Imprecision in n-Parallel Right Linear Grammar and its Application

Abstract

Various types of grammar such as regular, context-free, context-sensitive and recursive enumerable grammar exists. All these grammars have their acceptance power which is limited to a certain domain only. Context free grammars are not able to display all features of natural languages and context sensitive grammars have many limitations like that of membership problem, emptiness problem. To overcome these dependencies, the concept of regulated grammar has been introduced. What regulated grammar basically does is to put some types of regulations on the context free grammar rules. In this way we take context free rules, apply some regulation on some rules so that if one rule is used then it also necessary that the bounded rules must be used along with it. The number of bounded rules depends on the problem statement. There can be as many number of production rules which can be regulated. In this way we can solve many problems which previously used context sensitive grammar, for them we can build regulated grammar. We have used the concept of fuzziness on n-parallel right linear grammar. Previously when we have used the grammar to generate a certain string, either that string is completely generated or it is not. With the addition of fuzziness in the grammar we can also accept a string which was previously not accepted can now be accepted with a degree of membership. This degree of membership for erroneous string lies between 0 and 1. The degree of membership for a particular production is determined on the basis of data sets. There is different degree of membership for different kind of rules, whether it is for deletion of an alphabet or addition of a new alphabet or substitution of a new alphabet. We have applied the concept of regulated automata on the Chinese tones and constructed a grammar for the same.