Ch(k) Grammars: A Characterization of LL(k) Languages

From the point of view of parsing the LL(K] grammars constitute a very attractive class of context-free grammars. For each LL{K] grammar a top-down parsing algorithm can be devised which is essentially a one-state deterministic push-down automaton. From a more theoretiG point of view LL[K) grammars are attractive as well. It is well-known, for example, that it is decidable whether two LLfk) grammars are equivalent. Also the hierarchy of LL[K) languages with regard to the length k of the look-ahead is a characteristic property. The class of LL[k] grammars is properly contained in the class of LR[K] grammars, and even the family of LLCK) languages is properly contained in the family of LR(K) languages. If we focus on the "gap" between LL~K) and LR[K] grammars the following points are of interest, [i] There is the obvious difference in grammar definition. (ii) The generating capacities are different. (iii) Apart From the difference between LR[O) and LR(1) languages the length k of the look-ahead does not play a role for LR[K] languages. [iv] Every LL(K] grammar is both left parsable and right parsable but there are LR[K] grammars which are not left parsable [i]. We consider the present paper as a contribution to the research which tries to clarify the differences between LL(K) and LR[K) grammars. Research in this area has been reported e. paper we introduce the class of so called Ch[K] grammars [pronounced "chain K grammars"]. This class of grammars is properly contained in the class of LR(K] grammars and it properly contains the LL(K] grammars. However, the family of Ch[K] languages coincides with the family of LL(K] languages. Nevertheless, the parsing properties of Ch[K] grammars are quite different from the parsing properties of LL~KI grammars. The class of Ch[K) grammars can be considered as a generalization of the class of simple chain grammars [6] in the same sense as the class of LL[K] grammars is a generalization of the class of simple LL[I] grammars. The present paper is organized as follows. In Section 2 we define the necessary 391 background concerning context-free ~rammars and parsing. The Ch[K) grammars are