Stochastic Parse-Tree Recognition by a Pushdown Automaton.

TLDR: The stochastic generalization of what is usually called correctness theorems is presented: the probabilities computed operationally by the parsing algorithms are the same as those defined denotationally on the trees and forests defined by the grammar.

Abstract: We present the stochastic generalization of what is usually called correctness theorems: we guarantee that the probabilities computed operationally by the parsing algorithms are the same as those defined denotationally on the trees and forests defined by the grammar The main idea of the paper is to precisely relate the parsing strategy with a parse-tree exploration strategy: a computational path of a parsing algorithm simply performs an exploration of a parse-tree for the input portion already parsed This approach is applied in particular to Earley and Left-Corner parsing algorithms Probability computations follow parsing operations: looping problems (in rule prediction and subtree recognition) are solved by introducing probability variables (which may not be immediately evaluated) Convergence is ensured by the syntactic construction that leads to stochastic equations systems, which are solved as soon as possible Our algorithms accept any (probabilistic) CF grammar No restrictions are made such as prescribing normal form, proscribing empty rules or cyclic grammars