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Block-stochastic matrices and associated finite-state languages

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Summary

Finite automata are considered whose transition matrix is blockstochastic. The block-stochastic structure defines an equivalence relation among states of the automata. The implications of this relation are investigated, especially with respect to the languages accepted in the states of the automata.

Zusammenfassung

Es werden Endliche Automaten betrachtet, deren Übergangsmatrix block-stochastisch ist. Die block-stochastische Struktur definiert eine Äquivalenzbeziehung zwischen Zuständen des Automaten. Die Bedeutung und Auswirkung dieser Relation wird untersucht, und zwar insbesonders in Hinsicht auf die in den einzelnen Zuständen des Automaten angenommenen Sprachen.

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References

  1. Haynsworth, E. V.: Applications of a Theorem on Partitioned Matrices. —Journ. of Research of the National Bureau of Standards — B. Mathematics and Matheamtical Physics 62 B (1959), p. 73–78.

    Google Scholar 

  2. Walk, K.: Entropy and Testability of Context-Fre Languages. Paper presented at the IFIP Working Conference on Language Description Languages. Vienna (1964). IBM Techn. Report No. 25.5.008.

  3. Chomsky, N., Miller, G. A.: Finite State Languages — Information and Control 1 (1957–1958), p. 91–112.

    Google Scholar 

  4. Wieland, H.: Unzerlegbare nicht negative Matrizen. — Math. Z. 52 (1950), p. 642–648.

    Google Scholar 

  5. Brauer, A.: Limits for the Characteristic Roots of a Matrix IV. — Duke Math. Journ. 19 (1952), p. 75.

    Google Scholar 

  6. Zürmuhl, R.: Matrizen und ihre technischen Anwendungen. — Springer-Verlag, Berlin-Göttingen-Heidelberg, (1961).

    Google Scholar 

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Authors and Affiliations

  1. I.B.M. Labor Wien, Parkring 10, 1010, Wien, Österreich

    W. Kuich &  K. Walk

Authors
  1. W. Kuich
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  2. K. Walk
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Kuich, W., Walk, K. Block-stochastic matrices and associated finite-state languages. Computing 1, 50–61 (1966). https://doi.org/10.1007/BF02235852

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  • DOI: https://doi.org/10.1007/BF02235852

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