Probabilistic Context-Free Grammars (PCFGs) and variations on them have recently become some of the most common formalisms for parsing. It is common with PCFGs to compute the inside and outside probabilities. When these probabilities are multiplied together and normalized, they produce the probability that any given non-terminal covers any piece of the input sentence. The traditional use of these probabilities is to improve the probabilities of grammar rules. In this thesis we show that these values are useful for solving many other problems in Statistical Natural Language Processing. We give a framework for describing parsers. The framework generalizes the inside and outside values to semirings. It makes it easy to describe parsers that compute a wide variety of interesting quantities, including the inside and outside probabilities, as well as related quantities such as Viterbi probabilities and n-best lists. We also present three novel uses for the inside and outside probabilities. T...

this paper is that all five of these commonly computed quantities can be described as elements of complete semirings (Kuich 1997). The relationship between grammars and semirings was discovered by Chomsky and Schtitzenberger (1963), and for parsing with the CKY algorithm, dates back to Teitelbaum (1973). A complete semiring is a set of values over which a multiplicative operator and a commutative additive operator have been defined, and for which infinite summations are defined. For parsing algorithms satisfying certain conditions, the multiplicative and additive operations of any complete semiring can be used in place of/x and , and correct values will be returned. We will give a simple normal form for describing parsers, then precisely define complete semirings, and the conditions for correctness

We present the concepts of weighted language, ~ansduction and au-tomaton from algebraic automata theory as a general framework for describing and implementing decoding cascades in speech and lan-guage processing. This generality allows us to represent uniformly such information sources as pronunciation dictionaries, language models artd lattices, and to use uniform algorithms for building de-coding stages and for optimizing and combining them. In particular, a single automata join algorithm can be used either to combine in-formation sources such as a pronunciation dictionary and a context-dependency model during the construction of a decoder, or dynam-ically during the operation of the decoder. Applications to speech recognition and to Chinese text segmentation will be discussed. 1.

this paper is to discuss the scope and limitations of this approach, and to examine the suitability of several syntactic formalisms on the criterion of their ability to handle it. 2 Parsing as intersection

Bernard Lang defines parsing as the calculation of the intersection of a FSA (the input) and a CFG. Viewing the input for parsing as a FSA rather than as a string combines well with some approaches in speech understanding systems, in which parsing takes a word lattice as input (rather than a word string). Furthermore, certain techniques for robust parsing can be modelled as finite state transducers.

Bernard LANG INRIA B.P. 105, 78153 Le Chesnay, France lang@inria.inria.fr The intent of this presentation is to exhibit the commonalities between the following syntactic problems: 1. parsing ambiguous or incomplete input, often known as word lattice parsing; 2. parsing ill-formed input, i.e. input that does not belong to the language formally defined by a grammar; 3. syntactic disambiguation of ambiguous sentences; 4. accounting for deviant syntactic structures in grammatical language descriptions. The key idea behind this work is that of a weighted grammar. For simplicity we consider here only a special case of the more general definition given in [Teitelbaum 73], which could lead to other interesting variations (e.g. probabilities as weights, using multiplication instead of addition as below). We define a weighted grammar as a Context-Free (CF) grammar with a numeric weight attached to each of its rules. We attach to any derivation tree a weight that is the sum of the weights of a...

ion (Johnson and Dorre, [39]) ffl x(A,B,f(A,B),g(A,h(B,i(C)))) =) x(A,B,f(,),g(,)) ffl parsewithweakening(Cat,P0,P,E0,E) :- weaken(Cat,WeakenedCat), parse(WeakenedCat,P0,P,E0,E), Cat=WeakenedCat. ffl Really helps! Ambiguity Packing ffl A parser should not construct all parse trees (exponential) ffl Instead, a compact representation of all such parse trees are constructed -- grammar [42, 9] -- parse forest [76] -- packed structures [3] ffl Here: for every `result item' keep track of the lexical entry and references of other result items that were used to create it ffl Results in a lexicalized tree substitution grammar ffl which generates the input sentence with all its parse trees Bottom-up Inactive-chart Parser Item form: [i;X; j] Axioms: Goals: [0;S;n] Inference Rules: Scan [q i ;wi; qi+1 ] Complete [q k ;X1; q k 0][q k 0;X2; q k 00] : : : [q m0;Xl; qm] [q k ;X0; qm] X0 !X1:::Xl Bottom-up Inactive-chart Parser Inference Rules: Scan [q i ;wi; qi+...

Abstract. We study Valiant’s classical algorithm for Context Free Grammar recognition in sub-cubic time, and extract features that are common to problems on which Valiant’s approach can be applied. Based on this, we describe several problem templates, and formulate generic algorithms that use Valiant’s technique and can be applied to all problems which abide by these templates. These algorithms obtain new worst case running time bounds for a large family of important problems within the world of RNA Secondary Structures and Context Free Grammars. 1

Reducing the worst case running times of a