Article ID Journal Published Year Pages File Type
6424138 European Journal of Combinatorics 2015 21 Pages PDF
Abstract

We study the joint distribution of the input sum and the output sum of a deterministic transducer. Here, the input of this finite-state machine is a uniformly distributed random sequence.We give a simple combinatorial characterization of transducers for which the output sum has bounded variance, and we also provide algebraic and combinatorial characterizations of transducers for which the covariance of input and output sum is bounded, so that the two are asymptotically independent.Our results are illustrated by several examples, such as transducers that count specific blocks in the binary expansion, the transducer that computes the Gray code, or the transducer that computes the Hamming weight of the width-w non-adjacent form digit expansion. The latter two turn out to be examples of asymptotic independence.

Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics
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