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Post Correspondence Problem with Partially Commutative Alphabets [chapter]

Barbara Klunder, Wojciech Rytter
2010 Lecture Notes in Computer Science  
In particular solvability is shown for the partially commutative PCP for two special cases: the binary case of PCP (denoted by PCP (2) ), and the case with one periodic morphism.  ...  We introduce a version of Post Correspondence Problem (PCP, in short) generalized to words over partially commutative alphabets.  ...  Acknowledgment The authors thank J. Leroux, S. Lasota and Eryk Kopczynski for helpful comments related to Lemma 8.  ... 
doi:10.1007/978-3-642-13089-2_30 fatcat:7mzgxiiy4zeatg3jrrbm6wg4mu

Page 3355 of Mathematical Reviews Vol. , Issue 2001E [page]

2001 Mathematical Reviews  
sets, and Post correspondence problem.  ...  In addition, a result on mutual invertibility of finite automata is given.” 2001¢:68109 68Q45 03D05 Turakainen, Paavo (FIN-OUL; Oulu) On the decidability of some problems concerning morphisms, regular  ... 

Flatwords and Post Correspondence Problem

Tero Harju, Marjo Lipponen, Alexandru Mateescu
1996 Theoretical Computer Science  
In this paper we introduce k-flatwords and investigate some of their properties. We also study the relationship between k-flatwords and the Post Correspondence Problem.  ...  The suitability of the Post Correspondence Problem for reduction arguments is due to the fact that in some sense the essence of computations is captured by PCP.  ...  Where is the borderline between decidability and undecidability in this case? Flat prime solutions of the Post Correspondence Problem We now return to the usual Post Correspondence Problem.  ... 
doi:10.1016/0304-3975(95)00092-5 fatcat:fcwv2jwguzc4tdwca3qamdqgxa

On post correspondence problem for letter monotonic languages

Vesa Halava, Jarkko Kari, Yuri Matiyasevich
2009 Theoretical Computer Science  
In other words, we prove that the Post Correspondence Problem is decidable if the solutions are restricted to be from this special language.  ...  This yields a nice example of an undecidable problem in integral matrices which cannot be directly proved undecidable using the traditional reduction from the Post Correspondence Problem.  ...  Acknowledgement The second author was supported by the Academy of Finland under grant 211967.  ... 
doi:10.1016/j.tcs.2009.01.040 fatcat:b63hqkgmvzaq7k62aw35o2fife

Computing Blocker Sets for the Regular Post Embedding Problem [chapter]

Pierre Chambart, Philippe Schnoebelen
2010 Lecture Notes in Computer Science  
Blocker and coblocker sets are regular languages involved in the algorithmic solution of the Regular Post Embedding Problem.  ...  We investigate the computability of these languages and related decision problems.  ...  Acknowledgements We thank Sylvain Schmitz for his numerous remarks and suggestions about this work.  ... 
doi:10.1007/978-3-642-14455-4_14 fatcat:axzobqizvnce7j6rnaisyn7l54

Decision Questions Concerning Semilinearity, Morphisms, and Commutation of Languages [chapter]

Tero Harju, Oscar Ibarra, Juhani Karhumäki, Arto Salomaa
2001 Lecture Notes in Computer Science  
We give examples of how this result can be used to show the decidability of certain problems concerning the equivalence of morphisms on languages.  ...  We show that if the languages defined by are effectively semilinear, then so are the languages defined by , and, hence, their emptiness problem is decidable.  ...  The equality set of and is defined to be ´ µ Û ¾ ¦ £ ´Ûµ ´Ûµ The problem whether ´ µ is undecidable for the equality sets of morphisms. This problem is known as the Post Correspondence Problem.  ... 
doi:10.1007/3-540-48224-5_48 fatcat:gvlbyixy75exfj72xib7zzybly

Page 2542 of Mathematical Reviews Vol. , Issue 83f [page]

1983 Mathematical Reviews  
This problem has led to a renewed interest in bounded delay codes and the Post correspondence problem, which are discussed in Chapter 4.  ...  DOL and OL systems are the topics of Chapter 5; in particular, a proof of the decidability of the DOL equivalence problem is given.  ... 

