Closure properties of certain classes of languages under generalized morphic replication

Z. Fang, J. S. Deogun

Research output: Contribution to journalArticle

Abstract

In this paper a new language operator, a generalized morphic replication, is introduced. Let Ω be a finite set of morphisms and reversal morphisms from ∑* into Δ*, and ω be in Ω*. A morphic replicator is defined as follows: for each x in ∑* define ω(x) to be h1(x) ... hm(x), where |ω| = m and ω = h1 ... hm. A generalized morphic replication extends ω to languages by ω(L) = {ω(x): x is in L} and to sets W of morphic replicators, where W ⊆ Ω*, W(x) = {ω(x): ω is in W} and W(L) = UW(x), where the union is taken over all x in L.It is shown that the class of languages accepted in real time by a non-deterministic reversal-bounded multitape Turing machine, the class of NP, and the class of the recursively enumerable sets, are all closed under the generalized morphic replication when the morphisms and the reversal morphisms are, respectively, linear-erasing, polynomial-erasing, and arbitrary.

Original languageEnglish (US)
Pages (from-to)325-329
Number of pages5
JournalComputer Journal
Volume31
Issue number4
DOIs
StatePublished - Aug 1 1988

Fingerprint

Turing machines
Closure Properties
Morphisms
Replication
Language
Reversal
Polynomials
language
Recursively Enumerable Set
Turing Machine
Finite Set
Union
Closed
Polynomial
Class
Arbitrary
Operator

ASJC Scopus subject areas

  • Computer Science(all)

Cite this

Closure properties of certain classes of languages under generalized morphic replication. / Fang, Z.; Deogun, J. S.

In: Computer Journal, Vol. 31, No. 4, 01.08.1988, p. 325-329.

Research output: Contribution to journalArticle

@article{2ffbd67aee1f4a67adb414a000720fcd,
title = "Closure properties of certain classes of languages under generalized morphic replication",
abstract = "In this paper a new language operator, a generalized morphic replication, is introduced. Let Ω be a finite set of morphisms and reversal morphisms from ∑* into Δ*, and ω be in Ω*. A morphic replicator is defined as follows: for each x in ∑* define ω(x) to be h1(x) ... hm(x), where |ω| = m and ω = h1 ... hm. A generalized morphic replication extends ω to languages by ω(L) = {ω(x): x is in L} and to sets W of morphic replicators, where W ⊆ Ω*, W(x) = {ω(x): ω is in W} and W(L) = UW(x), where the union is taken over all x in L.It is shown that the class of languages accepted in real time by a non-deterministic reversal-bounded multitape Turing machine, the class of NP, and the class of the recursively enumerable sets, are all closed under the generalized morphic replication when the morphisms and the reversal morphisms are, respectively, linear-erasing, polynomial-erasing, and arbitrary.",
author = "Z. Fang and Deogun, {J. S.}",
year = "1988",
month = "8",
day = "1",
doi = "10.1093/comjnl/31.4.325",
language = "English (US)",
volume = "31",
pages = "325--329",
journal = "Computer Journal",
issn = "0010-4620",
publisher = "Oxford University Press",
number = "4",

}

TY - JOUR

T1 - Closure properties of certain classes of languages under generalized morphic replication

AU - Fang, Z.

AU - Deogun, J. S.

PY - 1988/8/1

Y1 - 1988/8/1

N2 - In this paper a new language operator, a generalized morphic replication, is introduced. Let Ω be a finite set of morphisms and reversal morphisms from ∑* into Δ*, and ω be in Ω*. A morphic replicator is defined as follows: for each x in ∑* define ω(x) to be h1(x) ... hm(x), where |ω| = m and ω = h1 ... hm. A generalized morphic replication extends ω to languages by ω(L) = {ω(x): x is in L} and to sets W of morphic replicators, where W ⊆ Ω*, W(x) = {ω(x): ω is in W} and W(L) = UW(x), where the union is taken over all x in L.It is shown that the class of languages accepted in real time by a non-deterministic reversal-bounded multitape Turing machine, the class of NP, and the class of the recursively enumerable sets, are all closed under the generalized morphic replication when the morphisms and the reversal morphisms are, respectively, linear-erasing, polynomial-erasing, and arbitrary.

AB - In this paper a new language operator, a generalized morphic replication, is introduced. Let Ω be a finite set of morphisms and reversal morphisms from ∑* into Δ*, and ω be in Ω*. A morphic replicator is defined as follows: for each x in ∑* define ω(x) to be h1(x) ... hm(x), where |ω| = m and ω = h1 ... hm. A generalized morphic replication extends ω to languages by ω(L) = {ω(x): x is in L} and to sets W of morphic replicators, where W ⊆ Ω*, W(x) = {ω(x): ω is in W} and W(L) = UW(x), where the union is taken over all x in L.It is shown that the class of languages accepted in real time by a non-deterministic reversal-bounded multitape Turing machine, the class of NP, and the class of the recursively enumerable sets, are all closed under the generalized morphic replication when the morphisms and the reversal morphisms are, respectively, linear-erasing, polynomial-erasing, and arbitrary.

UR - http://www.scopus.com/inward/record.url?scp=0024064031&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0024064031&partnerID=8YFLogxK

U2 - 10.1093/comjnl/31.4.325

DO - 10.1093/comjnl/31.4.325

M3 - Article

AN - SCOPUS:0024064031

VL - 31

SP - 325

EP - 329

JO - Computer Journal

JF - Computer Journal

SN - 0010-4620

IS - 4

ER -