On the Relation between Context-Free Grammars and Parsing Expression Grammars

Context-Free Grammars (CFGs) and Parsing Expression Grammars (PEGs) have several similarities and a few differences in both their syntax and semantics, but they are usually presented through formalisms that hinder a proper comparison. In this paper we present a new formalism for CFGs that highlights the similarities and differences between them. The new formalism borrows from PEGs the use of parsing expressions and the recognition-based semantics. We show how one way of removing non-determinism from this formalism yields a formalism with the semantics of PEGs. We also prove, based on these new formalisms, how LL(1) grammars define the same language whether interpreted as CFGs or as PEGs, and also show how strong-LL(k), right-linear, and LL-regular grammars have simple language-preserving translations from CFGs to PEGs

The equivalence problem for LL- and LR-regular grammars

It will be shown that the equivalence problem for LL-regular grammars is decidable. Apart from extending the known result for LL(k) grammar equivalence to LLregular grammar equivalence, we obtain an alternative proof of the decidability of LL(k) equivalence. The equivalence prob]em for LL-regular grammars has been studied before, but not solved. Our proof that this equivalence problem is decidable is simple. However, this is mainly because we can reduce the problem to the equivalence problem for real-time strict deterministic grammlars, which is decidable

Simple chain grammars

A subclass of the LR(0)-grammars, the class of simple chain grammars is introduced. Although there exist simple chain grammars which are not LL(k) for any k, this new class of grammars is very close related to the class of LL(1) and simple LL(1) grammars. In fact it can be proved (not in this paper) that each simple chain grammar has an equivalent simple LL(1) grammar. A very simple (bottom-up) parsing method is provided. This method follows directly from the definition of a simple chain grammar and can easily be given in terms of the well-known LR(0) parsing method