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Improved Undecidability Results on the Emptiness Problem of Probabilistic and Quantum Cut-Point Languages

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SOFSEM 2007: Theory and Practice of Computer Science (SOFSEM 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4362))

Abstract

We give constructions of small probabilistic and MO-type quantum automata that have undecidable emptiness problem for the cut-point languages.

Supported by the Academy of Finland under grant 208797.

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References

  1. Blondel, V.D., Canterini, V.: Undecidable Problems for Probabilistic Automata of Fixed Dimension. Theory of Computing Systems 36, 231–245 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  2. Blondel, V.D., Jeandel, E., Koiran, P., Portier, N.: Decidable and Undecidable Problems About Quantum Automata. SIAM Journal of Computing 34(6), 1464–1473 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  3. Derksen, H., Jeandel, E., Koiran, P.: Quantum Automata and Algebraic Groups. Journal of Symbolic Computation 39, 357–371 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  4. Claus, V.: Some Remarks on PCP(k) and Related Problems. Bulletin of EATCS 12, 54–61 (1980)

    Google Scholar 

  5. Eilenberg, S.: Automata, Languages, and Machines. Academic Press, San Diego (1974)

    MATH  Google Scholar 

  6. Halava, V., Harju, T., Hirvensalo, M.: Lowering the Undecidability Bounds for Integer Matrices Using Claus Instances of the PCP. TUCS Technical Report 766 (2006)

    Google Scholar 

  7. Harju, T., Karhumäki, J.: Morphisms. Springer, Heidelberg (1997)

    Google Scholar 

  8. Hirvensalo, M.: Quantum Computing, 2nd edn. Springer, Heidelberg (2003)

    Google Scholar 

  9. Matiyasevich, Y., Sénizergues, G.: Decision Problems for Semi-Thue Systems with a Few Rules. Theoretical Computer Science 330(1), 145–169 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  10. Moore, C., Crutchfield, J.P.: Quantum Automata and Quantum Grammars. Theoretical Computer Science 237, 275–306 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  11. Paz, A.: Introduction to Probabilistic Automata. Academic Press, San Diego (1971)

    MATH  Google Scholar 

  12. Renegar, J.: On the Complexity and Geometry of the First-Order Theory of the Reals. Journal of Symbolic Computation 13(3), 255–352 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  13. Sheng, Y.: Regular Languages. Springer, Heidelberg (1997)

    Google Scholar 

  14. Świerczkowski, S.: On a Free Group of Rotations of the Euclidean Space. Indagationes Mathematicae 20, 376–378 (1958)

    Google Scholar 

  15. Świerczkowski, S.: A Class of Free Rotation Groups. Indagationes Mathematicae (N.S.) 5(2), 221–226 (1994)

    Article  MATH  Google Scholar 

  16. Turakainen, P.: Generalized Automata and Stochastic Languages. Proceedings of American Mathematical Society 21, 209–303 (1969)

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Turku, FIN-20014 Turku, Finland

    Mika Hirvensalo

  2. TUCS – Turku Centre for Computer Science,  

    Mika Hirvensalo

Authors
  1. Mika Hirvensalo
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Editor information

Jan van Leeuwen Giuseppe F. Italiano Wiebe van der Hoek Christoph Meinel Harald Sack František Plášil

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Hirvensalo, M. (2007). Improved Undecidability Results on the Emptiness Problem of Probabilistic and Quantum Cut-Point Languages. In: van Leeuwen, J., Italiano, G.F., van der Hoek, W., Meinel, C., Sack, H., Plášil, F. (eds) SOFSEM 2007: Theory and Practice of Computer Science. SOFSEM 2007. Lecture Notes in Computer Science, vol 4362. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69507-3_25

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  • DOI: https://doi.org/10.1007/978-3-540-69507-3_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69506-6

  • Online ISBN: 978-3-540-69507-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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