Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Applications of Generating Functions to Stochastic Processes and to the Complexity of the Knapsack Problem

Version 1 : Received: 25 April 2021 / Approved: 27 April 2021 / Online: 27 April 2021 (11:59:44 CEST)

How to cite: Jormakka, J.; Ghosh, S. Applications of Generating Functions to Stochastic Processes and to the Complexity of the Knapsack Problem. Preprints 2021, 2021040706 (doi: 10.20944/preprints202104.0706.v1). Jormakka, J.; Ghosh, S. Applications of Generating Functions to Stochastic Processes and to the Complexity of the Knapsack Problem. Preprints 2021, 2021040706 (doi: 10.20944/preprints202104.0706.v1).

Abstract

The paper describes a method of solving some stochastic processes using generating functions. A general theorem of generating functions of a particular type is derived. A generating function of this type is applied to a stochastic process yielding polynomial time algorithms for certain partitions. The method is generalized to a stochastic process describing a rather general linear transform. Finally, the main idea of the method is used in deriving a theoretical polynomial time algorithm to the knapsack problem.

Subject Areas

stochastic processes; generating functions; polynomial time algorithms; partitions; knapsacks

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