Applying Probability Measures to Abstract Languages

By T. Booth, Richarda . Thompson. 1973

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Citations in the corpus

Grammar Variational Autoencoder (2017, background): “By assigning probabilities to each production rule in the grammar, it is possible to deﬁne a probability distribution over parse trees (Baker, 1979; Booth & Thompson, 1973).”
Head-Driven Statistical Models for Natural Language Parsing (2003, background): “…by n applications of context-free rules LHS i → RHS i (where LHS stands for “left-hand side,” RHS for “right-hand side”), 1 ≤ i ≤ n , under the PCFG is Booth and Thompson (1973) specify the conditions under which the PCFG does in fact deﬁne a distribution over the possible derivations…”
Recognition of Visual Activities and Interactions by Stochastic Parsing (2000, methodology): “A simple introduction of probabilistic measures into grammars and parsing was shown by Booth and Thompson [ 7 ], Thomason [36], and others.”
On the parameter space of generative lexicalized statistical parsing models (2004, methodology): “Some of the earliest analysis of the properties of such grammars, particularly of probabilistic CFGs (PCFGs), was performed by Booth and Thompson (1973).”
A Probabilistic Earley Parser as a Psycholinguistic Model (2001, background): “This de(cid:12)nes a probabilistic language (Grenander, 1967) (Booth and Thompson, 1973) (Soule, 1974) (Wetherell, 1980).”
Relating Probabilistic Grammars and Automata (1999, unknown): “We define the weight of a tree d, denoted condition for the consistency of a PCFG is given in (Booth and Thompson, 1973).”
Recurrent Neural Networks as Weighted Language Recognizers (2017, background): “Not all probabilistic context-free grammars are consistent; necessary and sufficient conditions for consistency are given by Booth and Thompson (1973). However, probabilistic context-free grammars obtained by training on a finite corpus using popular methods (such as expectation-maximization) are gu”
Consistency of a Recurrent Language Model with Respect to Incomplete Decoding (2020, unknown): “This notion of consistency was raised and analyzed earlier, for instance by Booth & Thompson (1973) and Chen et al. (2017), in terms of whether the distribution induced by p θ is concentrated on ﬁnite sequences.”
Intricacies of Collins’ Parsing Model (2004, background): “Because all of these trees have the same, non-zero probability, the sum ¿·À c_Á e diverges, where Á is a possible tree generated by the model, meaning the model is inconsistent (Booth and Thompson, 1973).”
Accurate Unlexicalized Parsing (2003, background): “In the early 1990s, as probabilistic methods swept NLP , parsing work revived the investigation of probabilistic context-free grammars ( PCFG s) (Booth and Thomson, 1973; Baker, 1979).”
A bibliographical study of grammatical inference (2005, background): “Booth and Thompson[131] give consistency conditions which are proved to hold if the probabilities are estimated from the data[132].”