A natural Extension of Chomsky s Hierarchy


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    • Author:  by Can Adam Albayrak  Gerald L?ttgen  

    • Abstract:  We present a class of languages which is naturally embedded in Chomsky's hierarchy . Moreover, we consider algebraic properties and some decidability and complexity results for this class. 1 Introduction In 1956 Noam Chomsky #Cho56# gave a formalism for the description of languages. He classi- #ed languages - presented by grammars - into four classes: type-0, type-1, type-2 , and type-3 languages. In this paper we extend Chomsky's classi#cation by a new class of grammars which we will call type-4 grammars. This class possesses desirable algebraic properties: it is closed under intersection, union and cartesian product. The characteristic of our extension is the correspondence between grammars and languagerecognizing automata. This correspondence completes the well-known complexity hierarchy. The remainder of the paper is structured as follows. The next section recalls basic de#nitions of language theory . In Section 3 we extend Chomsky's hierarchy and present our main results on...

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