## Time-bounded controlled bidirectional grammars (1990)

Venue: | International Journal of Computer Mathematics |

Citations: | 4 - 3 self |

### BibTeX

@ARTICLE{Hogendorp90time-boundedcontrolled,

author = {Jan Anne Hogendorp},

title = {Time-bounded controlled bidirectional grammars},

journal = {International Journal of Computer Mathematics},

year = {1990}

}

### OpenURL

### Abstract

Abstract — 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. KEY WORDS: controlled context-free grammar, production and reduction (i.e. reversed production), mode of derivation, normal form, closure

### Citations

487 | Regular Languages
- Yu
(Show Context)
Citation Context ...ithout any restriction or in a controlled fashion. Considerably less research has been done in defining derivations in terms of reductions. One major example is the concept of analytical grammar; cf. =-=[16]-=-. For context-free grammars the use of both productions and reductions in the derivational process has been studied in [6]. A special subclass of these latter grammars is formed by the NTS or nontermi... |

320 |
Introduction to Formal Language Theory
- Harrison
- 1978
(Show Context)
Citation Context ...de this section by establishing some properties of timebounded RCB-grammars and their languages. For all unexplained notations and concepts from formal language theory we refer to standard texts like =-=[1, 7, 11, 12]-=-. Let G = (V, Σ,P,S) be a context-free grammar with alphabet V, terminal alphabet Σ, set of productions P and initial symbol S. By P �� we denote the set of reductions corresponding to P, i.e., if an ... |

61 |
Algebraic and Automata-Theoretic Properties of Formal Languages
- Ginsburg
- 1974
(Show Context)
Citation Context ...d under inverse homomorphism. Proof: It is sufficient to prove that RCB/RO-languages are closed under intersection with a regular language, regular substitution and union with a regular language; cf. =-=[9]-=- Proposition 3.7.1 and its Corollary. The latter fact follows from the observation that the regular languages form a subset of the RCB-languages; cf. Proposition 2.4.(1). The other premisses are prove... |

40 |
Languages and Machines: An Introduction to the Theory of Computer Science. Pearson international edition
- Sudkamp
- 2006
(Show Context)
Citation Context ...de this section by establishing some properties of timebounded RCB-grammars and their languages. For all unexplained notations and concepts from formal language theory we refer to standard texts like =-=[1, 7, 11, 12]-=-. Let G = (V, Σ,P,S) be a context-free grammar with alphabet V, terminal alphabet Σ, set of productions P and initial symbol S. By P �� we denote the set of reductions corresponding to P, i.e., if an ... |

28 |
Programmed grammars and classes of formal languages
- Rosenkrantz
- 1969
(Show Context)
Citation Context ...f a sentence from the language by means of a control mechanism which directs the derivational process. In the literature this subject has been investigated with various different ways of control; cf. =-=[10, 13, 14, 15, 16, 19]-=- for controlled Chomsky-grammars, whereas in [1, 2, 3, 4] parallel grammars provided with control are studied. In all these controlled grammars the rules are applied in a productive fashion only. In t... |

26 |
The Theory of Parsing, Translation and Compiling, volume I: Parsing
- Aho, Ullman
- 1972
(Show Context)
Citation Context ...e a counter each time we can apply a rule (i.e., a production or a reduction) according to this control language C. As long as this counter does not exceed φ (n) we perform the normal parsing actions =-=[1, 2]-=-, (however, with some extensions, due to the fact that we have to deal with reductions in the control language as well); otherwise we have to backtrack. Now the fact that (G,C) is bounded by φ guarant... |

26 |
Church-Rosser Thue systems and formal languages
- McNaughton, Narendran, et al.
- 1988
(Show Context)
Citation Context ...erminal by means of both productions and reductions can also be derived by the use of productions only. Since in RCB-grammars reductions are allowed, there is also a connection with Thue systems; cf. =-=[5, 10]-=-. An RCBgrammar can be considered as a particular kind of Thue system with a restricted use (viz. a controlled use) of the rewriting rules. The context-free grammar G of an RCB-grammar (G,C) is referr... |

17 | Thue systems as rewriting systems - Book - 1987 |

13 |
Control sets on grammars
- Ginsburg, Spanier
- 1968
(Show Context)
Citation Context ...f a sentence from the language by means of a control mechanism which directs the derivational process. In the literature this subject has been investigated with various different ways of control; cf. =-=[10, 13, 14, 15, 16, 19]-=- for controlled Chomsky-grammars, whereas in [1, 2, 3, 4] parallel grammars provided with control are studied. In all these controlled grammars the rules are applied in a productive fashion only. In t... |

10 |
NTS Languages are Deterministic and Congruential
- Boasson, Senizergues
- 1985
(Show Context)
Citation Context ...both productions and reductions in the derivational process has been studied in [6]. A special subclass of these latter grammars is formed by the NTS or nonterminal separating grammars [17]; cf. also =-=[5, 6, 7, 8, 18]-=-. In this type of grammar, each sentential form which can be derived from a nonterminal by means of both productions and reductions can also be derived by the use of productions only. This property is... |

10 |
The equivalence and inclusion problems for NTS languages
- Sénizergues
- 1985
(Show Context)
Citation Context ...both productions and reductions in the derivational process has been studied in [6]. A special subclass of these latter grammars is formed by the NTS or nonterminal separating grammars [17]; cf. also =-=[5, 6, 7, 8, 18]-=-. In this type of grammar, each sentential form which can be derived from a nonterminal by means of both productions and reductions can also be derived by the use of productions only. This property is... |

