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Non-uniform automata over groups

  • David A. Barrington
  • Denis Thérien
Formal Languages And Automata
Part of the Lecture Notes in Computer Science book series (LNCS, volume 267)

Abstract

A new model, non-uniform deterministic finite automata (NUDFA's) over general finite monoids, has recently been developed as a strong link between the theory of finite automata and low-level parallel complexity. Achievements of this model include the proof that width 5 branching programs recognize exactly the languages in non-uniform NC1 [Ba86], NUDFA characterizations of several important subclasses of NC1 [BT87], and a new proof [BT87] of the old result [BK78] that the dot-depth hierarchy is infinite, using Sipser's work [Si83] on constant depth circuits.

Here we outline these earlier results and extend this theory to NUDFA's over solvable groups (NUDFA's over non-solvable groups have the maximum possible computing power [Ba86]). We characterize the power of NUDFA's over nilpotent groups and prove some optimal lower bounds for NUDFA's over certain groups which are solvable but not nilpotent.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • David A. Barrington
    • 1
  • Denis Thérien
    • 2
  1. 1.Dept. of Computer and Information ScienceUniversity of MassachusettsAmherstUSA
  2. 2.School of Computer ScienceMcGill UniversityMontréalCanada

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