Undecidability of infinite post correspondence problem for instances of size 8

Jing Dong; Qinghui Liu

RAIRO - Theoretical Informatics and Applications (2012)

  • Volume: 46, Issue: 3, page 451-457
  • ISSN: 0988-3754

Abstract

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The infinite Post Correspondence Problem (ωPCP) was shown to be undecidable by Ruohonen (1985) in general. Blondel and Canterini [Theory Comput. Syst. 36 (2003) 231–245] showed that ωPCP is undecidable for domain alphabets of size 105, Halava and Harju [RAIRO–Theor. Inf. Appl. 40 (2006) 551–557] showed that ωPCP is undecidable for domain alphabets of size 9. By designing a special coding, we delete a letter from Halava and Harju’s construction. So we prove that ωPCP is undecidable for domain alphabets of size 8.

How to cite

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Dong, Jing, and Liu, Qinghui. "Undecidability of infinite post correspondence problem for instances of size 8." RAIRO - Theoretical Informatics and Applications 46.3 (2012): 451-457. <http://eudml.org/doc/222079>.

@article{Dong2012,
abstract = {The infinite Post Correspondence Problem (ωPCP) was shown to be undecidable by Ruohonen (1985) in general. Blondel and Canterini [Theory Comput. Syst. 36 (2003) 231–245] showed that ωPCP is undecidable for domain alphabets of size 105, Halava and Harju [RAIRO–Theor. Inf. Appl. 40 (2006) 551–557] showed that ωPCP is undecidable for domain alphabets of size 9. By designing a special coding, we delete a letter from Halava and Harju’s construction. So we prove that ωPCP is undecidable for domain alphabets of size 8.},
author = {Dong, Jing, Liu, Qinghui},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {ωPCP; semi-Thue system; undecidable; theory of computation; PCP; undecidability},
language = {eng},
month = {8},
number = {3},
pages = {451-457},
publisher = {EDP Sciences},
title = {Undecidability of infinite post correspondence problem for instances of size 8},
url = {http://eudml.org/doc/222079},
volume = {46},
year = {2012},
}

TY - JOUR
AU - Dong, Jing
AU - Liu, Qinghui
TI - Undecidability of infinite post correspondence problem for instances of size 8
JO - RAIRO - Theoretical Informatics and Applications
DA - 2012/8//
PB - EDP Sciences
VL - 46
IS - 3
SP - 451
EP - 457
AB - The infinite Post Correspondence Problem (ωPCP) was shown to be undecidable by Ruohonen (1985) in general. Blondel and Canterini [Theory Comput. Syst. 36 (2003) 231–245] showed that ωPCP is undecidable for domain alphabets of size 105, Halava and Harju [RAIRO–Theor. Inf. Appl. 40 (2006) 551–557] showed that ωPCP is undecidable for domain alphabets of size 9. By designing a special coding, we delete a letter from Halava and Harju’s construction. So we prove that ωPCP is undecidable for domain alphabets of size 8.
LA - eng
KW - ωPCP; semi-Thue system; undecidable; theory of computation; PCP; undecidability
UR - http://eudml.org/doc/222079
ER -

References

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  1. V.D. Blondel and V. Canterini, Undecidable problems for probabilistic automata of fixed dimension. Theor. Comput. Syst.36 (2003) 231–245.  Zbl1039.68061
  2. A. Ehrenfeucht, J. Karhumäki and G. Rozenberg, The (generalized) Post Correspondence Problem with lists consisting of two words is decidable. Theoret. Comput. Sci.21 (1982) 119–144.  Zbl0493.68076
  3. V. Halava and T. Harju, Undecibability of infinite Post Correspondence Problem for instances of size 9. RAIRO–Theor. Inf. Appl.40 (2006) 551–557.  Zbl1114.03035
  4. V. Halava, T. Harju and M. Hirvensalo, Binary (generalized) Post Correspondence Problem. Theoret. Comput. Sci.276 (2002) 183–204.  Zbl1023.03038
  5. Y. Matiyasevich and G. Sénizergues, Decision problems for semi-Thue systems with a few rules. Theoret. Comput. Sci.330 (2005) 145–169.  Zbl1078.03033
  6. E. Post, A variant of a recursively unsolvable problem. Bull. Amer. Math. Soc.52 (1946) 264–268.  Zbl0063.06329
  7. K. Ruohonen, Reversible machines and Posts Correspondence Problem for biprefix morphisms. J. Inform. Process. Cybernet.EIK21 (1985) 579–595.  Zbl0604.68057

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