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Chomsky hierarchy and communication complexity

  • Galina Jirásková
Chapter 1 Languages
Part of the Lecture Notes in Computer Science book series (LNCS, volume 381)

Abstract

Chomsky hierarchy is compared with the hierarchy of communication complexity for VLSI. It is shown that only regular languages belong to the same levels of both hierarchies. There are hard languages according to Chomsky hierarchy that belong to the lowest level in communication complexity hierarchy. On the other hand there is a deterministic linear language that requires the highest (linear) communication complexity. This is the main result because it implies that VLSI circuits need Θ(n) area and Θ(n2) area. (time)2 complexity to recognize deterministic context-free languages which solves an open problem of Hromkovič [7].

Keywords

Boolean Function Communication Complexity Regular Language Input Word VLSI Circuit 
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.

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References

  1. [1]
    A.V. Aho, J.D. Ullman and M. Yannakakis, On notions of information transfer in VLSI circuits. Proc. 15th Ann. ACM Symp. on Theory of Computing (1983) 133–139.Google Scholar
  2. [2]
    P. Ďuriš, Z. Galil and G. Schnitger, Lower bounds on communication complexity. Inform. and Comput. 73, 1 (1987) 1–22.Google Scholar
  3. [3]
    S. Hornick and M. Sarrafzatch, On problems transformability in VLSI. Algorithmica 1(1987) 97–112.Google Scholar
  4. [4]
    J. Hromkovič, The advantages of a new approach to defining the communication complexity for VLSI. Theoret. Comput. Sci. 57 (1988) 97–111.Google Scholar
  5. [5]
    J. Hromkovič, Communication complexity hierarchy. Theoret. Comput. Sci. 48(1986) 109–115.Google Scholar
  6. [6]
    J. Hromkovič, Lower bound techniques for VLSI algorithms. Proc. IMYCS '86, Hungarian Academy of Sciences (1986) 9–19.Google Scholar
  7. [7]
    J. Hromkovič, Relation between Chomsky hierarchy and communication complexity hierarchy. Acta Math. Univ. Comenian. 48–49 (1986) 311–317.Google Scholar
  8. [8]
    J. Ja, Ja and V.K. Prasanna Kumar, Information transfer in distributed computing with applications to VLSI. J. Assoc. Comput. Mach. 31 (1984) 150–162.Google Scholar
  9. [9]
    J. Ja, Ja, V.K. Prasanna Kumar and J. Simon, Information transfer under different sets of protocols. SIAM J. Comput. 13(1984) 840–849.Google Scholar
  10. [10]
    Ch. Papadimitriou and M. Sipser, Communication complexity. Proc. 14th Ann. ACM Symp. on Theory of Computing (1982) 196–200.Google Scholar
  11. [11]
    A.C. Yao, The entropic limitations of VLSI computations, Proc. 13th Ann. ACM Symp. on Theory of Computing (1981) 308–311.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Galina Jirásková
    • 1
  1. 1.Mathematical InstituteSlovak Academy of SciencesKošiceCzechoslovakia

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