Algorithms on strings

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  • Let's begin with the picture on the front cover. You may have observed that the portra让of Alan Turing is constructed from a number of pictures ("tiles") of great computer scientists and mathematicians. Suppose you were asked in an interview to design a program that takes an 垃nage and a collection of s x s-sized tiles and produce a mosaic from the tiles that resembles the image. A good way to begin may be to partition the image into s x s-sized squares, compute the average color of each such image square, and then find the tile that is closest to it in the color space. Here distance in...

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  • This book is to examine the most important algorithms in use on today's computers and to teach the basic techniques with the increasing number who was interested in computer users becoming increasingly serious. It is appropriate for use as a textbook for a course Monday, Tuesday or Wednesday in the computer Science: After students have had some programming skills and familiarity computer system, but before they have advanced specialized courses field of computer science or computer applications.

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  • Shimon Even’s Graph Algorithms, published in 1979, was a seminal introductory book on algorithms read by everyone engaged in the field. This thoroughly revised second edition,with a foreword byRichard M.Karp and notes byAndrewV.Goldberg, continues the exceptional presentation from the first edition and explains algorithms in formal but simple language with a direct and intuitive presentation. The material covered by the book begins with basic material, including graphs and shortest paths, trees, depth-first search, and breadth-first search.

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  • We introduce a novel search algorithm for statistical machine translation based on dynamic programming (DP). During the search process two statistical knowledge sources are combined: a translation model and a bigram language model. This search algorithm expands hypotheses along the positions of the target string while guaranteeing progressive coverage of the words in the source string. We present experimental results on the Verbmobil task.

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  • It is by now well established that quantum machines can solve certain computational problems much faster than the best algorithms known in the standard Turing machine model. The complexity question of which problems can be feasibly computed by quantum machines has also been extensively investigated in recent years, both in the context of one machine models (quantum polynomial classes) and various flavors of multi-machine models (single and multiple prover quantum interactive proofs).

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  • In this paper, we propose a novel string-todependency algorithm for statistical machine translation. With this new framework, we employ a target dependency language model during decoding to exploit long distance word relations, which are unavailable with a traditional n-gram language model. Our experiments show that the string-to-dependency decoder achieves 1.48 point improvement in BLEU and 2.53 point improvement in TER compared to a standard hierarchical string-tostring system on the NIST 04 Chinese-English evaluation set. ...

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  • We present an algorithm for generating strings from logical form encodings that improves upon previous algorithms in that it places fewer restrictions on the class of grammars to which it is applicable. In particular, unlike an Earley deduction generator (Shieber, 1988), it allows use of semantically nonmonotonic grammars, yet unlike topdown methods, it also permits left-recursion. The enabling design feature of the algorithm is its implicit traversal of the analysis tree for the string being generated in a semantic-head-driven fashion. ...

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  • In the literature, Tree Adjoining Grammars (TAGs) are propagated to be adequate for natural language description - - analysis as well as generation. In this paper we concentrate on the direction of analysis. Especially important for an implementation of that task is how efficiently this can be done, i.e., how readily the word problem can be solved for TAGs. Up to now, a parser with O(n 6) steps in the worst case was known where n is the length of the input string. In this paper, the result is improved to O(n 4 log n) as a new lowest...

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  • In this thesis we are concerned with constructing algorithms that address prob- lems of biological relevance. This activity is part of a broader interdisciplinary area called computational biology, or bioinformatics, that focuses on utiliz- ing the capacities of computers to gain knowledge from biological data. The majority of problems in computational biology relate to molecular or evolu- tionary biology, and focus on analyzing and comparing the genetic material of organisms.

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  • We present a syntax-based statistical translation model. Our model transforms a source-language parse tree into a target-language string by applying stochastic operations at each node. These operations capture linguistic differences such as word order and case marking. Model parameters are estimated in polynomial time using an EM algorithm. The model produces word alignments that are better than those produced by IBM Model 5. is conditioned only on word classes and positions in the string, and the duplication and translation are conditioned only on the word identity. ...

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  • We augment a model of translation based on re-ordering nodes in syntactic trees in order to allow alignments not conforming to the original tree structure, while keeping computational complexity polynomial in the sentence length. This is done by adding a new subtree cloning operation to either tree-to-string or tree-to-tree alignment algorithms.

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  • CAI 2009 was the Third International Conference on Algebraic Informatics. It was intended to cover the topics of algebraic semantics on graphs and trees, formal power series, syntactic objects, algebraic picture processing, finite and infinite computations, acceptors and transducers for strings, trees, graphs, arrays, etc., decision problems, algebraic characterization of logical theories, process algebra, algebraic algorithms, algebraic coding theory, algebraic aspects of cryptography.

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  • The KMP algorithm [Knuth et al. 1997] creates a prefix function from the pattern to define transition functions that expedite the search. The prefix func- tion is built in O(m) time, and the algorithm has a worst case time complex- ity of O(nCm), independent from the alphabet size. Exhaustive experiments [Wright et al. 1998] show that, in general, KMP has the best performance. Be- cause of its good performance, and its independence from the alphabet size, KMP provides a natural basis for dealing with the more general problem of optimizing database queries on sequences.

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  • Often one may wish to learn a tree-to-tree mapping, training it on unaligned pairs of trees, or on a mixture of trees and strings. Unlike previous statistical formalisms (limited to isomorphic trees), synchronous TSG allows local distortion of the tree topology. We reformulate it to permit dependency trees, and sketch EM/Viterbi algorithms for alignment, training, and decoding.

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  • Valiant showed that Boolean matrix multiplication (BMM) can be used for CFG parsing. We prove a dual result: CFG parsers running in time O([Gl[w[3-e) on a grammar G and a string w can be used to multiply m x m Boolean matrices in time O(m3-e/3). In the process we also provide a formal definition of parsing motivated by an informal notion due to Lang. Our result establishes one of the first limitations on general CFG parsing: a fast, practical CFG parser would yield a fast, practical BMM algorithm, which is not believed to exist. 1 Introduction The standard method...

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  • The inside-outside algorithm for inferring the parameters of a stochastic context-free grammar is extended to take advantage of constituent information (constituent bracketing) in a partially parsed corpus. Experiments on formal and natural language parsed corpora show that the new algorithm can achieve faster convergence and better modeling of hierarchical structure than the original one.

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