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 NC 1 [Ba86], NUDFA characterizations of several important subclasses of NC 1 [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.
Supported by NSF grant MCS-8304769 and US Air Force grant AFOSR-82-0326.
Supported by NSERC grant A4546 and FCAR grant 86-EQ-2933.
Address for 1986-87: Laboratoire Informatique Théorique et Programmation, Université P. et M. Curie, 2, Place Jussieu, 75221 Paris, France.
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Barrington, D.A., Thérien, D. (1987). Non-uniform automata over groups. In: Ottmann, T. (eds) Automata, Languages and Programming. ICALP 1987. Lecture Notes in Computer Science, vol 267. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18088-5_13
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DOI: https://doi.org/10.1007/3-540-18088-5_13
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