9 |
Controlled iteration grammars and full hyper-AFL’s
- Asveld
- 1977
(Show Context)
Citation Context ...directs the derivational process. In the literature this subject has been investigated with various different ways of control; cf. [10, 13, 14, 15, 16, 19] for controlled Chomsky-grammars, whereas in =-=[1, 2, 3, 4]-=- parallel grammars provided with control are studied. In all these controlled grammars the rules are applied in a productive fashion only. In this paper the control language is a regular language over... |

8 |
Time bounded grammars and their languages
- Book
- 1971
(Show Context)
Citation Context ...mber n, if T (G,C)(n) is defined then T (G,C)(n) ≤ φ (n). Time-bounded grammars have originally been introduced in [6] to describe the derivational complexity of general phrase-structure grammars. In =-=[4]-=- bounding functions have been used to generate particular language families; thus this paper may also be considered as an extension of [4]. In this framework it is now possible to write parsers for φ-... |

7 |
Dérivations et réductions dans les grammaires algébriques, in J.W. de Bakker
- Boasson
- 1980
(Show Context)
Citation Context ...s of reductions. One major example is the concept of analytical grammar; cf. [16]. For context-free grammars the use of both productions and reductions in the derivational process has been studied in =-=[6]-=-. A special subclass of these latter grammars is formed by the NTS or nonterminal separating grammars [17]; cf. also [5, 6, 7, 8, 18]. In this type of grammar, each sentential form which can be derive... |

4 |
Space-bounded complexity classes and iterated deterministic substitution
- Asveld
- 1980
(Show Context)
Citation Context ...directs the derivational process. In the literature this subject has been investigated with various different ways of control; cf. [10, 13, 14, 15, 16, 19] for controlled Chomsky-grammars, whereas in =-=[1, 2, 3, 4]-=- parallel grammars provided with control are studied. In all these controlled grammars the rules are applied in a productive fashion only. In this paper the control language is a regular language over... |

4 |
Engelfriet: Iterated deterministic substitution
- Asveld, J
- 1977
(Show Context)
Citation Context ...directs the derivational process. In the literature this subject has been investigated with various different ways of control; cf. [10, 13, 14, 15, 16, 19] for controlled Chomsky-grammars, whereas in =-=[1, 2, 3, 4]-=- parallel grammars provided with control are studied. In all these controlled grammars the rules are applied in a productive fashion only. In this paper the control language is a regular language over... |

4 |
Sénizergues: Langages de parenthèses, langages N.T.S. et homomorphismes inverses
- Autebert, Boasson, et al.
- 1984
(Show Context)
Citation Context ...both productions and reductions in the derivational process has been studied in [6]. A special subclass of these latter grammars is formed by the NTS or nonterminal separating grammars [17]; cf. also =-=[5, 6, 7, 8, 18]-=-. In this type of grammar, each sentential form which can be derived from a nonterminal by means of both productions and reductions can also be derived by the use of productions only. This property is... |

3 |
Leeuwen: Infinite chains of hyper-AFL’s, TWmemorandum No
- Asveld, van
- 1975
(Show Context)
Citation Context |

3 |
Simple deterministic NTS languages
- Frougny
- 1981
(Show Context)
Citation Context |

3 | Nonterminal separating macro grammars
- Hogendorp
(Show Context)
Citation Context ...s of both productions and reductions can also be derived by the use of productions only. This property is also definable for some extensions of context-free grammars, for instance macro grammars; cf. =-=[12]-=-. However, the name NTS for this type of context-free grammar is confusing. It stems from a derived property of these grammars, viz., they have disjoint syntactic categories (DSC). This latter propert... |

3 | A new class of C.F.L. for which the equivalence is decidable - Sénizergues - 1981 |

3 |
Leeuwen: Rule-labeled programs − A study of a generalization of context-free and some classes of formal languages
- van
- 1972
(Show Context)
Citation Context ...f a sentence from the language by means of a control mechanism which directs the derivational process. In the literature this subject has been investigated with various different ways of control; cf. =-=[10, 13, 14, 15, 16, 19]-=- for controlled Chomsky-grammars, whereas in [1, 2, 3, 4] parallel grammars provided with control are studied. In all these controlled grammars the rules are applied in a productive fashion only. In t... |

3 |
On the complexity of derivations in phrase-structure grammar. Algebri i Logika Sem
- Gladkii
- 1964
(Show Context)
Citation Context ...d to as a bounding function of (G,C) (or (G,C) is bounded by φ) if for any natural number n, if T (G,C)(n) is defined then T (G,C)(n) ≤ φ (n). Time-bounded grammars have originally been introduced in =-=[6]-=- to describe the derivational complexity of general phrase-structure grammars. In [4] bounding functions have been used to generate particular language families; thus this paper may also be considered... |

2 |
On grammars with restricted use of productions
- Salomaa
- 1969
(Show Context)
Citation Context |

2 |
On some families of formal languages obtained by regulated derivations
- Salomaa
- 1970
(Show Context)
Citation Context |

2 |
Controlled bidirectional grammars, Memorandum INF-88-16
- Hogendorp
(Show Context)
Citation Context ...lgorithms 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. 1. Introduction In =-=[8]-=- we introduced RCB-grammars, i.e., context-free grammars in which the rules can be used in both a productive as in a reductive fashion. The application of these rules is controlled by a regular langua... |

2 | Controlled rewriting using productions and reductions
- Hogendorp
- 1988
(Show Context)
Citation Context ...CNF. � This definition can be adapted to time-bounded λRCB-grammars in the obvious way. We showed that for every RCB/RN/B/f-grammar (G 0,C 0) there exists an equivalent RCB/RN/B/f-grammar in weak CNF =-=[8,9]-=-. The same holds for the time-bounded variant. Proposition 3.5. Let Φ be a family of bounding functions. If Φ is equal to LIN, POLY (k) or POLY, then for every Φ RN /B /f -grammar (G 0,C 0) there exis... |