Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Comparing Linear Conjunctive Languages to Subfamilies of the Context-Free Languages

  • Conference paper
SOFSEM 2011: Theory and Practice of Computer Science (SOFSEM 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6543))

Abstract

Linear conjunctive grammars define the same family of languages as one-way real-time cellular automata (Okhotin, “On the equivalence of linear conjunctive grammars to trellis automata”, RAIRO ITA, 2004), and this family is known to be incomparable to the context-free languages (Terrier, “On real-time one-way cellular array”, Theoret. Comput. Sci., 1995). This paper investigates subclasses of the context-free languages for possible containment in this class. It is shown that every visibly pushdown automaton (Alur, Madhusudan, “Visibly pushdown languages”, STOC 2004) can be simulated by a one-way real-time cellular automaton, but already for LL(1) context-free languages and for one-counter DPDAs no simulation is possible.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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.

Similar content being viewed by others

References

  1. Alur, R., Madhusudan, P.: Visibly pushdown languages. In: ACM Symposium on Theory of Computing, STOC 2004, Chicago, USA, June 13–16, pp. 202–211 (2004)

    Google Scholar 

  2. Berstel, J., Boasson, L.: Balanced grammars and their languages. In: Brauer, W., Ehrig, H., Karhumäki, J., Salomaa, A. (eds.) Formal and Natural Computing. LNCS, vol. 2300, pp. 3–25. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  3. Crespi-Reghizzi, S., Mandrioli, D.: Algebraic properties of structured context-free languages: old approaches and novel developments. In: WORDS (2009)

    Google Scholar 

  4. Čulík II, K., Gruska, J., Salomaa, A.: Systolic trellis automata. International Journal of Computer Mathematics 15, 195–212 (1984); 16, 3–22 (1984)

    MathSciNet  MATH  Google Scholar 

  5. Dyer, C.: One-way bounded cellular automata. Information and Control 44, 261–281 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ibarra, O.H., Kim, S.M.: Characterizations and computational complexity of systolic trellis automata. Theoretical Computer Science 29, 123–153 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  7. Jeż, A.: Conjunctive grammars can generate non-regular unary languages. International Journal of Foundations of Computer Science 19(3), 597–615 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Jeż, A., Okhotin, A.: Conjunctive grammars over a unary alphabet: undecidability and unbounded growth. Theory of Computing Systems 46(1), 27–58 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kountouriotis, V., Nomikos, C., Rondogiannis, P.: A game-theoretic characterization of Boolean grammars. In: Diekert, V., Nowotka, D. (eds.) DLT 2009. LNCS, vol. 5583, pp. 334–347. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  10. McNaughton, R.: Parenthesis grammars. Journal of the ACM 14(3), 490–500 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  11. Okhotin, A.: Conjunctive grammars. Journal of Automata, Languages and Combinatorics 6(4), 519–535 (2001)

    MathSciNet  MATH  Google Scholar 

  12. Okhotin, A.: On the equivalence of linear conjunctive grammars to trellis automata. Informatique Théorique et Applications 38(1), 69–88 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  13. Okhotin, A.: Boolean grammars. Information and Computation 194(1), 19–48 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  14. Okhotin, A.: Unambiguous Boolean grammars. Information and Computation 206, 1234–1247 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  15. Okhotin, A.: Fast parsing for Boolean grammars: a generalization of Valiant’s algorithm. In: Gao, Y., Lu, H., Seki, S., Yu, S. (eds.) DLT 2010. LNCS, vol. 6224, pp. 340–351. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  16. Okhotin, A., Reitwießner, C.: Conjunctive grammars with restricted disjunction. Theoretical Computer Science 411(26-28), 2559–2571 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  17. Terrier, V.: On real-time one-way cellular array. Theoretical Computer Science 141, 331–335 (1995)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Turku, Academy of Finland, Turku, FI–20014, Finland

    Alexander Okhotin

Authors
  1. Alexander Okhotin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Ivana Černá, Department of Computer Science, Faculty of Informatics, Faculty of Informatics, Masaryk University, Botanicka 68 a, 602 00, Brno, Czech Republic

    Ivana Černá

  2. Department of Software Engineering, University of Szeged, Árpád tér 2., 6720, Szeged, Hungary

    Tibor Gyimóthy

  3. Informationstechnologie und Ausbildung, CAB F 16, F 13.1, Universitätstraße 6, ETH Zürich, 8092, Zürich, Switzerland

    Juraj Hromkovič

  4. School of History and Anthropology, Queen’s University, 15 University Square, BT7 1NN, Belfast, UK

    Keith Jefferey

  5. Department of Computer Science, Comenius University, 84248, Bratislava, Slovakia

    Rastislav Králović

  6. EURECOM, 2229 2229 Route des Crêtes, BP 193, 06904, Sophia Antipolis cedex, France

    Marko Vukolić

  7. Institute of Theoretical Computer Science, ETH Zürich, IFW E49.1, Haldeneggsteig 4, 8092, Zürich, Switzerland

    Stefan Wolf

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Okhotin, A. (2011). Comparing Linear Conjunctive Languages to Subfamilies of the Context-Free Languages. In: Černá, I., et al. SOFSEM 2011: Theory and Practice of Computer Science. SOFSEM 2011. Lecture Notes in Computer Science, vol 6543. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18381-2_36

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-18381-2_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-18380-5

  • Online ISBN: 978-3-642-18381-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation