SOME REMARKS ON THE HAIRPIN COMPLETION

2010 ◽  
Vol 21 (05) ◽  
pp. 859-872 ◽  
Author(s):  
FLORIN MANEA ◽  
VICTOR MITRANA ◽  
TAKASHI YOKOMORI
Keyword(s):  
Regular Language ◽  
Regular Languages ◽  
Decision Problems ◽  
Strict Sense ◽  
Closure Properties ◽  
New Words ◽  
The Family

We consider several problems regarding the iterated or non-iterated hairpin completion of some subclasses of regular languages. Thus we obtain a characterization of the class of regular languages as the weak-code images of the k-hairpin completion of center-disjoint k-locally testable languages in the strict sense. This result completes two results from [3] and [11]. Then we investigate some decision problems and closure properties of the family of the iterated hairpin completion of singleton languages. Finally, we discuss some algorithms regarding the possibility of computing the values of k such that the non-iterated or iterated k-hairpin completion of a given regular language does not produce new words.

scholarly journals Iterative arrays with self-verifying communication cell

2020 ◽  
Author(s):  
Martin Kutrib
Keyword(s):  
Cellular Automata ◽  
Time Complexity ◽  
Input Word ◽  
Closure Properties ◽  
Multiplicative Factor ◽  
Computational Capacity ◽  
The Family ◽  
Computation Path

Abstract We study the computational capacity of self-verifying iterative arrays ($${\text {SVIA}}$$ SVIA ). A self-verifying device is a nondeterministic device whose nondeterminism is symmetric in the following sense. Each computation path can give one of the answers yes, no, or do not know. For every input word, at least one computation path must give either the answer yes or no, and the answers given must not be contradictory. It turns out that, for any time-computable time complexity, the family of languages accepted by $${\text {SVIA}}$$ SVIA s is a characterization of the so-called complementation kernel of nondeterministic iterative array languages, that is, languages accepted by such devices whose complementation is also accepted by such devices. $${\text {SVIA}}$$ SVIA s can be sped-up by any constant multiplicative factor as long as the result does not fall below realtime. We show that even realtime $${\text {SVIA}}$$ SVIA are as powerful as lineartime self-verifying cellular automata and vice versa. So they are strictly more powerful than the deterministic devices. Closure properties and various decidability problems are considered.

Context-sensitive languages and G-automata

2017 ◽  
Vol 27 (02) ◽  
pp. 237-249
Author(s):  
Rachel Bishop-Ross ◽  
Jon M. Corson ◽  
James Lance Ross
Keyword(s):  
Word Problem ◽  
Finitely Generated ◽  
Closure Properties ◽  
Finitely Generated Group ◽  
Context Sensitive ◽  
The Family

For a given finitely generated group [Formula: see text], the type of languages that are accepted by [Formula: see text]-automata is determined by the word problem of [Formula: see text] for most of the classical types of languages. We observe that the only exceptions are the families of context-sensitive and recursive languages. Thus, in general, to ensure that the language accepted by a [Formula: see text]-automaton is in the same classical family of languages as the word problem of [Formula: see text], some restriction must be imposed on the [Formula: see text]-automaton. We show that restricting to [Formula: see text]-automata without [Formula: see text]-transitions is sufficient for this purpose. We then define the pullback of two [Formula: see text]-automata and use this construction to study the closure properties of the family of languages accepted by [Formula: see text]-automata without [Formula: see text]-transitions. As a further consequence, when [Formula: see text] is the product of two groups, we give a characterization of the family of languages accepted by [Formula: see text]-automata in terms of the families of languages accepted by [Formula: see text]- and [Formula: see text]-automata. We also give a construction of a grammar for the language accepted by an arbitrary [Formula: see text]-automaton and show how to get a context-sensitive grammar when [Formula: see text] is finitely generated with a context-sensitive word problem and the [Formula: see text]-automaton is without [Formula: see text]-transitions.

