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Efficient Simulation of Finite Automata by Neural Nets
 

Summary: Efficient Simulation of Finite Automata
by Neural Nets
NOGA ALON
Tel Aviv University, Ramat Aviv, Tel Aviv, Israel
A. K. DEWDNEY
University of Western Ontario, London, Ontario, Canada
AND
TEUNIS J. OTT
Bell Communications Research, Morristown, New Jersey
Abstract. Let K(m) denote the smallest number with the property that every m-state finite automaton
can be built as a neural net using K(m) or fewer neurons. A counting argument shows that K(m) is at
least ~((m log m)' 13), and a construction shows that K(m) is at most 0(m3/4). The counting
argument and the construction allow neural nets with arbitrarily complex local structure and thus may
require neurons that themselves amount to complicated networks. Mild, and in practical situations
almost necessary, constraints on the local structure of the network give, again by a counting argument
and a construction, lower and upper bounds for K(m) that are both linear in m.
Categories and Subject Descriptors: F. 1.1 [Computation by Abstract Devices]: Models of Computa-
tion--automata, relations between models
General Terms: Neural nets, Finite automata
Additional Key Words and Phrases: Mealy Machines

  

Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University

 

Collections: Mathematics