Nonterminal Separating Macro Grammars

We extend the concept of nonterminal separating (or NTS) context-free grammar to nonterminal separating $m$-macro grammar where the mode of derivation $m$ is equal to "unrestricted". "outside-in' or "inside-out". Then we show some (partial) characterization results for these NTS $m$-macro grammars

Controlled Rewriting Using Productions and Reductions

We investigate context-free grammars the rules of which can be used in a productive and in a reductive fashion, while the application of these rules is controlled by a regular language. We distinguish several modes of derivation for this kind of grammar. The resulting language families (properly) extend the family of context-free languages. We establish some closure properties of these language families and some grammatical transformations which yield a few normal forms for this type of grammar. Finally, we consider some special cases (viz. the context-free grammar is linear or left-linear), and generalizations, in particular, the use of arbitrary rather than regular control languages

Regularly Controlled Bidirectional Linear Basic Grammars

We investigate the bidirectional application of grammar productions -- i.e., using the productions in the reversed direction too -- to linear basic grammars. As in the case of regularly controlled bidirectional context-free grammars (or RCB grammars), we provide bidirectional linear basic grammars with a regular control language over the rules (i.e., productions and their corresponding reductions). Our main result shows that under the so-called RS/B/f-mode of derivation, bidirectionality gives rise to a dramatic increase in generating power compared with (regularly controlled unidirectional) linear basic grammars.\ud \u

Time-Bounded Controlled Bidirectional Grammars

We study regularly controlled bidirectional (RCB) grammars from the viewpoint of time-bounded grammars. RCB-grammars are context-free grammars of which the rules can be used in a productive and in a reductive fashion, while the application of these rules is controlled by a regular language. Several modes of derivation can be distinguished for this kind of grammar. A time-bound on such a grammar is a measure of its derivational complexity. For some families of time bounds and for some modes of derivation we establish closure properties and a normal form theorem. In addition parsing algorithms are given for some modes of derivation. We conclude with considering generalizations with respect to the family of control languages and the family of bounding functions

Controlled Bidirectional Grammars

We investigate context-free grammars the rules of which can be used in a productive and in a reductive fashion, while the application of these rules is controlled by a regular language. We distinguish several modes of derivation for this kind of grammar. The resulting language families (properly) extend the family of context-free languages. We establish some closure properties of these language families and some grammatical transformations which yield a few normal forms for this type of grammar. Finally, we consider some special cases (viz. the context-free grammar is linear or left-linear), and generalizations, in particular, the use of arbitrary rather than regular control languages

On the Generating Power of Regularly Controlled Bidirectional Grammars

RCB-grammars or regularly controlled bidirectional grammars are context-free grammars of which the rules can be used in a productive and in a reductive fashion. In addition, the application of these rules is controlled by a regular language. Several modes of derivation can be distinguished for this kind of grammar. In this paper the generating power of the derivation mode that uses right-occurrence rewriting (RO-mode) is determined. Furthermore, a new mode called RA is introduced, which is a better formalization of the intuitive idea of right-occurrence rewriting than the RO-mode. The RO- and RA-mode have the same generating power, viz. the corresponding RCB-grammars both generate the recursively enumerable languages. Consequently, providing RCB/RO-grammars with a time bound results in a less powerful grammar model

Regularly controlled bidirectional extended linear basic grammars (revised and extended version)

We study the concept of bidirectional application of productions − i.e., using a production of a grammar as a reduction too − with respect to regularly controlled extended linear basic (macro) grammars [3], provided with a restricted mode of derivation. So this new grammatical model is in essence equal to the regularly controlled bidirectional context-free grammars of [15] in which the underlying context-free grammar is replaced by an extended linear basic grammar. We establish closure properties of the corresponding family of languages; viz. for the outside-in or OI-mode we obtain a full substitution-closed AFL, and for the inside-out or IO-mode we obtain a full QAFL closed under deterministic substitution. The notion of bidirectionality gives rise to a dramatic increase of generating power; even under minor assumptions the OI [IO] instance of such grammars generate all OI-macro [IO-macro, respectively] languages. Furthermore, in case of free application of productions and reductions we obtain a generating capacity equal to the one of phrase-structure grammars