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. Preprints2021, 2021040706. https://doi.org/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. https://doi.org/10.20944/preprints202104.0706.v1
Jormakka, J.; Ghosh, S. Applications of Generating Functions to Stochastic Processes and to the Complexity of the Knapsack Problem. Preprints2021, 2021040706. https://doi.org/10.20944/preprints202104.0706.v1
APA Style
Jormakka, J., & Ghosh, S. (2021). Applications of Generating Functions to Stochastic Processes and to the Complexity of the Knapsack Problem. Preprints. https://doi.org/10.20944/preprints202104.0706.v1
Chicago/Turabian Style
Jormakka, J. and Sourangshu Ghosh. 2021 "Applications of Generating Functions to Stochastic Processes and to the Complexity of the Knapsack Problem" Preprints. https://doi.org/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.
Keywords
stochastic processes; generating functions; polynomial time algorithms; partitions; knapsacks
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
