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Decision problems concerning algebraic series with noncommuting variables

  • Algebra of Languages
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Structures in Logic and Computer Science

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1261))

Abstract

Equivalence and rationality problems are shown to be decidable for algebraic series with noncommuting variables having bounded supports. As a tool, Parikh simplifying mappings are defined and studied.

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References

  1. Berstel, J. and Reutenauer, C.: Rational Series and Their Languages (Springer, Berlin, 1988).

    Google Scholar 

  2. Eilenberg, S.: Automata, Languages and Machines, Vol. A (Academic Press, New York, 1974).

    Google Scholar 

  3. Ginsburg, S.: The Mathematical Theory of Context-Free Languages (McGraw-Hill, New York, 1966).

    Google Scholar 

  4. Ginsburg, S. and Spanier, E. H.: Bounded regular sets, Proc. Amer. Math. Soc. 17 (1966) 1043–1049.

    Google Scholar 

  5. Harju, T. and Karhumäki, J.: The equivalence problem of multitape finite automata, Theoret. Comput. Sci. 78 (2) (1991) 347–355.

    Google Scholar 

  6. Honkala, J.: On images of algebraic series, J. Univ. Comput. Sci. 2 (4) (1996) 217–223.

    Google Scholar 

  7. Honkala, J.: On the equivalence problem of algebraic series with commuting variables, EATCS Bulletin 59 (1996) 157–162.

    Google Scholar 

  8. Kuich, W.: On the multiplicity equivalence problem for context-free grammars, in J. Karhumäki, H. Maurer and G. Rozenberg (eds.): Results and Trends in Theoretical Computer Science (Springer, Berlin, 1994) pp. 232–250.

    Google Scholar 

  9. W. Kuich, Semirings and formal power series: their relevance to formal languages and automata, in G. Rozenberg and A. Salomaa (eds.): Handbook of Formal Languages (Springer, Berlin, 1997), to appear.

    Google Scholar 

  10. Kuich, W. and Salomaa, A.: Semirings, Automata, Languages (Springer, Berlin, 1986).

    Google Scholar 

  11. Raz, D.: Deciding multiplicity equivalence for certain context-free languages, in G. Rozenberg and A. Salomaa (eds.): Developments in Language Theory (World Scientific, Singapore, 1994) pp. 18–29.

    Google Scholar 

  12. Raz, D.: Length considerations in context-free languages, Theoret. Comput. Sci., to appear.

    Google Scholar 

  13. Salomaa, A.: Formal Languages (Academic Press, New York, 1973).

    Google Scholar 

  14. Salomaa, A. and Soittola, M.: Automata-Theoretic Aspects of Formal Power Series (Springer, Berlin, 1978).

    Google Scholar 

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Jan Mycielski Grzegorz Rozenberg Arto Salomaa

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© 1997 Springer-Verlag Berlin Heidelberg

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Honkala, J. (1997). Decision problems concerning algebraic series with noncommuting variables. In: Mycielski, J., Rozenberg, G., Salomaa, A. (eds) Structures in Logic and Computer Science. Lecture Notes in Computer Science, vol 1261. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63246-8_17

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  • DOI: https://doi.org/10.1007/3-540-63246-8_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63246-7

  • Online ISBN: 978-3-540-69242-3

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