Showing papers on "Chomsky hierarchy published in 1983"

Labelled formal languages and their uses

Abstract: This research augments formal languages with the machinery to describe labelled combinatorial objects such as trees, permutations, and networks. These objects typically have requirements for their labels (trees, for example, can be equivalent under permutation of subtrees) that make certain labellings invalid or redundant. To deal with this problem, formal languages are augmented with partial orders--derived strings have partial orders specifying acceptable labellings, and productions of the grammar contain fragments of partial orders. The traditional rewrite step in a derivation is now coupled with a substitution that joins two partial orders. The most attractive feature of this method of describing combinatorial objects is the direct translation to generating functions. Treating the grammar of an ordinary formal language as a set of equations and then solving these equations yields an enumerating generating function. This is still true of labelled formal languages although the equations are usually differential rather than rational or algebraic. There are two promising applications for labelled formal languages. In the analysis of algorithms one often identifies combinatorial quantities that can be described with labelled formal languages and, using the translation mentioned above, these quantities can be easily computed. The other application uses labelled formal languages to control a general-purpose system for the ranking, sequencing, and selection of combinatorial objects. Both of these applications demonstrate the value of labelled formal languages as a descriptive and analytic tool.

Modelling economic processes by means of formal grammars: A survey of results at the middle of 1981

Abstract: This paper briefly presents the topics of research and the results obtained by using formal language techniques (mainly Chomsky grammars) in modelling economic processes. This ‘grammatical approach’ to economics is a fairly new way of applying a very modern mathematical theory, and most of the results in this field were obtained by the Roumanian School of Mathematical Linguistics. The survey covers the results reported before the summer of 1981 (those summarized in the monograph [44]). A later survey will present more recent results, some of which are still developing.