Characterizing Structural Descriptions Produced by Various Grammatical Formalisms

We consider the structural descriptions produced by various grammatical formalisms in terms of the complexity of the paths and the relationship between paths in the sets of structural descriptions that each system can generate. In considering the relationships between formalisms, we show that it is useful to abstract away from the details of the formalism, and examine the nature of their derivation process as reflected by properties of their derivation trees. We find that several of the formalisms considered can be seen as being closely re1aled since they have derivation tree sets with the same structure as those produced by Context-Free Grammars. On the basis of this observation, we describe a class of formalisms which we call Linear Context Free Rewriting Systems, and show they are recognizable in polynomial time and generate only semilinear languages.