Regular and linear permutation languages

2018 ◽  
Vol 52 (2-3-4) ◽  
pp. 219-234 ◽  
Author(s):  
Grzegorz Madejski
Keyword(s):  
Similar Model ◽  
Closure Properties ◽  
Generative Power ◽  
Sentential Form ◽  
Context Free

A permutation rule is a non-context-free rule whose both sides contain the same multiset of symbols with at least one non-terminal. This rule does not add or substitute any symbols in the sentential form, but can be used to change the order of neighbouring symbols. In this paper, we consider regular and linear grammars extended with permutation rules. It is established that the generative power of these grammars relies not only on the length of the permutation rules, but also whether we allow or forbid the usage of erasing rules. This is quite surprising, since there is only one non-terminal in sentential forms of derivations for regular or linear grammars. Some decidability problems and closure properties of the generated families of languages are investigated. We also show a link to a similar model which mixes the symbols: grammars with jumping derivation mode.

scholarly journals A Pumping Lemma for Permitting Semi-Conditional Languages

2019 ◽  
Vol 30 (01) ◽  
pp. 73-92
Author(s):  
Zsolt Gazdag ◽  
Krisztián Tichler ◽  
Erzsébet Csuhaj-Varjú
Keyword(s):  
Open Problem ◽  
Generative Power ◽  
Context Sensitive ◽  
Sentential Form ◽  
Pumping Lemma ◽  
Context Free ◽  
Context Free Grammars

Permitting semi-conditional grammars (pSCGs) are extensions of context-free grammars where each rule is associated with a word [Formula: see text] and such a rule can be applied to a sentential form [Formula: see text] only if [Formula: see text] is a subword of [Formula: see text]. We consider permitting generalized SCGs (pgSCGs) where each rule [Formula: see text] is associated with a set of words [Formula: see text] and [Formula: see text] is applicable only if every word in [Formula: see text] occurs in [Formula: see text]. We investigate the generative power of pgSCGs with no erasing rules and prove a pumping lemma for their languages. Using this lemma we show that pgSCGs are strictly weaker than context-sensitive grammars. This solves a long-lasting open problem concerning the generative power of pSCGs. Moreover, we give a comparison of the generating power of pgSCGs and that of forbidding random context grammars with no erasing rules.

scholarly journals Generative Power and Closure Properties of Watson-Crick Grammars

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Nurul Liyana Mohamad Zulkufli ◽  
Sherzod Turaev ◽  
Mohd Izzuddin Mohd Tamrin ◽  
Azeddine Messikh
Keyword(s):  
Proper Subset ◽  
Computational Power ◽  
Closure Properties ◽  
Generative Power ◽  
Context Sensitive ◽  
Closure Operations ◽  
The Family ◽  
Grammar Rules ◽  
Almost All ◽  
Context Free

We defineWK linear grammars, as an extension of WK regular grammars with linear grammar rules, andWK context-free grammars, thus investigating their computational power and closure properties. We show that WK linear grammars can generate some context-sensitive languages. Moreover, we demonstrate that the family of WK regular languages is the proper subset of the family of WK linear languages, but it is not comparable with the family of linear languages. We also establish that the Watson-Crick regular grammars are closed under almost all of the main closure operations.

ON COMPETENCE IN CD GRAMMAR SYSTEMS WITH PARALLEL REWRITING

2007 ◽  
Vol 18 (06) ◽  
pp. 1425-1439 ◽  
Author(s):  
MAURICE H. TER BEEK ◽  
ERZSÉBET CSUHAJ-VARJÚ ◽  
GYÖRGY VASZIL ◽  
MARKUS HOLZER
Keyword(s):  
Generative Power ◽  
Sentential Form ◽  
Grammar Systems ◽  
Context Free

We continue our investigation of the generative power of cooperating distributed grammar systems (CDGSs), using the previously introduced ≤k-, =k-, and ≥k-competence-based cooperation strategies and context-free components that rewrite the sentential form in a parallel manner. This leads to new characterizations of the languages generated by (random context) ET0L systems and recurrent programmed grammars.

