Syntactic stochastic processes: Definitions, models, and related inference problems

We define a Syntactic Stochastic Process (SSP) as a stochastic process valued in the set of terminal symbols of a grammar, and whose realizations are terminal strings generated by some stochastic grammar. and show that any SSP generated by a Stochastic Context Free Grammar (SCFG) can be consistently...

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Bibliographic Details
Published inInformation and computation Vol. 281; p. 104667
Main Authors Carravetta, Francesco, White, Langford B.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.12.2021
Subjects
Branching processes
Graphs
Languages
Markov fields
Smoothing
Speech processing
Trees
Trees
Markov fields
Smoothing
Graphs
Languages
Branching processes
Speech processing
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Summary:We define a Syntactic Stochastic Process (SSP) as a stochastic process valued in the set of terminal symbols of a grammar, and whose realizations are terminal strings generated by some stochastic grammar. and show that any SSP generated by a Stochastic Context Free Grammar (SCFG) can be consistently indexed by a subset of nodes of a suitable defined Graphical Random Field (GRF). In the second part of the paper we propose a definition of Stochastic Context-Sensitive Grammar (SCSG), and that the stochastic process generated by a SCFG admits a representation as a GRF. Finally, we show that strings generated by a Stochastic Tree Adjoining Grammar (STAG) are reciprocal processes, which allows the solution of the inference problem with a complexity linear with respect to string length.
ISSN:0890-5401
1090-2651
DOI:10.1016/j.ic.2020.104667