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On the equivalence problem for binary DOL systems

1981
*
Information and Control
*

It is shown that to test whether two D O L sequences in

doi:10.1016/s0019-9958(81)90367-3
fatcat:m3trvdu6wfbzpfzo5mrxmxqq5m
*the*binary case coincide it is enough to test whether four first words of these sequences are*the*same.*The*result is optimal. ... ACKNOWLEDGMENTS*The*author is grateful to Dr. M. Linna*for*useful comments and to*the*Academy of Finland*for**the*excellent working conditions under which this research was carried out. ... INTRODUCTION*For*several years*the*DOL*equivalence**problem*was*one*of*the*most interesting open*problems*within*the*theory of formal languages.*The**problem*is as follows. ...##
###
On infinite words obtained by iterating morphisms

1982
*
Theoretical Computer Science
*

*The*papet investigates infinite words, and sets of them, associated with DOL and

*DTOL*

*systems*. &fain emphasis is

*on*characterization and decidability results. ...

*The*ba.sic open

*problem*is

*the*decidability of

*the*o-word

*equivalence*

*problem*; several reductions of this

*problem*are presented. Section 4 deals with limit languages of

*DTOL*

*systems*. ...

*For*instance,

*the*ordinary DOL sequence

*equivalence*

*problem*and

*the*corresponding

*problem*

*for*infinite words are related, as seen in Section 3 below. ...

##
###
On D0L systems with finite axiom sets

2003
*
Acta Cybernetica
*

We give a new solution

dblp:journals/actaC/Honkala03
fatcat:hu2ef4hd2jbu3oh4qlpmbkamu4
*for**the*language*equivalence**problem*of DOL*systems*with finite axiom sets by using*the*decidability of*the**equivalence**problem*of finite valued transducers*on*HDTOL languages proved ... Introduction*The*language*equivalence**problem**for*DOL*systems*with finite axiom sets was solved in [4] .*The**problem*turns out to be much more difficult*for*DFOL*systems*than*for*DOL*systems*. ... In that respect it resembles*the*solutions of*the*DOL*equivalence**problem*based*on*Hilbert's basis theorem which also are short but do not,*for*example, give any bounds*for**the**problem*(see [3] ). ...##
###
On a public-key cryptosystem based on iterated morphisms and substitutions

1986
*
Theoretical Computer Science
*

We also discuss

doi:10.1016/0304-3975(86)90099-x
fatcat:escscmw67fechpwx3tjnfy7qiq
*the*desirable properties of*the*underlying*DTOL**system*such as different types of backward determinism and*the*role of growth. ...*The**system*is very flexible in many respects,*for*instance, as regards*the*plaintext blocksize. 0304-3975/86/$3.50 © 1986, Elsevier Science Publishers B.V. (North-Holland) 284 A. Salomaa, S. Yu ... Sheng Yu was visiting*the*University of Turku during*the*spring term of 1986. We want to thank*the*Academy of Finland*for*a grant making possible this visit. ...##
###
Life and death in Markov deterministic tabled OL systems

1981
*
Information and Control
*

We prove that expected cell-distribution and expected growth

doi:10.1016/s0019-9958(81)90618-5
fatcat:p3pezd56azgl7iyzrjlvuqlxym
*equivalence*are decidable, that*the*question of whether or not a Markov*DTOL**system*generates a dead word is*equivalent*to an open question ...*for*Z-rational series, and that it is decidable whether or not a given word survives in a given propagating Markov*DTOL**system*. ... In Section 4*the*question of whether or not a Markov*DTOL**system*generates a dead word is shown to be*equivalent*to a long-standing open*problem**for*Z-rational series. ...##
###
Page 4680 of Mathematical Reviews Vol. , Issue 83k
[page]

1983
*
Mathematical Reviews
*

*The*limit language decision

*problem*

*for*

*DTOL*

*systems*is

*the*

*problem*of deciding whether,

*for*two such

*systems*G, and G,, lim(L(G,))=lim(L(G,)). ... An algorithm

*for*this conjecture yields an algorithm

*for*

*the*DOL sequence

*equivalence*

*problem*.

*The*conjecture implies that

*the*limit language

*equivalence*

*problem*is decidable

*for*DOL

*systems*. ...

##
###
Page 4456 of Mathematical Reviews Vol. , Issue 82j
[page]

1982
*
Mathematical Reviews
*

*The*

*problem*occurs in

*the*context of

*systems*G=(2,9, {ao,---,a,—,}), in which § is a set of homomorphisms g;

*on*=* and a,;€=*.

