scholarly journals On the Expressive Power of Stateless Ordered Restart-Delete Automata

2021 ◽  
Author(s):  
Friedrich Otto
Keyword(s):  
Expressive Power ◽  
Single Letter ◽  
Regular Languages ◽  
Descriptional Complexity ◽  
Context Free

AbstractStateless ordered restart-delete automata (stl-ORD-automata) are studied. These are obtained from the stateless ordered restarting automata (stl-ORWW-automata) by introducing an additional restart-delete operation, which, based on the surrounding context, deletes a single letter. While the stl-ORWW-automata accept the regular languages, we show that the swift stl-ORD-automata yield a characterization for the class of context-free languages. Here a stl-ORD-automaton is called swift if it can move its window to any position after performing a restart. We also study the descriptional complexity of swift stl-ORD-automata and relate them to limited context restarting automata.

RESTRICTED SETS OF TRAJECTORIES AND DECIDABILITY OF SHUFFLE DECOMPOSITIONS

2005 ◽  
Vol 16 (05) ◽  
pp. 897-912 ◽  
Author(s):  
MICHAEL DOMARATZKI ◽  
KAI SALOMAA
Keyword(s):  
Regular Languages ◽  
Decomposition Problem ◽  
Open Question ◽  
Free Set ◽  
Context Free ◽  
Undecidability Result

The decidability of the shuffle decomposition problem for regular languages is a long standing open question. We consider decompositions of regular languages with respect to shuffle along a regular set of trajectories and obtain positive decidability results for restricted classes of trajectories. Also we consider decompositions of unary regular languages. Finally, we establish in the spirit of the Dassow-Hinz undecidability result an undecidability result for regular languages shuffled along a fixed linear context-free set of trajectories.

scholarly journals Descriptional Complexity of Bounded Regular Languages

2016 ◽  
pp. 138-152 ◽  
Author(s):  
Andrea Herrmann ◽  
Martin Kutrib ◽  
Andreas Malcher ◽  
Matthias Wendlandt
Keyword(s):  
Regular Languages ◽  
Descriptional Complexity

CONJUNCTIVE GRAMMARS GENERATE NON-REGULAR UNARY LANGUAGES

2008 ◽  
Vol 19 (03) ◽  
pp. 597-615 ◽  
Author(s):  
ARTUR JEŻ
Keyword(s):  
Negative Answer ◽  
The Body ◽  
Regular Languages ◽  
Natural Numbers ◽  
Open Problems ◽  
Conjunctive Grammars ◽  
Unary Languages ◽  
Context Free ◽  
Conjunctive Grammar ◽  
Context Free Grammars

Conjunctive grammars, introduced by Okhotin, extend context-free grammars by an additional operation of intersection in the body of any production of the grammar. Several theorems and algorithms for context-free grammars generalize to the conjunctive case. Okhotin posed nine open problems concerning those grammars. One of them was a question, whether a conjunctive grammars over a unary alphabet generate only regular languages. We give a negative answer, contrary to the conjectured positive one, by constructing a conjunctive grammar for the language {a4n : n ∈ ℕ}. We also generalize this result: for every set of natural numbers L we show that {an : n ∈ L} is a conjunctive unary language, whenever the set of representations in base-k system of elements of L is regular, for arbitrary k.

scholarly journals BOND-FREE LANGUAGES: FORMALIZATIONS, MAXIMALITY AND CONSTRUCTION METHODS

2005 ◽  
Vol 16 (05) ◽  
pp. 1039-1070 ◽  
Author(s):  
LILA KARI ◽  
STAVROS KONSTANTINIDIS ◽  
PETR SOSÍK
Keyword(s):  
Polynomial Time ◽  
Structural Characterization ◽  
Regular Languages ◽  
Important Case ◽  
Similarity Relation ◽  
Construction Methods ◽  
Large Sets ◽  
Code Property ◽  
Context Free

The problem of negative design of DNA languages is addressed, that is, properties and construction methods of large sets of words that prevent undesired bonds when used in DNA computations. We recall a few existing formalizations of the problem and then define the property of sim-bond-freedom, where sim is a similarity relation between words. We show that this property is decidable for context-free languages and polynomial-time decidable for regular languages. The maximality of this property also turns out to be decidable for regular languages and polynomial-time decidable for an important case of the Hamming similarity. Then we consider various construction methods for Hamming bond-free languages, including the recently introduced method of templates, and obtain a complete structural characterization of all maximal Hamming bond-free languages. This result is applicable to the θ-k-code property introduced by Jonoska and Mahalingam.

