Simple Matrix Grammars and Their Leftmost Variants

In essence, simple matrix grammars can be seen as sequences of context-free grammars, referred to as their components, which work in parallel. The present paper demonstrates that two-component simple matrix grammars are as powerful as ordinary matrix grammars. Then, it places three leftmost derivation restrictions upon these grammars and demonstrates that under two of these restrictions, simple matrix grammars are computational complete — that is, they are equivalent with Turing machines. From a historical perspective, concerning simple matrix grammars, the paper also makes several remarks that correct false statements published about them in the past.

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ON ALTERNATING PHRASE-STRUCTURE GRAMMARS

International Journal of Foundations of Computer Science ◽

10.1142/s0129054110007106 ◽

2010 ◽

Vol 21 (01) ◽

pp. 1-25

Author(s):

ETSURO MORIYA ◽

FRIEDRICH OTTO

Keyword(s):

Phrase Structure ◽

Expressive Power ◽

Context Sensitive ◽

Leftmost Derivation ◽

Context Free ◽

Pushdown Automata ◽

Context Free Grammars

The concepts of alternation and of state alternation are extended from context-free grammars to context-sensitive and arbitrary phrase-structure grammars. For the resulting classes of alternating grammars the expressive power is investigated with respect to the leftmost derivation mode and with respect to the unrestricted derivation mode. In particular new grammatical characterizations for the class of languages that are accepted by alternating pushdown automata are obtained in this way.

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ON THE LEFTMOST DERVIATION IN MATRIX GRAMMARS

International Journal of Foundations of Computer Science ◽

10.1142/s012905419900006x ◽

1999 ◽

Vol 10 (01) ◽

pp. 61-79 ◽

Cited By ~ 8

Author(s):

JÜRGEN DASSOW ◽

HENNING FERNAU ◽

GHEORGHE PĂUN

Keyword(s):

Systematic Study ◽

Regular Language ◽

Formal Languages ◽

Open Problems ◽

Recursively Enumerable ◽

Leftmost Derivation ◽

Context Free ◽

Recursively Enumerable Languages ◽

Context Free Grammars

Matrix grammars are one of the classical topics of formal languages, more specifically, regulated rewriting. Although this type of control on the work of context-free grammars is one of the earliest, matrix grammars still raise interesting questions (not to speak about old open problems in this area). One such class of problems concerns the leftmost derivation (in grammars without appearance checking). The main point of this paper is the systematic study of all possibilities of defining leftmost derivation in matrix grammars. Twelve types of such a restriction are defined, only four of which being discussed in literature. For seven of them, we find a proof of a characterization of recursively enumerable languages (by matrix grammars with arbitrary context-free rules but without appearance checking). Other three cases characterize the recursively enumerable languages modulo a morphism and an intersection with a regular language. In this way, we solve nearly all problems listed as open on page 67 of the monograph [7], which can be seen as the main contribution of this paper. Moreover, we find a characterization of the recursively enumerable languages for matrix grammars with the leftmost restriction defined on classes of a given partition of the nonterminal alphabet.

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Tree Valence Controlled Grammars

International Journal on Perceptive and Cognitive Computing ◽

10.31436/ijpcc.v3i1.48 ◽

2017 ◽

Vol 3 (1) ◽

Author(s):

Salbiah Ashaari ◽

SHERZOD TURAEV ◽

Abdurahim Okhunov

Keyword(s):

Structural Properties ◽

Context Free Grammar ◽

The Past ◽

New Variant ◽

Main Production ◽

Number Of Publications ◽

Regular Sets ◽

Context Free ◽

Ordinary Context ◽

Context Free Grammars

Beyond a shadow of a doubt, the studying of context-free grammars with restricted derivationtrees known as tree controlled grammars have achieved plentiful remarkable results within formallanguage theory as demonstrated in a number of publications on this subject for the past forty five years.In principle, these grammars generate their languages as an ordinary context-free grammar except theirderivation trees need to be satisfied by certain prescribed conditions. Our paper is a continuing of studyingof this kind of grammars, where we introduce a new variant of tree controlled grammar called a treevalence controlled grammar, which replaces regular sets with valences where every main production withcertain integer value will be derived into sub-productions with the value of combination of zero and one orzero and minus represented in matrices form with the permutations of each matrix row yield a zero value(at every level of tree derivation, the summation of valence value is zero). We also investigate thegenerative capacity and structural properties of these grammars.

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