Max-product grammars and languages

Abstract In this paper, two equivalent formulations of max-product grammars are presented. The families of languages generated by various types of max-product grammars are examined. In particular, the family /oL of languages generated by finitary weak regular max-product grammars with cut-point is studied in detail. It is shown that /oL may also be characterized by regular max-product grammars, asynchronous max-product automata, maxproduct automata, and type 3 weighted grammars under maximal interpretation. Moreover, it is shown that /oL contains the family of regular languages as a proper subfamily and that there are context-free and stochastic languages which are not in /oL.