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On Parikh slender context-free languages

2001
*
Theoretical Computer Science
*

In this paper Parikh

doi:10.1016/s0304-3975(00)00393-5
fatcat:rptfvqxqlbcofetape6aar5hyq
*slender**context*-*free**languages*are characterized. The characterization has diverse applications. ... In a recent paper we deÿned and studied Parikh*slender**languages*and showed that they can be used in simplifying ambiguity proofs of*context*-*free**languages*. ... Parikh*slender**context*-*free**languages*Before the characterization of Parikh*slender**context*-*free**languages*we need*one*lemma. Lemma 8. ...##
###
On a conjecture about slender context-free languages

1994
*
Theoretical Computer Science
*

.,

doi:10.1016/0304-3975(94)00042-5
fatcat:lutxwfiqwffdbf7shiyggszcga
*On*a conjecture about*slender**context*-*free**languages*, Theoretical Computer Science 132 (1994) 4277434. ... We prove that every*slender**context*-*free**language*is a union of paired loops, thus confirming a conjecture of Paun and Salomaa to appear. ... all*slender**context*-*free**languages*. ...##
###
Recognition of Linear-Slender Context-Free Languages by Real Time One-Way Cellular Automata
[chapter]

2015
*
Lecture Notes in Computer Science
*

A linear-

doi:10.1007/978-3-662-47221-7_19
fatcat:jnzhmozvwrg7xj5s5rto4ecuja
*slender**context*-*free**language*is a*context*-*free**language*whose number of words of length n is linear in n. ... Thanks to this characterization, we show that every linear-*slender**context*-*free**language*is recognizable by a real time*one*-way cellular automaton. ... A*context*-*free**language*is poly-*slender*if and only if it is bounded. ...##
###
Chomsky-Schützenberger Type Characterizations of Poly-Slender and Parikh Slender Context-Free Languages1 1Work supported by the Grants-in Aid for Scientific Research No. 1 0440034, Japan Society for the Promotion of Sciences and the Dirección General de Enseñanza Superior e Investigación Cientifica, SB 97-00110508

2004
*
Electronical Notes in Theoretical Computer Science
*

*context*-

*free*

*languages*. ... A similar characterization is obtained for Parikh

*slender*

*context*-

*free*

*languages*. ½ ... This improvment is based

*on*the same characterization of poly-

*slender*

*context*-

*free*

*languages*, by [8] via Theorem 2.1. ...

##
###
Length considerations in context-free languages

1997
*
Theoretical Computer Science
*

Thus, we present a length characterization for bounded

doi:10.1016/s0304-3975(96)00308-8
fatcat:bcsghpe6vrflfd262icx6kzije
*context*-*free**languages*. We then study*slender**context*-*free**languages*, i.e., those containing at most a constant number of words of each length. ... We first show that the*context*-*free**languages*for which the number of words of every length is bounded by a fixed polynomial are exactly the bounded*context*-*free**languages*in the sense of Ginsburg (1966 ... Hence, L(&) is a*slender*linear*language*. 0 Every*slender**context*-*free**language*consists of two parts:*one*, the regular part, and the other, the (more interesting)*context*-*free*part. ...##
###
On Parikh Slender Languages and Power Series

1996
*
Journal of computer and system sciences (Print)
*

As an application we get a new method for ambiguity proofs of

doi:10.1006/jcss.1996.0014
fatcat:4q5xjwiecrdobnuwbsp26xll3q
*context*-*free**languages*and a new proof of an earlier result of Autebert, Flajolet, and Gabarro concerning prefixes of infinite words. ] ... We define and study Parikh*slender**languages*and power series. A*language*is Parikh*slender*if the number of words in the*language*with the same Parikh vector is bounded from above. ... Suppose*on*the contrary that L 7* is an unambiguous*context*-*free**language*such that L c & R is Parikh*slender*, where R 7* is a regular*language*. (If L & R is Parikh*slender*the argument is similar.) ...##
###
A decision method for Parikh slenderness of context-free languages

1997
*
Discrete Applied Mathematics
*

Results concerning Pa&h

doi:10.1016/s0166-218x(96)00023-6
fatcat:vd6t5jsdovh35kjvvxqsqire4e
*slender**languages*can be applied in ambiguity proofs of*context*-*free**languages*. ... In this paper an algorithm is presented for deciding whether or not a given*context*-*free**language*is Parikh ... The decision method We proceed to decide whether or not a given*context*-*free**language*is Par&h*slender*. Suppose L&C* is a*context*-*free**language*. ...##
###
On differentiation functions, structure functions, and related languages of context-free grammars