GENERATIVE CAPACITY OF SUBREGULARLY TREE CONTROLLED GRAMMARS

2010 ◽  
Vol 21 (05) ◽  
pp. 723-740 ◽  
Author(s):  
JÜRGEN DASSOW ◽  
RALF STIEBE ◽  
BIANCA TRUTHE
Keyword(s):  
Regular Language ◽  
Regular Languages ◽  
Derivation Tree ◽  
Generative Capacity ◽  
The Family ◽  
Context Free ◽  
Context Free Grammars

Tree controlled grammars are context-free grammars where the associated language only contains those terminal words which have a derivation where the word of any level of the corresponding derivation tree belongs to a given regular language. We present some results on the power of such grammars where we restrict the regular languages to some known subclasses of the family of regular languages.

A Note on Pf(k) – Parsable Languages

1991 ◽  
Vol 14 (3) ◽  
pp. 283-286
Author(s):  
Tudor Balanescu ◽  
Marian Gheorghe
Keyword(s):  
Homomorphic Image ◽  
Regular Language ◽  
Regular Languages ◽  
Infinite Hierarchy ◽  
The Family ◽  
Pumping Lemma

This paper investigates the class of regular languages which are pf(k) – parsable. It is shown that k induces an infinite hierarchy in the family of regular languages and that every regular language is a homomorphic image of a pf(O) -parsable language. A pumping lemma for pf – parsable languages is also provided.

Two-Sided Strictly Locally Testable Languages

2021 ◽  
Vol 180 (1-2) ◽  
pp. 29-51
Author(s):  
Markus Holzer ◽  
Martin Kutrib ◽  
Friedrich Otto
Keyword(s):  
Binary Relation ◽  
Regular Languages ◽  
Decision Problems ◽  
Closure Properties ◽  
Positive Data ◽  
Proper Subclass ◽  
Testable Language ◽  
Even Linear Languages

A two-sided extension of strictly locally testable languages is presented. In order to determine membership within a two-sided strictly locally testable language, the input must be scanned from both ends simultaneously, whereby it is synchronously checked that the factors read are correlated with respect to a given binary relation. The class of two-sided strictly locally testable languages is shown to be a proper subclass of the even linear languages that is incomparable to the regular languages with respect to inclusion. Furthermore, closure properties of the class of two-sided strictly locally testable languages and decision problems are studied. Finally, it is shown that two-sided strictly k-testable languages are learnable in the limit from positive data.

SHUFFLE DECOMPOSITIONS OF REGULAR LANGUAGES

2002 ◽  
Vol 13 (06) ◽  
pp. 799-816 ◽  
Author(s):  
C. CÂMPEANU ◽  
K. SALOMAA ◽  
S. VÁGVÖLGYI
Keyword(s):  
Regular Language ◽  
Regular Languages ◽  
Equivalence Relations ◽  
Closure Properties ◽  
Context Free

We study the shuffle quotient operation and introduce equivalence relations it defines with respect to a (regular) language. Corresponding to an arbitrary shuffle decomposition we construct a normalized decomposition that is defined in terms of maximal languages. Using closure properties of the normalized decompositions we show that for certain subclasses of regular languages we can effectively decide whether or not the language has a non-trivial shuffle decomposition. We show that shuffle decomposition is undecidable for context-free languages.

Union-Freeness Revisited — Between Deterministic and Nondeterministic Union-Free Languages

2021 ◽  
pp. 1-23
Author(s):  
Benedek Nagy
Keyword(s):  
Normal Form ◽  
Regular Language ◽  
Regular Expression ◽  
Finite Automata ◽  
Finite Union ◽  
Regular Languages ◽  
Regular Expressions ◽  
Closure Properties ◽  
Language Class ◽  
Union Operation

