This paper summarizes some recent results concerned with the extension of formal languages to their corresponding stochastic versions. Weighted grammars and languages are first defined, and stochastic grammars and languages are defined as a special case of weighted grammars and languages. Fuzzy grammars and languages, which have some properties similar to weighted grammars and languages, are also discussed. Stochastic automata are defined from the language recognition viewpoint. Languages accepted by stochastic finite-state and pushdown automata, with and without a cutpoint, are studied. Weighted and stochastic programmed and indexed grammars, and stochastic nested stack automata are defined. Finally, some decidability problems of stochastic (weighted, fuzzy) languages are discussed, and problems for further research are suggested.

Stochastic grammars and languages

This paper describes some relations between stochastic automata and stochastic languages, and the possible application of stochastic languages to pattern recognition problems. Stochastic finite-state and stochastic context-free languages are defined. The problem of probability assignment in stochastic languages is discussed. The properties of stochastic finite automata and stochastic pushdown automata used as acceptors are investigated. The use of formal languages in pattern recognition problems is illustrated. The potential application of stochastic languages for pattern description is demonstrated, and the possibility of employing stochastic automata as pattern classifiers is discussed.

Stochastic Automata, Stochastic Languages and Pattern Recognition

Stochastic syntactic analysis for programmed grammars and syntactic pattern recognition

Modeling rule-based systems by stochastic programmed production systems

: Context-free programmed grammars with probabilities attached to the 'go-to' fields are studied as realistic models for syntactical information sources. The model is formally defined and examples of its output are given. Simplifications that follow from the imposition of leftmost derivations are displayed. Source models for languages that are known to be context-free are studied, and for these a first-order Markov approximating source is obtained; standard methods are then used to calculate its entropy. (Author)

Celso De Renna e Souza

Papers

Probabilities in context-free programmed grammars,