive visual tracking and camera control

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    Cognitive visual tracking is the process of observing and understanding the behaviour of a moving person. This paper presents an efficient solution to extract, in real-time, high-level information from an observed scene, and generate the most appropriate commands for a set of pan-tilt-zoom (PTZ) cameras in a surveillance scenario. Such a high-level feedback control loop, which is the main novelty of our work, will serve to reduce uncertainties in the observed scene and to maximize the amount of information extracted from it. It is implemented with a distributed camera system using SQL tables as virtual communication channels, and Situation Graph Trees for knowledge representation, inference and high-level camera control. A set of experiments in a surveillance scenario show the effectiveness of our approach and its potential for real applications of cognitive vision
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