Abstract
Artificial intelligence is used whenever problems need to be solved that humans can understand and define, but which they cannot solve due to the complexity of the problem.
A distinction is made between two basic forms of complexity: polynomial and exponential complexity.
A typical example of exponential complexity is a family tree: every person has two parents, four grandparents, and eight great-grandparents. This means that such a family tree quickly becomes wider and wider toward the top.
An example of polynomial complexity are search problems, the search for a particular book in a bookcase, etc.
A number of combinatorial problems are given as examples of the different complexities, and it is shown how to overcome these difficulties.
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References
Bernd Steinbach, Christian Posthoff. Logic Functions and Equations—Fundamentals and Applications using the XBOOLE-Monitor, Third Edition, Springer Nature, 2021.
Christian Posthoff, Bernd Steinbach. Mathematik—Ohne Sorgen an der Uni II—Nutze Microsoft Mathematics, bookboon.com, 2017, 978-87-403-1949-1
https://en.wikipedia.org/wiki/WilesproofofFermat'sLastTheorem
https://www.en.wikipedia.org/wiki/Four-color-theoremhttps://www.ki-strategie-deutschland.de/home.html
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Posthoff, C. (2024). Polynomial and Exponential Complexity. In: Artificial Intelligence for Everyone. Springer, Cham. https://doi.org/10.1007/978-3-031-57208-1_5
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DOI: https://doi.org/10.1007/978-3-031-57208-1_5
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