The Ehrenfeucht conjecture: a compactness claim for finitely generated free monoids

Juhani Karhumäki
1984 Theoretical Computer Science  
DOL languages, then the HDOL sequence eql:ivalence problem is decidable. Furthermore. we give examples of when the con jecture is known to hold.  ...  on Z* the equation g(x) = h(x) holds for all x in L if and only if it holds for all x in F.  ...  Acknowledgment This work could not exist without thz support of the Academy of Finland.  ... 
doi:10.1016/0304-3975(84)90004-5 fatcat:4vpzemym5zff7o2yrspf53vkyy

The undecidability of form equivalence for context-free and E0L forms

Valtteri Niemi
1984 Theoretical Computer Science  
This paper studies the decidability status of various equivalence problems in form theory. Most of our discussions concern the notion of a language form. We compare the form equivalence problem be!  ...  We prove that the form equivalence problem is undecidable for (a) context-free grammar forms, and (b) EOL forms. The proofs of these results are based on our investigations concerning language forms.  ...  . _ ' of the Post Correspondence Problem, where the CY'S and /3's m-t' nonempty words over the alphabet (a, hj. Two context-free grammars G, and G2 are defned in the proof, and it is shown tk A: !  ... 
doi:10.1016/0304-3975(84)90045-8 fatcat:dxldpzae6fcpfmuxtdbo42ty2e

Some Decision Problems Concerning Semilinearity and Commutation

Tero Harju, Oscar Ibarra, Juhani Karhumäki, Arto Salomaa
2002 Journal of computer and system sciences (Print)  
We give examples of how this result can be used to show the decidability of certain problems concerning the equivalence of morphisms on languages.  ...  We show that if the languages defined by M are effectively semilinear, then so are the languages defined by M c , and, hence, their emptiness problem is decidable.  ...  This problem is known as the Post Correspondence Problem. Let F be a family of mappings between word monoids, and let L be a language family.  ... 
doi:10.1006/jcss.2002.1836 fatcat:jbmvukk7o5d67dhmzhza3u47gi

Conferences WORDS, years 1997-2017: Open Problems and Conjectures

Jean Néraud
2018 Bulletin of the European Association for Theoretical Computer Science  
The contribution by Jean Néraud collects and classifies several open problems and conjectures presented during more than 20 years.  ...  Words is a well-established international conference devoted to all aspects of Combinatorics on Words.  ...  The Post Correspondence Problem The famous Post Correspondence Problem (PCP for short) consists in asking, given two morphisms h, g, whether or not the equation h(x) = g(x) has a solution distinct of the  ... 
dblp:journals/eatcs/Neraud18 fatcat:mnojery2ifgj7odnkzakfwrr2m

Test sets for morphisms with bounded delay

Christian Choffrut, Juhani Karhumäki
1985 Discrete Applied Mathematics  
In other words, we show that for each language L over a finite alphabet there exists a finite subset F of L such that for arbitrary morphisms h and g having deciphering delay bounded by p, the equation  ...  We prove the Ehrenfeucht Conjecture for morphisms having deciphering delay bounded by p.  ...  Acknowledgement The authors are grateful to the referees for careful reading of the manuscript. Note added in proof  ... 
doi:10.1016/0166-218x(85)90063-0 fatcat:ymxoiyz43zd43otju7hizwqilu

Extension of the decidability of the marked PCP to instances with unique blocks

Vesa Halava, Tero Harju, Juhani Karhumäki, Michel Latteux
2007 Theoretical Computer Science  
In the Post Correspondence Problem (PCP) an instance (h, g) consists of two morphisms h and g, and the problem is to determine whether or not there exists a nonempty word w such that h(w) = g(w).  ...  These results establish a new and larger class of decidable instances of the PCP, including the class of marked instances.  ...  Acknowledgements The first author was Supported by the Academy of Finland under grant 208414. The third author was supported by the Academy of Finland under grant 44087.  ... 
doi:10.1016/j.tcs.2007.03.024 fatcat:mmdmwvphlbcn3l5t64t6uzurlm

Page 3208 of Mathematical Reviews Vol. , Issue 98E [page]

1998 Mathematical Reviews  
Summary: “Colored Gauss codes and tangent codes correspond- ing to curves both on the plane and on the torus are studied. Language-theoretic characterizations of sets of codes are proved.  ...  {For the entire collection see MR 98d:68004. } Friedrich Otto (D-KSSL; Kassel) 98e:68144 68Q45 03D05 Lipponen, Marjo (FIN-TURK; Turku) On F-prime solutions of the Post correspondence problem.  ... 

Dominoes over a free monoid

Karel Culik, Tero Harju
1982 Theoretical Computer Science  
Dominoes over a free monoid and operations on them are introduced. Related algebraic systems and their applications to decidability problems about morphisms on free monoilds are studied.  ...  to pr~e that the unity problem is undecidable for FI, we shall consider instances of the Post correspondence problem, PCP in short, Let is a regular set.  ...  Introduction Decidability and other problems concerning morphisms on free monoids have been extensively studied recently, see survey [2] .  ... 
doi:10.1016/0304-3975(82)90070-6 fatcat:lhbazq4vmfg65jv7godjfdbzcu
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