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Post Correspondence Problem with Partially Commutative Alphabets
[chapter]

2010
*
Lecture Notes in Computer Science
*

In particular solvability is shown for

doi:10.1007/978-3-642-13089-2_30
fatcat:7mzgxiiy4zeatg3jrrbm6wg4mu
*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. ...##
###
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

1996
*
Theoretical Computer Science
*

In this paper we introduce k-flatwords

doi:10.1016/0304-3975(95)00092-5
fatcat:fcwv2jwguzc4tdwca3qamdqgxa
*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*. ...##
###
On post correspondence problem for letter monotonic languages

2009
*
Theoretical Computer Science
*

In other words, we prove that

doi:10.1016/j.tcs.2009.01.040
fatcat:b63hqkgmvzaq7k62aw35o2fife
*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. ...##
###
Computing Blocker Sets for the Regular Post Embedding Problem
[chapter]

2010
*
Lecture Notes in Computer Science
*

Blocker

doi:10.1007/978-3-642-14455-4_14
fatcat:axzobqizvnce7j6rnaisyn7l54
*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. ...##
###
Decision Questions Concerning Semilinearity, Morphisms, and Commutation of Languages
[chapter]

2001
*
Lecture Notes in Computer Science
*

We give examples

doi:10.1007/3-540-48224-5_48
fatcat:gvlbyixy75exfj72xib7zzybly
*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*. ...##
###
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

1984
*
Theoretical Computer Science
*

DOL languages, then

doi:10.1016/0304-3975(84)90004-5
fatcat:4vpzemym5zff7o2yrspf53vkyy
*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. ...##
###
The undecidability of form equivalence for context-free and E0L forms

1984
*
Theoretical Computer Science
*

This paper studies

doi:10.1016/0304-3975(84)90045-8
fatcat:dxldpzae6fcpfmuxtdbo42ty2e
*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: ! ...##
###
Some Decision Problems Concerning Semilinearity and Commutation

2002
*
Journal of computer and system sciences (Print)
*

We give examples

doi:10.1006/jcss.2002.1836
fatcat:jbmvukk7o5d67dhmzhza3u47gi
*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. ...##
###
Conferences WORDS, years 1997-2017: Open Problems and Conjectures

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*...

##
###
Test sets for morphisms with bounded delay

1985
*
Discrete Applied Mathematics
*

In other words, we show that for each language L over a finite alphabet there exists a finite subset F

doi:10.1016/0166-218x(85)90063-0
fatcat:ymxoiyz43zd43otju7hizwqilu
*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 ...##
###
Extension of the decidability of the marked PCP to instances with unique blocks

2007
*
Theoretical Computer Science
*

In

doi:10.1016/j.tcs.2007.03.024
fatcat:mmdmwvphlbcn3l5t64t6uzurlm
*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. ...##
###
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

1982
*
Theoretical Computer Science
*

Dominoes over a free monoid

doi:10.1016/0304-3975(82)90070-6
fatcat:lhbazq4vmfg65jv7godjfdbzcu
*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] . ...
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