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On the equivalence problem for binary DOL systems

Juhani Karhumäki
1981 Information and Control  
It is shown that to test whether two D O L sequences in 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.  ... 
doi:10.1016/s0019-9958(81)90367-3 fatcat:m3trvdu6wfbzpfzo5mrxmxqq5m

On infinite words obtained by iterating morphisms

Karel Culik, Arto Salomaa
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.  ... 
doi:10.1016/0304-3975(82)90013-5 fatcat:4gnho4vienbp3a2kaqp42xswra

On D0L systems with finite axiom sets

Juha Honkala
2003 Acta Cybernetica  
We give a new solution 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] ).  ... 
dblp:journals/actaC/Honkala03 fatcat:hu2ef4hd2jbu3oh4qlpmbkamu4

On a public-key cryptosystem based on iterated morphisms and substitutions

Arto Salomaa, Sheng Yu
1986 Theoretical Computer Science  
We also discuss 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.  ... 
doi:10.1016/0304-3975(86)90099-x fatcat:escscmw67fechpwx3tjnfy7qiq

Life and death in Markov deterministic tabled OL systems

H. Jürgensen, D. Matthews, D. Wood
1981 Information and Control  
We prove that expected cell-distribution and expected growth 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.  ... 
doi:10.1016/s0019-9958(81)90618-5 fatcat:p3pezd56azgl7iyzrjlvuqlxym

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

Juha Honkala
1994 Theoretical Computer Science  
., 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] ).  ... 
doi:10.1016/0304-3975(94)90043-4 fatcat:dj5ljqjqonfpfolw44gq3erive

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

Juhani Karhumäki
1979 Theoretical Computer Science  
Restricted versions of 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.  ... 
doi:10.1016/0304-3975(79)90025-2 fatcat:sd66fo2fcbdw7nqtxlsjzdgpii

On the decidability of homomorphism equivalence for languages

K. Culik, Arto Salomaa
1978 Journal of computer and system sciences (Print)  
In 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.  ... 
doi:10.1016/0022-0000(78)90002-8 fatcat:vg57dlei5rbfhouy7bhklipa3u

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

Keijo Ruohonen
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).  ... 
doi:10.1016/0022-0000(81)90020-9 fatcat:gyi4jkjdsjc2jdeefmrafkk4b4
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