Advertisement

Toward a Compositional Theory of Leftist Grammars and Transformations

  • Pierre Chambart
  • Philippe Schnoebelen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6014)

Abstract

Leftist grammars [Motwani et al., STOC 2000] are special semi-Thue systems where symbols can only insert or erase to their left. We develop a theory of leftist grammars seen as word transformers as a tool toward rigorous analyses of their computational power. Our main contributions in this first paper are (1) constructions proving that leftist transformations are closed under compositions and transitive closures, and (2) a proof that bounded reachability is NP-complete even for leftist grammars with acyclic rules.

Keywords

Transitive Closure Regular Language Relation Algebra 3SAT Instance Compositional Foundation 
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.

References

  1. 1.
    Chambart, P., Schnoebelen, P.: Post embedding problem is not primitive recursive, with applications to channel systems. In: Arvind, V., Prasad, S. (eds.) FSTTCS 2007. LNCS, vol. 4855, pp. 265–276. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  2. 2.
    Chambart, P., Schnoebelen, P.: The ω-regular Post embedding problem. In: Amadio, R.M. (ed.) FOSSACS 2008. LNCS, vol. 4962, pp. 97–111. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  3. 3.
    Chambart, P., Schnoebelen, P.: The ordinal recursive complexity of lossy channel systems. In: Proc. LICS 2008, pp. 205–216. IEEE Comp. Soc. Press, Los Alamitos (2008)Google Scholar
  4. 4.
    Jurdziński, T.: On complexity of grammars related to the safety problem. Theoretical Computer Science 389(1-2), 56–72 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Jurdziński, T.: Leftist grammars are nonprimitive recursive. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 51–62. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  6. 6.
    Jurdziński, T., Loryś, K.: Leftist grammars and the Chomsky hierarchy. Mathematical Systems Theory 41(2), 233–256 (2007)zbMATHGoogle Scholar
  7. 7.
    Motwani, R., Panigrahy, R., Saraswat, V.A., Venkatasubramanian, S.: On the decidability of accessibility. In: Proc. STOC 2000, pp. 306–315. ACM Press, New York (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Pierre Chambart
    • 1
  • Philippe Schnoebelen
    • 1
  1. 1.LSVENS Cachan, CNRSCachanFrance

Personalised recommendations