We develop a general dynamic programming technique for the tabulation of transition-based dependency parsers, and apply it to obtain novel, polynomial-time algorithms for parsing with the arc-standard and arc-eager models. We also show how to reverse our technique to obtain new transition-based dependency parsers from existing tabular methods. Additionally, we provide a detailed discussion of the conditions under which the feature models commonly used in transition-based parsing can be integrated into our algorithms. ...
Note immediately one diﬀerence between linear equations and polynomial equations:
theorems for linear equations don’t depend on which ﬁeld k you are working over,
but those for polynomial equations depend on whether or not k is algebraically closed
and (to a lesser extent) whether k has characteristic zero. Since I intend to emphasize
the geometry in this course, we will work over algebraically closed ﬁelds for the major
part of the course.
The lexicalist approach to Machine Translation offers significant advantages in the development of linguistic descriptions. However, the Shake-and-Bake generation algorithm of (Whitelock, 1992) is NPcomplete. We present a polynomial time algorithm for lexicalist MT generation provided that sufficient information can be transferred to ensure more determinism.
We introduce a polynomial-time algorithm for statistical machine translation. This algorithm can be used in place of the expensive, slow best-first search strategies in current statistical translation architectures. The approach employs the stochastic bracketing transduction grammar (SBTG) model we recently introduced to replace earlier word alignment channel models, while retaining a bigram language model. The new algorithm in our experience yields major speed improvement with no significant loss of accuracy. ...
Many problems of practical significance are NPcomplete
but are too important to abandon merely
because obtaining an optimal solution is intractable
(khó). If a problem is NP-complete, we are unlikely to find
a polynomial time algorithm for solving it exactly, but
it may still be possible to find near-optimal solution
in polynomial time.
Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Research Article Polynomial-Time Algorithm for Controllability Test of a Class of Boolean Biological Networks
Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí y học Molecular Biology cung cấp cho các bạn kiến thức về ngành sinh học đề tài: A polynomial time biclustering algorithm for finding approximate expression patterns in gene expression time series...
Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí y học Molecular Biology cung cấp cho các bạn kiến thức về ngành sinh học đề tài: Polynomial algorithms for the Maximal Pairing Problem: efficient phylogenetic targeting on arbitrary trees...
This paper investigates the class of TreeTuple MCTAG with Shared Nodes, TTMCTAG for short, an extension of Tree Adjoining Grammars that has been proposed for natural language processing, in particular for dealing with discontinuities and word order variation in languages such as German. It has been shown that the universal recognition problem for this formalism is NP-hard, but so far it was not known whether the class of languages generated by TT-MCTAG is included in PTIME. We provide a positive answer to this question, using a new characterization of TTMCTAG. ...
We introduce an algorithm for designing a predictive left to right shift-reduce non-deterministic push-down machine corresponding to an arbitrary unrestricted context-free grammar and an algorithm for efficiently driving this machine in pseudo-parallel. The performance of the resulting parser is formally proven to be superior to Earley's parser (1970). The technique employed consists in constructing before run-time a parsing table that encodes a nondeterministic machine in the which the predictive behavior has been compiled out. ...
In this paper we present a polynomial time parsing algorithm for Combinatory Categorial Grammar. The recognition phase extends the CKY algorithm for CFG. The process of generating a representation of the parse trees has two phases. Initially, a shared forest is build that encodes the set of all derivation trees for the input string. This shared forest is then pruned to remove all spurious ambiguity.
In this paper we consider a combinatorial optimization problem that is similar to the bottleneck traveling salesman problem. We show that an optimal tour for this problem is pyramidal tour (1, 3, 5,…, n,…, 6, 4, 2) or consists of some pyramidal subtours. The above 7methods can be extended to complete bipartite graphs. 1.
It is well-known that the traveling salesman problem (TSP) is strongly NP-hard (cf. , p. 353). But for some special cases of the TSP can be solvable in polynomial time. ...
In this book you find the basic mathematics that is needed by engineers and university students . The author will help you to understand the meaning and function of mathematical concepts. The best way to learn it, is by doing it, the exercises in this book will help you do just that.
This topic reviews the basic mathematics required in this course: A justification for a mathematical framework, the ceiling and floor functions, L’Hôpital’s rule, logarithms, arithmetic and other polynomial series, geometric series, recurrence relations, weighted averages, combinations.
In this topic, we will look at: Justification for analysis, quadratic and polynomial growth, counting machine instructions, Landau symbols, Big-Q as an equivalence relation, little-o as a weak ordering.
We present a polynomial-time algorithm that provably recovers the signer’s secret DSA key when a few bits of the random nonces k (used at eachsignature generation) are known for a number of DSA signatures at most linear inlog q (q denoting as usual the small prime of DSA), under a reasonable assumption on the hash function used in DSA.
We discuss the use of social networks in implementing viral
marketing strategies. While influence maximization has
been studied in this context (see Chapter 24 of ), we
study revenue maximization, arguably, a more natural objective.
In our model, a buyer’s decision to buy an item is
influenced by the set of other buyers that own the item and
the price at which the item is offered.
We focus on algorithmic question of finding revenue maximizing
marketing strategies. When the buyers are completely
symmetric, we can find the optimal marketing strategy
in polynomial time.
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.
We present a new chart parsing method for Lambek grammars, inspired by a method for DTree grammar parsing. The formulae of a Lambek sequent are firstly converted into rules of an indexed grammar formalism, which are used in an Earley-style predictive chart algorithm. The method is non-polynomial, but performs well for practical purposes - - much better than previous chart methods for Lambek grammars.
We propose an O(M(n2)) time algorithm for the recognition of Tree Adjoining Languages (TALs), where n is the size of the input string and M(k) is the time needed to multiply two k x k boolean matrices. Tree Adjoining Grammars (TAGs) are formalisms suitable for natural language processing and have received enormous attention in the past among not only natural language processing researchers but also algorithms designers. The first polynomial time algorithm for TAL parsing was proposed in 1986 and had a run time of O(n6). has been proposed. ...