*The*special cases G=(2, {80,---,8m—1},@) are

*DTOL*

*systems*of rank m. ... Finally, given automata @ ,, @, over 3, let G,, G, be

*the*

*equivalent*

*DTOL*

*systems*of Lemma 2. ...

##
###
Page 1005 of Mathematical Reviews Vol. 56, Issue 3
[page]

1978
*
Mathematical Reviews
*

., 11; Fri8, I. 7335

*The*decidability of*the**equivalence**problem**for*DOL-*systems*. Information and Control 35 (1977), no. 1, 20-39. ... Theorem 2 shows that this notion of determinism is more general than*the*normal*one**for*OL*systems*(DOL), but less powerful than*the*table-driven deterministic*one*(*DTOL*), i.c., DOLS QDOLSDTOL. ...##
###
Page 1221 of Mathematical Reviews Vol. , Issue 83c
[page]

1983
*
Mathematical Reviews
*

{

*For**the*entire collection see MR 80a:68005. } H. Jiirgensen (Zb| 435:68059) Ruohonen, Keijo 83c:68098*The*decidability of*the*DOL-*DTOL**equivalence**problem*. J. Comput. ... Lange, Klaus-Jérn 83c:68096*Equivalence*of adult languages and extensions*for**DTOL**systems*. Inform. and Control 47 (1980), no. 2, 107-112. ...##
###
On generalized DT0L systems and their fixed points

1994
*
Theoretical Computer Science
*

.,

doi:10.1016/0304-3975(94)90043-4
fatcat:dj5ljqjqonfpfolw44gq3erive
*On*generalized*DTOL**systems*and their fixed points, Theoretical Computer Science 127 (1994) 269-286. ... We call*the*least fixed points of such pairs generalized*DTOL*languages and study their basic properties. ...*The*sequence*equivalence*and language*equivalence**problems*are decidable*for*DOL*systems*(see [12] ). ...##
###
Page 7064 of Mathematical Reviews Vol. , Issue 2003i
[page]

2003
*
Mathematical Reviews
*

This is

*one*of*the*deepest results concerning morphisms of free monoids. Another deep result is*the*decidability of*the*sequence*equivalence**problem**for**DTOL**systems*[see K. Culik, II and J. ... In this note we discuss three generalizations of these*problems*.*The*first*one*is*the**DTOL*w-sequence*equivalence**problem*.*The*decidability status of this*problem*remains open. ...##
###
On commutative DT0L systems

1979
*
Theoretical Computer Science
*

Restricted versions of

doi:10.1016/0304-3975(79)90025-2
fatcat:sd66fo2fcbdw7nqtxlsjzdgpii
*DTOL**systems*, so-called commutative*DTOL**systems*, are considered. In these*systems**the*length of a word derived is independent of*the*order of tables used. ... Moreover, this approach makes it possible to give new (and slightly generalized) proofs*for*some undecidability results concerning*DTOL*functions. ... Acknowledgment*The*author is grateful to Professor Arto Salomaa*for*useful comments. ...##
###
On the decidability of homomorphism equivalence for languages

1978
*
Journal of computer and system sciences (Print)
*

In

doi:10.1016/0022-0000(78)90002-8
fatcat:vg57dlei5rbfhouy7bhklipa3u
*the*case of DOL*systems*, we can reduce either*one*of these*problem*to*the*other; cf. [3] . This reduction does not work*for**DTOL**systems*. ... Note also that*the**equivalence**problem**for**DTOL*languages is known to be undecidable but,*the**equivalence**problem**for**DTOL*sequences remains open. ... ACKNOWLEDGMENT*The*authors are grateful to J. L. Richier*for*discovering an error in an earlier version of*the*proof of*the*main Theorem 4.2 and*for*proposing how to overcome it. ...##
###
Page 4896 of Mathematical Reviews Vol. , Issue 80M
[page]

1980
*
Mathematical Reviews
*

*Systems*Man Cybernet. 8 (1978), no. 11, 829-833, Picture segmentation is

*one*of

*the*central

*problems*of image processing. ... Horst Reichel (Magdeburg) Karhumaki, Juhani 80m:68075

*On*commutative

*DTOL*

*systems*. Theoret. Comput. Sci. 9 (1979), no. 2, 207-220. ...

##
###
The decidability of the DOL-DTOL equivalence problem

1981
*
Journal of computer and system sciences (Print)
*

*The*proof is based

*on*

*the*decidability of

*the*DOL

*equivalence*

*problem*and a powerful result of Berstel's and Nielsen's [ 1 ] concerning DOL growth sequences. ...

*The*language generated by a

*DTOL*

*system*H is denoted by L(H), i.e., we will always assume that L(H) is infinite (finiteness and membership

*problems*are decidable

*for*

*DTOL*languages, too). ...

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