Union-free expressions are regular expressions without using the union operation. Consequently, (nondeterministic) union-free languages are described by regular expressions using only concatenation and Kleene star. The language class is also characterised by a special class of finite automata: 1CFPAs have exactly one cycle-free accepting path from each of their states. Obviously such an automaton has exactly one accepting state. The deterministic counterpart of such class of automata defines the deterministic union-free (d-union-free, for short) languages. In this paper [Formula: see text]-free nondeterministic variants of 1CFPAs are used to define n-union-free languages. The defined language class is shown to be properly between the classes of (nondeterministic) union-free and d-union-free languages (in case of at least binary alphabet). In case of unary alphabet the class of n-union-free languages coincides with the class of union-free languages. Some properties of the new subregular class of languages are discussed, e.g., closure properties. On the other hand, a regular expression is in union normal form if it is a finite union of union-free expressions. It is well known that every regular expression can be written in union normal form, i.e., all regular languages can be described as finite unions of (nondeterministic) union-free languages. It is also known that the same fact does not hold for deterministic union-free languages, that is, there are regular languages that cannot be written as finite unions of d-union-free languages. As an important result here we show that every regular language can be defined by a finite union of n-union-free languages. This fact also allows to define n-union-complexity of regular languages.

AN EFFICIENT ALGORITHM TO TEST WHETHER A BINARY AND PROLONGEABLE REGULAR LANGUAGE IS GEOMETRICAL

2009 ◽  
Vol 20 (04) ◽  
pp. 763-774 ◽  
Author(s):  
JEAN-MARC CHAMPARNAUD ◽  
JEAN PHILIPPE DUBERNARD ◽  
HADRIEN JEANNE
Keyword(s):  
Discrete Geometry ◽  
Efficient Algorithm ◽  
Regular Language ◽  
Practical Interest ◽  
Regular Languages ◽  
Regular Case ◽  
Deterministic Automaton ◽  
Model Based ◽  
Temporal Validation ◽  
The Family

Our aim is to present an efficient algorithm that checks whether a binary regular language is geometrical or not, based on specific properties of its minimal deterministic automaton. Geometrical languages have been introduced in the framework of off-line temporal validation of real-time softwares. Actually, validation can be achieved through both a model based on regular languages and a model based on discrete geometry. Geometrical languages are intended to develop a link between these two models. The regular case is of practical interest regarding to implementation features, which motivates the design of an efficient geometricity test addressing the family of regular languages.

ON LANGUAGES FACTORIZING THE FREE MONOID

1996 ◽  
Vol 06 (04) ◽  
pp. 413-427 ◽  
Author(s):  
MARCELLA ANSELMO ◽  
ANTONIO RESTIVO
Keyword(s):  
General Result ◽  
Regular Language ◽  
Regular Expression ◽  
Free Monoid ◽  
Complete Characterization ◽  
Regular Languages ◽  
Combinatorial Characterization

A language X⊂A* is called factorizing if there exists a language Y⊂A* such that XY = A* This work was partially supported by ESPRIT-EBRA project ASMICS contact 6317 and project 40% MURST “Algoritmi, Modelli di Calcolo e Strutture Informative”. and the product is unambiguous. First we give a combinatorial characterization of factorizing languages. Further we prove that it is decidable whether a regular language X is factorizing and we construct an automaton recognizing the corresponding language Y. For finite languages we show that it suffices to consider words of bounded length. A complete characterization of factorizing languages with three words and explicit regular expression for the corresponding language Y are also given. Finally we prove a more general result stating that, given two regular languages X and T, it is decidable whether there exists a language Y such that XY=T and the product is unambiguous.

RECOGNIZABLE PICTURE LANGUAGES

1992 ◽  
Vol 06 (02n03) ◽  
pp. 241-256 ◽  
Author(s):  
DORA GIAMMARRESI ◽  
ANTONIO RESTIVO
Keyword(s):  
Two Dimensional ◽  
Closure Properties ◽  
One Dimensional ◽  
New Family ◽  
The Family ◽  
Emptiness Problem ◽  
Picture Languages ◽  
Local Languages

The purpose of this paper is to propose a new notion of recognizability for picture (two-dimensional) languages extending the characterization of one-dimensional recognizable languages in terms of local languages and alphabetic mappings. We first introduce the family of local picture languages (denoted by LOC) and, in particular, prove the undecidability of the emptiness problem. Then we define the new family of recognizable picture languages (denoted by REC). We study some combinatorial and language theoretic properties of REC such as ambiguity, closure properties or undecidability results. Finally we compare the family REC with the classical families of languages recognized by four-way automata.

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