Remarks on external contextual grammars with selection

Dassow, Jürgen

doi:10.1016/j.tcs.2020.07.028

Cited by 3 publications

(4 citation statements)

References 9 publications

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“…Additionally, other subfamilies of regular languages could be taken into consideration. Recently, external contextual grammars have been investigated where the selection languages are ideals or codes [5,6]. This reseach could be extended to internal contextual grammars with ideals or codes as selection languages.…”

Section: Discussionmentioning

confidence: 99%

Relations of contextual grammars with strictly locally testable selection languages

Dassow,

Truthe

2023

RAIRO-Theor. Inf. Appl.

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We continue the research on the generative capacity of contextual grammars where contexts are adjoined around whole words (externally) or around subwords (internally) which belong to special regular selection languages. All languages generated by contextual grammars where all selection languages are elements of a certain subregular language family form again a language family. We investigate the computational capacity of contextual grammars with strictly locally testable selection languages and compare those families to families which are based on finite, monoidal, nilpotent, combinational, definite, suffix-closed, ordered, commutative, circular, non-counting, power-separating, or union-free languages. With these results, also an open problem regarding ordered and non-counting selection languages is solved.

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Section: Discussionmentioning

confidence: 99%

Relations of contextual grammars with strictly locally testable selection languages

Dassow,

Truthe

2023

RAIRO-Theor. Inf. Appl.

Self Cite

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show abstract

“…Additionally, other subfamilies of regular languages could be taken into consideration. Recently, by Jürgen Dassow, external contextual grammars have been investigated where the selection languages are ideals or codes ( [6,7]). This reseach could be extended to internal contextual grammars with ideals or codes as selection languages.…”

Section: Discussionmentioning

confidence: 99%

“…Theorem 2. 7 The inclusion relations presented in Figure 1 hold. An arrow from an entry X to an entry Y depicts the proper inclusion X ⊂ Y ; if two families are not connected by a directed path, then they are incomparable.…”

Section: Lemma 26mentioning

confidence: 94%

On the Generative Capacity of Contextual Grammars with Strictly Locally Testable Selection Languages

Dassow

Truthe

2022

Electron. Proc. Theor. Comput. Sci.

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We continue the research on the generative capacity of contextual grammars where contexts are adjoined around whole words (externally) or around subwords (internally) which belong to special regular selection languages. All languages generated by contextual grammars where all selection languages are elements of a certain subregular language family form again a language family. We investigate contextual grammars with strictly locally testable selection languages and compare those families to families which are based on finite, monoidal, nilpotent, combinational, definite, suffixclosed, ordered, commutative, circular, non-counting, power-separating, or union-free languages.

show abstract

“…Additionally, other subfamilies of regular languages could be taken into consideration. Recently, in [6,7], external contextual grammars have been investigated where the selection languages are ideals or codes. This reseach could be extended to internal contextual grammars with ideals or codes as selection languages.…”

Section: Conclusion and Further Workmentioning

confidence: 99%

Merging two Hierarchies of Internal Contextual Grammars with Subregular Selection

Truthe

2023

Electron. Proc. Theor. Comput. Sci.

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In this paper, we continue the research on the power of contextual grammars with selection languages from subfamilies of the family of regular languages. In the past, two independent hierarchies have been obtained for external and internal contextual grammars, one based on selection languages defined by structural properties (finite, monoidal, nilpotent, combinational, definite, ordered, noncounting, power-separating, suffix-closed, commutative, circular, or union-free languages), the other one based on selection languages defined by resources (number of non-terminal symbols, production rules, or states needed for generating or accepting them). In a previous paper, the language families of these hierarchies for external contextual grammars were compared and the hierarchies merged. In the present paper, we compare the language families of these hierarchies for internal contextual grammars and merge these hierarchies.

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Remarks on external contextual grammars with selection

Cited by 3 publications

References 9 publications

Relations of contextual grammars with strictly locally testable selection languages

Relations of contextual grammars with strictly locally testable selection languages

On the Generative Capacity of Contextual Grammars with Strictly Locally Testable Selection Languages

Merging two Hierarchies of Internal Contextual Grammars with Subregular Selection

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