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International Colloquium on Automata, Languages, and Programming

ICALP 1985: Automata, Languages and Programming pp 71–79Cite as

On total regulators generated by derivation relations

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 194))

Abstract

A derivation relation is a total regulator on Σ* if for every language L \(\subseteq\) Σ*, the set of all words derivable from L is a regular language. We show that for a wide class of derivation relations \(= \mathop = \limits_P^* > , = \mathop = \limits_P^* > \) is a total regulator on Σ* if and only if it is a well-quasi-order (wqo) on Σ*. Using wqo theory, we give a characterization of all non-erasing pure context-free (OS) derivation relations which are total regulators.

extended abstract

The authors gratefully acknowledge the support of NSF grants IST-8317918 and MCS-8110430, and the Austrian Bundesministerium fuer Wissenschaft und Forschung. Part of this work was conducted while the third author visited the Institutes for Information Processing at the Technical University of Graz and the other part while the first author visited the University of Denver. We would like to thank our respective host institutions for these generous invitations.

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References

  1. J.M. Autebert, J. Beauquier, L. Boasson, M. Nivat, Quelques problems ouverts en theorie des languages algebriques, RAIRO Inf. Theor. 13 (4) (1979) 363–378.

    Google Scholar 

  2. C. Choffrut, K. Culik II, On extendibility of unavoidable sets, Dis. Appl. Math., 9 (1984) 125–137.

    Article  Google Scholar 

  3. J. H. Conway, Regular Algebra and Finite Machines (Chapman & Hall, London, 1971) pp. 63–64.

    Google Scholar 

  4. N. Dershowitz, Orderings for term-rewriting systems, Theor. Comp. Sci. 17 (1982) 279–301.

    Article  Google Scholar 

  5. A. Ehrenfeucht, D. Haussler, G. Rozenberg, On regularity of context-free languages, Theor. Comp. Sci. 27 (1983) 311–332.

    Article  Google Scholar 

  6. L. H. Haines, On free monoids partially ordered by embedding, J. Combin. Th. 6 (1969) 94–98.

    Google Scholar 

  7. M. A. Harrison, Introduction to Formal Language Theory (Addison-Wesley, Reading, MA. 1978).

    Google Scholar 

  8. G. Higman, Ordering by divisibility in abstract algebras, Proc. London Math. Soc. 3 (2) (1952) 326–336.

    Google Scholar 

  9. J.B. Kruskal, The theory of well-quasi ordering: A frequently discovered concept, J. Combin. Theory (Ser. A) 13 (1972) 297–305.

    Article  Google Scholar 

  10. M. Latteux, G. Rozenberg, Commutative one-counter languages are regular, J. Comp. Sys. Sci. 29 (1984) 54–57.

    Article  Google Scholar 

  11. J. van Leeuwen, Effective constructions in well-partially-ordered monoids, Discrete Math., 21 (1978) 237–252.

    Article  Google Scholar 

  12. M. Main, An infinite squarefree co-CFL, Inf Proc. Let., to appear.

    Google Scholar 

  13. K. Ruohonen, A note on off-line machines with ‘Brownian’ input heads, Disc. App. Math. 9 (1984) 69–75.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Institutes for Information Processing, Technical University of Graz, A-8010, Graz, Austria

    W. Bucher, A. Ehrenfeucht & D. Haussler

  2. Department of Computer Science, University of Colorado, 80302, Boulder, Colorado, USA

    A. Ehrenfeucht

  3. Department of Mathematics and Computer Science, University of Denver, 80208, Denver, Colorado, USA

    D. Haussler

Authors
  1. W. Bucher
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  2. A. Ehrenfeucht
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  3. D. Haussler
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Wilfried Brauer

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© 1985 Springer-Verlag Berlin Heidelberg

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Bucher, W., Ehrenfeucht, A., Haussler, D. (1985). On total regulators generated by derivation relations. In: Brauer, W. (eds) Automata, Languages and Programming. ICALP 1985. Lecture Notes in Computer Science, vol 194. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015732

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  • DOI: https://doi.org/10.1007/BFb0015732

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15650-5

  • Online ISBN: 978-3-540-39557-7

  • eBook Packages: Springer Book Archive

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