WHEN CHURCH-ROSSER BECOMES CONTEXT FREE

2007 ◽  
Vol 18 (06) ◽  
pp. 1293-1302 ◽  
Author(s):  
MARTIN KUTRIB ◽  
ANDREAS MALCHER
Keyword(s):  
Linear Time ◽  
Membership Problem ◽  
Closure Properties ◽  
Context Free Language ◽  
Arithmetic Hierarchy ◽  
Context Free ◽  
Free Language

We investigate the intersection of Church-Rosser languages and (strongly) context-free languages. The intersection is still a proper superset of the deterministic context-free languages as well as of their reversals, while its membership problem is solvable in linear time. For the problem whether a given Church-Rosser or context-free language belongs to the intersection we show completeness for the second level of the arithmetic hierarchy. The equivalence of Church-Rosser and context-free languages is Π1-complete. It is proved that all considered intersections are pairwise incomparable. Finally, closure properties under several operations are investigated.

PUZZLE GRAMMARS AND CONTEXT-FREE ARRAY GRAMMARS

1991 ◽  
Vol 05 (05) ◽  
pp. 663-676 ◽  
Author(s):  
M. NIVAT ◽  
A. SAOUDI ◽  
K. G. SUBRAMANIAN ◽  
R. SIROMONEY ◽  
V. R. DARE
Keyword(s):  
Membership Problem ◽  
Generative Power ◽  
New Model ◽  
Regular Control ◽  
Emptiness Problem ◽  
Np Complete ◽  
Context Free ◽  
Rewriting Rules

We introduce a new model for generating finite, digitized, connected pictures called puzzle grammars and study its generative power by comparison with array grammars. We note how this model generalizes the classical Chomskian grammars and study the effect of direction-independent rewriting rules. We prove that regular control does not increase the power of basic puzzle grammars. We show that for basic and context-free puzzle grammars, the membership problem is NP-complete and the emptiness problem is undecidable.

scholarly journals Closure properties of static Watson-Crick linear and context-free grammars

2020 ◽  
Author(s):  
Aqilahfarhana Abdul Rahman ◽  
Wan Heng Fong ◽  
Nor Haniza Sarmin ◽  
Sherzod Turaev
Keyword(s):  
Closure Properties ◽  
Context Free ◽  
Context Free Grammars

Set Automata

2016 ◽  
Vol 27 (02) ◽  
pp. 187-214 ◽  
Author(s):  
Martin Kutrib ◽  
Andreas Malcher ◽  
Matthias Wendlandt
Keyword(s):  
Finite Automata ◽  
Point Of View ◽  
Storage Medium ◽  
Deterministic Finite Automaton ◽  
Closure Properties ◽  
Language Class ◽  
Trade Offs ◽  
Double Exponential ◽  
Order Of Magnitude ◽  
Context Free

We consider the model of deterministic set automata which are basically deterministic finite automata equipped with a set as an additional storage medium. The basic operations on the set are the insertion of elements, the removing of elements, and the test whether an element is in the set. We investigate the computational power of deterministic set automata and compare the language class accepted with the context-free languages and classes of languages accepted by queue automata. As result the incomparability to all classes considered is obtained. Furthermore, we examine the closure properties under several operations. Then we show that deterministic set automata may be an interesting model from a practical point of view by proving that their regularity problem as well as the problems of emptiness, finiteness, infiniteness, and universality are decidable. Finally, the descriptional complexity of deterministic and nondeterministic set automata is investigated. A conversion procedure that turns a deterministic set automaton accepting a regular language into a deterministic finite automaton is developed which leads to a double exponential upper bound. This bound is proved to be tight in the order of magnitude by presenting also a double exponential lower bound. In contrast to these recursive bounds we obtain non-recursive trade-offs when nondeterministic set automata are considered.

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