Skip to main content
SpringerLink
Log in

Second-Order Simple Grammars

  • Conference paper
CONCUR 2006 – Concurrency Theory (CONCUR 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4137))

Included in the following conference series:

Abstract

Higher-order notations for trees have a venerable history from the 1970s and 1980s when schemes (that is, functional programs without interpretations) and their relationship to formal language theory were first studied. Included are higher-order recursion schemes and pushdown automata. Automata and language theory study finitely presented mechanisms for generating languages. Instead of language generators, one can view them as process calculi, propagators of possibly infinite labelled transition systems. Recently, model-checking techniques have been successfully extended to these higher-order notations in the deterministic case [18,9,8,21].

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aehlig, K., De Miranda, J., Ong, C.-H.L.: Safety is not a restriction at level 2 for string languages. LNCS, vol. 3411, pp. 490–511 (2005)

    Google Scholar 

  2. Aho, A.: Indexed grammars–an extension of context-free grammars. Journal of ACM 15, 647–671 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  3. Aho, A.: Nested stack automata. Journal of ACM 16, 383–406 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  4. Baeten, J., Bergstra, J., Klop, J.: Decidability of bisimulation equivalence for processes generating context-free languages. Journal of ACM 40, 653–682 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  5. Blumensath, A.: A pumping lemma for higher-order pushdown automata (preprint 2004)

    Google Scholar 

  6. Bouajjani, A., Meyer, A.: Symbolic Reachability Analysis of Higher-Order Context-Free Processes. In: Lodaya, K., Mahajan, M. (eds.) FSTTCS 2004. LNCS, vol. 3328, pp. 135–147. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  7. Burkart, O., Caucal, D., Moller, F., Steffen, B.: Verification on infinite structures. In: Bergstra, J., Ponse, A., Smolka, S. (eds.) Handbook of Process Algebra, pp. 545–623. North-Holland, Amsterdam (2001)

    Chapter  Google Scholar 

  8. Cachat, T.: Higher order pushdown automata, the Caucal hierarchy of graphs and parity games. LNCS, vol. 2719, pp. 556–569 (2003)

    Google Scholar 

  9. Caucal, D.: On Infinite Terms Having a Decidable Monadic Theory. In: Diks, K., Rytter, W. (eds.) MFCS 2002. LNCS, vol. 2420, pp. 165–176. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  10. Courcelle, B.: A representation of trees by languages I and II. Theoretical Computer Science 6, 255–279 and 7, 25–55 (1978)

    Google Scholar 

  11. Damm, W.: The IO- and OI-hierarchy. Theoretical Computer Science 25, 95–169 (1982)

    Article  MathSciNet  Google Scholar 

  12. Damm, W., Goerdt, A.: An automata-theoretical characterization of the OI-hierarchy. Information and Control 71, 1–32 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  13. Engelfriet, J.: Iterated stack automata and complexity classes. Information and Computation 95, 21–75 (1991)

    Article  MathSciNet  Google Scholar 

  14. Fischer, M.: Grammars with macro-like productions. In: Procs. 9th Annual IEEE Symposium on Switching and Automata Theory, pp. 131–142 (1968)

    Google Scholar 

  15. Freidman, E.: The inclusion problem for simple languages. Theoretical Computer Science 1, 297–316 (1976)

    Article  Google Scholar 

  16. Gilman, R.: A shrinking lemma for indexed languages. Theoretical Computer Science 163, 277–281 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  17. Jančar, P., Srba, J.: Undecidability results for bisimilarity on prefix rewrite systems. In: Aceto, L., Ingólfsdóttir, A. (eds.) FOSSACS 2006. LNCS, vol. 3921, pp. 277–291. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  18. Knapik, T., Niwiński, D., Urzyczyn, P.: Higher-order pushdown trees are easy. In: Nielsen, M., Engberg, U. (eds.) FOSSACS 2002. LNCS, vol. 2303, pp. 205–222. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  19. Korenjak, A., Hopcroft, J.: Simple deterministic languages. In: Procs. 7th Annual IEEE Symposium on Switching and Automata Theory, pp. 36–46 (1966)

    Google Scholar 

  20. Maslov, A.: Multilevel stack automata. Problems of Information Transmission 12, 38–43 (1976)

    Google Scholar 

  21. Ong, C.-H.L.: On model-checking trees generated by higher-order recursion schemes (preprint 2006)

    Google Scholar 

  22. Parchmann, R., Duske, J., Specht, J.: On deterministic indexed languages. Information and Control 45, 48–67 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  23. Sénizergues, G.: L(A) = L(B)? decidability results from complete formal systems. Theoretical Computer Science 251, 1–166 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  24. Sénizergues, G.: L(A) = L(B)? a simplified decidability proof. Theoretical Computer Science 281, 555–608 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  25. Sénizergues, G.:The equivalence problem for t-turn DPDA is co-NP. LNCS, vol. 2719, pp. 478–489 (2003)

    Google Scholar 

  26. Sénizergues, G.: The bisimulation problem for equational graphs of finite out-degree. SIAM Journal of Computing 34, 1025–1106 (2005)

    Article  MATH  Google Scholar 

  27. Stirling, C.: Decidability of DPDA equivalence. Theoretical Computer Science 255, 1–31 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  28. Stirling, C.: Deciding DPDA equivalence is primitive recursive. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 821–832. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  29. Vijay-Shanker, K., Weir, D.: The equivalence of four extensions of context-free grammars. Mathematical Systems Theory 27, 511–546 (1994)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Informatics, University of Edinburgh, Edinburgh, EH9 3JZ, UK

    Colin Stirling

Authors
  1. Colin Stirling
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute for Theoretical Computer Science, Technical University Dresden, Germany

    Christel Baier

  2. INRIA, VASY, Grenoble Rhône-Alpes, France

    Holger Hermanns

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Stirling, C. (2006). Second-Order Simple Grammars. In: Baier, C., Hermanns, H. (eds) CONCUR 2006 – Concurrency Theory. CONCUR 2006. Lecture Notes in Computer Science, vol 4137. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11817949_34

Download citation

  • DOI: https://doi.org/10.1007/11817949_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-37376-6

  • Online ISBN: 978-3-540-37377-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation