Quantitative structural information for inferring context free grammars with an extended Cocke–Younger–Kasami algorithm

In this paper, we propose an approach to quantitative structural information for inferring context free grammars. First, we construct derivative capacity of nonterminal symbols in context free grammar, concomitant indicator and embedded dimensional number of strings in samples set, which are called as quantitative structural information; then, we rewrite Cocke–Younger–Kasami (CYK) algorithm for parsing in the form of the derivative set; third, we present the construction of new production rule and the descriptive procedure for inferring with an extended CYK algorithm by the quantitative structural information. Finally, we discuss the extended CYK algorithm for inferring context free grammars.

Research highlights
► The derivative set presents the derivative capacity of nonterminal symbols.
► The concomitant indicator shows concomitant relation amid strings.
► The embedded dimensional number indicates embedding relation amid strings.
► The construction of new production is used for the simultaneous regular equations.
► The extended CYK algorithm is built on the quantitative structural information.