19 Applications of stochastic languages

Abstract

Formal languages and their corresponding automata and parsing procedures have been used in the modeling and analysis of natural and computer languages and the description and recognition of patterns. One natural extension of one-dimensional string languages to high dimensional is tree languages. Interesting applications of tree languages to picture recognition include the classification of bubble chamber events, the recognition of fingerprint patterns and the interpretation of the LANDSAT data. In some applications, a certain amount of uncertainty exists in the process under study. This chapter introduces stochastic string languages. It describes three applications: communication and coding; syntactic pattern recognition; and error-correcting parsing. The stochastic tree languages are also introduced and their application to texture modeling is described. Two natural ways of extending the concept of formal languages to stochastic languages are to randomize the productions of grammars and the state transitions of recognition devices respectively. Some major results in stochastic grammars and stochastic syntax analysis are reviewed in the chapter.