2004
*
RAIRO - Theoretical Informatics and Applications
*

We present the basic properties of differentiation functions, especially we relate them to structure function of contextfree

doi:10.1051/ita:2004013
fatcat:lmb5bpsctzbffn36gmwy65doqu
*languages*and narrow grammars to*slender**languages*. ... We introduce the notion of a differentiation function of a*context*-*free*grammar which gives the number of terminal words that can be derived in a certain number of steps. ... (i) If L is a*slender**context*-*free*matrix*language*, then the*language*σ(L) is regular. (ii) If G is a narrow*context*-*free*grammar, then the*language*δ(G) is regular. Proof. ...##
###
Page 8508 of Mathematical Reviews Vol. , Issue 2002K
[page]

2002
*
Mathematical Reviews
*

*Context*-

*free*Parikh

*slender*lan- guages can be characterized as finite unions of simple Dyck loop

*languages*. ... .,

*context*-

*free*grammars where the applicability of rules is restricted. This allows non-

*context*-

*free*

*languages*to be generated while pre- serving many positive closure and decidability properties. ...

##
###
Page 517 of Mathematical Reviews Vol. , Issue 99a
[page]

1991
*
Mathematical Reviews
*

Summary: “We survey the main results concerning

*slender*lan- guages. We characterize*slender*regular and*context*-*free**languages*and show that*slenderness*is decidable for*context*-*free**languages*. ...*context*-*free**languages*. ...##
###
A characterization of poly-slender context-free languages

2000
*
RAIRO - Theoretical Informatics and Applications
*

We give a precise characterization of the kpoly-

doi:10.1051/ita:2000100
fatcat:u5cp7v5dancjvn6hw2rsdhf6wa
*slender**context*-*free**languages*. The well-known characterization of the k-poly-*slender*regular*languages*is an immediate consequence of ours. ... For a non-negative integer k, we say that a*language*L is k-poly-*slender*if the number of words of length n in L is of order O(n k ). ... For any poly-*slender**context*-*free**language*L, there exists a k 0 such that # L (n) = (n k ). ...##
###
Slender Siromoney matrix languages

2008
*
Information and Computation
*

In particular, it is shown that the

doi:10.1016/j.ic.2008.03.024
fatcat:2j5gwmvwejgkll4yslnlgcfdba
*slenderness*decision problem is decidable for Siromoney matrix grammars with*context*-*free*rules. ... Moreover, some closure and decidability questions for*slender*Siromoney matrix*languages*are discussed. ... Moreover, a*slender**context*-*free**language*can effectively be written as a finite union of properly 1-*slender**context*-*free**languages*. ...##
###
Page 1273 of Mathematical Reviews Vol. , Issue 99b
[page]

1991
*
Mathematical Reviews
*

We show a hierarchy of

*slender**languages*which is properly contained in the family of*context*-sensitive*languages*and which starts with the family of*slender**context*-*free**languages*, or*slender*regular ... Recently, it was proved that every*slender*regular*language*can be described by a finite union of terms of the form wv'w and every*slender**context*-*free**language*can be described by a finite union of terms ...##
###
Thin and slender languages

1995
*
Discrete Applied Mathematics
*

The present paper gives characterization results in the case of regular and

doi:10.1016/0166-218x(94)00014-5
fatcat:ptxvqnkktfawtateflcslo42c4
*context*-*free**languages*, as well as investigates decision problems. ... The paper investigates*languages*containing at most*one*word of every length, or a number of words bounded by a constant independent of the length. ... (The first*one*leads to*context*-*free*, the second to regular*languages*.) Case 1: a/b = c/d. ...##
###
Page 1198 of Mathematical Reviews Vol. , Issue 97B
[page]

1997
*
Mathematical Reviews
*

Then

*one*investigates*context*-*free*Parikh*slender**languages*, making use of results about algebraic series. The main result is the following: Suppose L C V* is a*context*-*free**language*. ... Summary: “There exists a regular (*context*-*free*) chain code picture*language*which is not described by any picture-unambiguous reg- ular (*context*-*free*)*language*. ...
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