Semilinearity of Families of Languages

2020 ◽  
pp. 1-20
Author(s):  
Oscar H. Ibarra ◽  
Ian McQuillan
Keyword(s):  
Closure Properties ◽  
The Family ◽  
Grammar Systems

Techniques are developed for creating new and general language families of only semilinear languages, and for showing families only contain semilinear languages. It is shown that for language families [Formula: see text] that are semilinear full trios, the smallest full AFL containing [Formula: see text] that is also closed under intersection with languages in [Formula: see text] (where [Formula: see text] is the family of languages accepted by [Formula: see text]s augmented with reversal-bounded counters), is also semilinear. If these closure properties are effective, this also immediately implies decidability of membership, emptiness, and infiniteness for these general families. From the general techniques, new grammar systems are given that are extensions of well-known families of semilinear full trios, whereby it is implied that these extensions must only describe semilinear languages. This also implies positive decidability properties for the new systems. Some characterizations of the new families are also given.

scholarly journals COMPLETELY REDUCIBLE SETS

2013 ◽  
Vol 23 (04) ◽  
pp. 915-941 ◽  
Author(s):  
DOMINIQUE PERRIN
Keyword(s):  
Closure Properties ◽  
Linear Representations ◽  
Complete Reducibility ◽  
The Family ◽  
Syntactic Representation ◽  
Completely Reducible ◽  
Rational Sets ◽  
Cyclic Sets

We study the family of rational sets of words, called completely reducible and which are such that the syntactic representation of their characteristic series is completely reducible. This family contains, by a result of Reutenauer, the submonoids generated by bifix codes and, by a result of Berstel and Reutenauer, the cyclic sets. We study the closure properties of this family. We prove a result on linear representations of monoids which gives a generalization of the result concerning the complete reducibility of the submonoid generated by a bifix code to sets called birecurrent. We also give a new proof of the result concerning cyclic sets.

Some properties of two families of classes of life distributions

2002 ◽  
Vol 39 (03) ◽  
pp. 581-589 ◽  
Author(s):  
N. R. Mohan ◽  
S. Ravi
Keyword(s):  
Discrete Analogue ◽  
Closure Properties ◽  
The Family ◽  
Life Distributions

We study the closure properties of the family ℒ(α) of classes of life distributions introduced by Lin (1998) under general compounding. We define a discrete analogue of this family and study some properties.

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-FREE GRAMMARS WITH LINKED NONTERMINALS

2007 ◽  
Vol 18 (06) ◽  
pp. 1271-1282 ◽  
Author(s):  
ANDREAS KLEIN ◽  
MARTIN KUTRIB
Keyword(s):  
Generative Capacity ◽  
Closure Properties ◽  
Rewriting Systems ◽  
Rewriting System ◽  
The Family ◽  
Infinite Degree ◽  
New Type ◽  
Equivalent Systems ◽  
Context Free ◽  
Context Free Grammars

We introduce a new type of finite copying parallel rewriting system, i. e., grammars with linked nonterminals, which extend the generative capacity of context-free grammars. They can be thought of as having sentential forms where some instances of a nonterminal may be linked. The context-free-like productions replace a nonterminal together with its connected instances. New links are only established between symbols of the derived subforms. A natural limitation is to bound the degree of synchronous rewriting. We present an infinite degree hierarchy of separated language families with the property that degree one characterizes the family of regular and degree two the family of context-free languages. Furthermore, the hierarchy is a refinement of the known hierarchy of finite copying rewriting systems. Several closure properties known from equivalent systems are summarized.

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.

scholarly journals MACROS, Iterated Substitution and Lindenmayer AFLs

1973 ◽  
Vol 2 (18) ◽  
Author(s):  
Arto Salomaa
Keyword(s):  
Lindenmayer Systems ◽  
Closure Properties ◽  
Open Problems ◽  
Weak Closure ◽  
The Family ◽  
Context Free

The notion of a K-iteration grammar, where K is a family of languages, provides a uniform framework for discussing the various language families obtained by context-free Lindenmayer systems. It is shown that the family of languages generated by K-iteration grammars possesses strong closure properties under the assumption that K itself has certain weak closure properties. Along these lines, the notion of a hyper-AFL is introduced and some open problems are posed.

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.

scholarly journals On certain classes of close-to-convex functions

1993 ◽  
Vol 16 (2) ◽  
pp. 329-336 ◽  
Author(s):  
Khalida Inayat Noor
Keyword(s):  
Unit Disk ◽  
Convex Functions ◽  
Hadamard Product ◽  
Univalent Functions ◽  
Integral Operators ◽  
Closure Properties ◽  
The Family

A functionf, analytic in the unit diskEand given by ,f(z)=z+∑k=2∞anzkis said to be in the familyKnif and only ifDnfis close-to-convex, whereDnf=z(1−z)n+1∗f,n∈N0={0,1,2,…}and∗denotes the Hadamard product or convolution. The classesKnare investigated and some properties are given. It is shown thatKn+1⫅KnandKnconsists entirely of univalent functions. Some closure properties of integral operators defined onKnare given.

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