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This study introduces a language processing model of one of the most prominent French computational linguists, Maurice Gross (1934~2001), discussing its computational applications. The methodology he proposed for describing syntactic properties of French simple sentences presupposes the exhaustive examination of all predicative entries, which gave it the name Lexicon-Grammar. The results of this approach are presented under a form of binary matrix: about 75,000 French predicates have been described and classified in syntactic tables. However, Gross realized that there still existed tremendous size of non-regular expressions, called compound words, frozen phrases or multi-word expressions, which can hardly can be described under syntactic and formal devices. Thus, he suggested a more processing-oriented framework named Local Grammar (LGG) which is represented as a directed graph like RTN (Recursive Transition Network). The LGGs are transformed into finite-state automata or transducers by means of FSTgraphEditor in UNITEX system, which is implemented, on one hand, for this purpose and, on the other hand, for the automatic corpus processing based on these finite graphs as well as electronic dictionaries included in the system. In this paper, various areas of LGG applications are discussed, such as the construction of linguistic resources, information extraction/opinion mining or formalization of frozen expressions for machine translation.