LR(0) Conjunctive Grammars and Deterministic Synchronized Alternating Pushdown Automata

  • Tamar Aizikowitz
  • Michael Kaminski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6651)


In this paper we introduce a sub-family of synchronized alternating pushdown automata, Deterministic Synchronized Alternating Pushdown Automata, and a sub-family of conjunctive grammars, LR(0) Conjunctive Grammars. We prove that deterministic SAPDA and LR(0) conjunctive grammars have the same recognition/generation power, analogously to the classical equivalence between acceptance by empty stack of deterministic PDA and LR(0) grammars. These models form the theoretical basis for efficient, linear, parsing of a rich sub-family of conjunctive languages, which properly includes all the boolean combinations of context-free LR(0) languages.


Conjunctive Rule Valid Item Pushdown Automaton Parsing Algorithm Conjunctive Grammar 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aizikowitz, T., Kaminski, M.: Conjunctive grammars and alternating pushdown automata. In: Hodges, W., de Queiroz, R. (eds.) Logic, Language, Information and Computation. LNCS (LNAI), vol. 5110, pp. 30–41. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  2. 2.
    Aizikowitz, T.: Synchronized Alternating Pushdown Automata. PhD thesis, Technion – Israel Institute of Technology (2010),
  3. 3.
    Chandra, A.K., Kozen, D.C., Stockmeyer, L.J.: Alternation. Journal of the ACM 28(1), 114–133 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Higginbotham, J.: English is not a context-free language. Linguistic Inquiry 15, 119–126 (1984)Google Scholar
  5. 5.
    Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley, Reading (1979)zbMATHGoogle Scholar
  6. 6.
    Knuth, D.E.: On the translation of languages from left to right. Information and Control 8, 607–639 (1965)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Ladner, R.E., Lipton, R.J., Stockmeyer, L.J.: Alternating pushdown and stack automata. SIAM Journal on Computing 13(1), 135–155 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Langendoen, T.D., Postal, P.M.: English and the class of context-free languages. Computational Linguistics 10(3-4), 177–181 (1984)Google Scholar
  9. 9.
    Okhotin, A.: Conjunctive grammars. Journal of Automata, Languages and Combinatorics 6(4), 519–535 (2001)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Okhotin, A.: Top-down parsing of conjunctive languages. Grammars 5(1), 21–40 (2002)CrossRefzbMATHGoogle Scholar
  11. 11.
    Okhotin, A.: LR parsing for conjunctive grammars. Grammars 5(2), 21–40 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Okhotin, A.: A recognition and parsing algorithm for arbitrary conjunctive grammars. Theoretical Computer Science 302, 81–124 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    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)CrossRefGoogle Scholar
  14. 14.
    Tomita, M.: Efficient Parsing for Natural Language: A Fast Algorithm for Practical Systems. Kluwer Academic Publishers, Norwell (1985)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Tamar Aizikowitz
    • 1
  • Michael Kaminski
    • 1
  1. 1.Department of Computer ScienceTechnion – Israel Institute of TechnologyHaifaIsrael

Personalised recommendations