scholarly journals Descriptional complexity of context-free grammar forms

1993 ◽  
Vol 112 (2) ◽  
pp. 277-289 ◽  
Author(s):  
Erzsébet Csuhaj-Varjú ◽  
Alica Kelemenová
Keyword(s):  
Context Free Grammar ◽  
Descriptional Complexity ◽  
Context Free

Regular patterns, regular languages and context-free languages

2010 ◽  
Vol 110 (24) ◽  
pp. 1114-1119 ◽  
Author(s):  
Sanjay Jain ◽  
Yuh Shin Ong ◽  
Frank Stephan
Keyword(s):  
Regular Languages ◽  
Context Free ◽  
Regular Patterns

scholarly journals Positive Neural Networks in Discrete Time Implement Monotone-Regular Behaviors

2015 ◽  
Vol 27 (12) ◽  
pp. 2623-2660 ◽  
Author(s):  
Tom J. Ameloot ◽  
Jan Van den Bussche
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Discrete Time ◽  
Expressive Power ◽  
Regular Languages ◽  
Regular Behavior ◽  
Multiple Input

We study the expressive power of positive neural networks. The model uses positive connection weights and multiple input neurons. Different behaviors can be expressed by varying the connection weights. We show that in discrete time and in the absence of noise, the class of positive neural networks captures the so-called monotone-regular behaviors, which are based on regular languages. A finer picture emerges if one takes into account the delay by which a monotone-regular behavior is implemented. Each monotone-regular behavior can be implemented by a positive neural network with a delay of one time unit. Some monotone-regular behaviors can be implemented with zero delay. And, interestingly, some simple monotone-regular behaviors cannot be implemented with zero delay.

scholarly journals REPRESENTATIONS AND CHARACTERIZATIONS OF LANGUAGES IN CHOMSKY HIERARCHY BY MEANS OF INSERTION-DELETION SYSTEMS

2008 ◽  
Vol 19 (04) ◽  
pp. 859-871 ◽  
Author(s):  
GHEORGHE PĂUN ◽  
MARIO J. PÉREZ-JIMÉNEZ ◽  
TAKASHI YOKOMORI
Keyword(s):  
Dna Computing ◽  
Research Direction ◽  
Regular Languages ◽  
Turing Computability ◽  
Chomsky Hierarchy ◽  
Recursively Enumerable ◽  
Enumerable Language ◽  
Language L ◽  
Context Free

Insertion-deletion operations are much investigated in linguistics and in DNA computing and several characterizations of Turing computability and characterizations or representations of languages in Chomsky hierarchy were obtained in this framework. In this note we contribute to this research direction with a new characterization of this type, as well as with representations of regular and context-free languages, mainly starting from context-free insertion systems of as small as possible complexity. For instance, each recursively enumerable language L can be represented in a way similar to the celebrated Chomsky-Schützenberger representation of context-free languages, i.e., in the form L = h(L(γ) ∩ D), where γ is an insertion system of weight (3, 0) (at most three symbols are inserted in a context of length zero), h is a projection, and D is a Dyck language. A similar representation can be obtained for regular languages, involving insertion systems of weight (2,0) and star languages, as well as for context-free languages – this time using insertion systems of weight (3, 0) and star languages.

scholarly journals A Novel method to represent Access Tree structure by Context Free Grammar with and-or graph in Key Policy based Attribute based Encryption

2018 ◽  
Vol 7 (4.10) ◽  
pp. 396
Author(s):  
K. Senthil Kumar ◽  
D. Malathi
Keyword(s):  
Access Control ◽  
Control Structure ◽  
Expressive Power ◽  
Third Party ◽  
Efficient Manner ◽  
Context Free Grammar ◽  
Fine Grained ◽  
Attribute Based Encryption ◽  
Key Policy ◽  
Context Free

Important and sensitivity data of users in a third party managed internet or cloud always pose various security as well as privacy issues. Attribute-based encryption (ABE) is a pleasant trend in the literature which addresses above problem in an efficient way, and provides data security and fine-grained access control in a decentralized manner,. Key-policy attribute-based encryption (KP-ABE) is an important type of ABE, in which user can decrypt his message with a set of attributes and private keys are embedded with a access control structure which defines which cipher text  an user can be allowed to decrypt. In this paper we use a probabilistic context free grammar with an And-Or structure to represent access control structure. And-Or graph has high expressive power hence access control structure can be represented in an efficient manner.  

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