Evolving Bent Quaternary Functions

Stjepan Picek, Karlo Knezevic, Luca Mariot, Domagoj Jakobovic, Alberto Leporati

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

2 Citations (Scopus)


Boolean functions have a prominent role in many real-world applications, which makes them a very active research domain. Throughout the years, various heuristic techniques proved to be an attractive choice for the construction of Boolean functions with different properties. One of the most important properties is nonlinearity, and in particular maximally nonlinear Boolean functions are also called bent functions. In this paper, instead of considering Boolean functions, we experiment with quaternary functions. The corresponding problem is much more difficult and presents an interesting benchmark as well as realworld applications. The results we obtain show that evolutionary metaheuristics, especially genetic programming, succeed in finding quaternary functions with the desired properties. The obtained results in the quaternary domain can also be translated into the binary domain, in which case this approach compares favorably with the state-of-the-art in Boolean optimization. Our techniques are able to find quaternary bent functions for up to 8 inputs, which corresponds to obtaining Boolean bent functions of 16 inputs.

Original languageEnglish
Title of host publication2018 IEEE Congress on Evolutionary Computation (CEC)
Subtitle of host publicationProceedings
Place of PublicationPiscataway, NJ
Number of pages8
ISBN (Electronic)978-1-5090-6017-7
ISBN (Print)978-1-5090-6018-4
Publication statusPublished - 2018
Event2018 IEEE Congress on Evolutionary Computation, CEC 2018 - Rio de Janeiro, Brazil
Duration: 8 Jul 201813 Jul 2018


Conference2018 IEEE Congress on Evolutionary Computation, CEC 2018
CityRio de Janeiro


  • Evolutionary computation

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