Tradeoffs for language recognition on parallel computing models

  • Juraj Hromkovič
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 226)


The alternating machine having a separate input tape with k two-way, read-only heads, and a certain number of internal configurations — AM(k) is considered as a parallel computing model. For the complexity measure TIME·SPACE·PARALLELISM (TSP), the optimal lower bounds ω(n2) and ω (n3/2) resp. are proved for the recognition of specific languages on AM (1), and AM(k) respectively. For the complexity measure REVERSALS·SPACE·PARALLELISM (RSP), the lower bound ω(n1/3/log2n) is established for the recognition of a specific language on AM(k). This result implies a polynomial lower bound on PTIME·HARDWARE of parallel RAM's. All lower bounds obtained are substantially improved for the case that SPACE ≥nɛ, for 0 < ɛ < 1. Several strongest lower bounds for two-way (and one-way) alternating (deterministic, and nondeterministic) multihead finite automata are obtained as direct consequences of these results.


Turing Machine Complexity Measure Specific Language Finite Automaton Universal State 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Juraj Hromkovič
    • 1
  1. 1.Dept. of Theoretical Cybernetics and Mathematical InformaticsComenius UniversityBratislavaCzechoslovakia

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