The More the Merrier: On Evolving Five-Valued Spectra Boolean Functions

Claude Carlet; Marko Đurasević; Domagoj Jakobovic; Luca Mariot; Stjepan Picek

doi:10.1007/978-3-031-90062-4_4

The More the Merrier: On Evolving Five-Valued Spectra Boolean Functions

Claude Carlet
, Marko Đurasević
, Domagoj Jakobovic^*
, Luca Mariot
, Stjepan Picek

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

4 Downloads (Pure)

Abstract

Evolving Boolean functions with specific properties is an interesting optimization problem since, depending on the combination of properties and Boolean function size, the problem can range from very simple to (almost) impossible to solve. Some problems are more interesting as there may be only a few options for generating the required Boolean functions. This paper investigates one such problem: evolving five-valued spectra Boolean functions, the functions whose Walsh-Hadamard coefficients can only take five distinct values. We experimented with three solution encodings, two fitness functions, and 12 Boolean function sizes and showed that the tree encoding is superior to other choices, as we can obtain five-valued Boolean functions with high nonlinearity.

Original language	English
Title of host publication	Applications of Evolutionary Computation - 28th European Conference, EvoApplications 2025, Held as Part of EvoStar 2025, Proceedings
Editors	Pablo García-Sánchez, Emma Hart, Sarah L. Thomson
Publisher	Springer
Pages	52-67
Number of pages	16
ISBN (Print)	9783031900617
DOIs	https://doi.org/10.1007/978-3-031-90062-4_4
Publication status	Published - 17 Apr 2025
Event	28th European Conference on Applications of Evolutionary Computation, EvoApplications 2025 - Trieste, Italy Duration: 23 Apr 2025 → 25 Apr 2025 Conference number: 28

Publication series

Name	Lecture Notes in Computer Science
Volume	15612 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	28th European Conference on Applications of Evolutionary Computation, EvoApplications 2025
Abbreviated title	EvoApplications 2025
Country/Territory	Italy
City	Trieste
Period	23/04/25 → 25/04/25
Other	held as part of EvoStar 2025

Keywords

2025 OA procedure
Evolutionary Algorithms
Five-valued Functions
Plateaudness
Boolean Functions

Access to Document

10.1007/978-3-031-90062-4_4

978-3-031-90062-4_4Final published version, 573 KBLicence: Taverne

Cite this

Carlet, C., Đurasević, M., Jakobovic, D., Mariot, L., & Picek, S. (2025). The More the Merrier: On Evolving Five-Valued Spectra Boolean Functions. In P. García-Sánchez, E. Hart, & S. L. Thomson (Eds.), Applications of Evolutionary Computation - 28th European Conference, EvoApplications 2025, Held as Part of EvoStar 2025, Proceedings (pp. 52-67). (Lecture Notes in Computer Science; Vol. 15612 LNCS). Springer. https://doi.org/10.1007/978-3-031-90062-4_4

Carlet, Claude ; Đurasević, Marko ; Jakobovic, Domagoj et al. / The More the Merrier : On Evolving Five-Valued Spectra Boolean Functions. Applications of Evolutionary Computation - 28th European Conference, EvoApplications 2025, Held as Part of EvoStar 2025, Proceedings. editor / Pablo García-Sánchez ; Emma Hart ; Sarah L. Thomson. Springer, 2025. pp. 52-67 (Lecture Notes in Computer Science).

@inproceedings{64cf24fcfa834d139baa77326610b1e7,

title = "The More the Merrier: On Evolving Five-Valued Spectra Boolean Functions",

abstract = "Evolving Boolean functions with specific properties is an interesting optimization problem since, depending on the combination of properties and Boolean function size, the problem can range from very simple to (almost) impossible to solve. Some problems are more interesting as there may be only a few options for generating the required Boolean functions. This paper investigates one such problem: evolving five-valued spectra Boolean functions, the functions whose Walsh-Hadamard coefficients can only take five distinct values. We experimented with three solution encodings, two fitness functions, and 12 Boolean function sizes and showed that the tree encoding is superior to other choices, as we can obtain five-valued Boolean functions with high nonlinearity.",

keywords = "2025 OA procedure, Evolutionary Algorithms, Five-valued Functions, Plateaudness, Boolean Functions",

author = "Claude Carlet and Marko {\D}urasevi{\'c} and Domagoj Jakobovic and Luca Mariot and Stjepan Picek",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.; 28th European Conference on Applications of Evolutionary Computation, EvoApplications 2025, EvoApplications 2025 ; Conference date: 23-04-2025 Through 25-04-2025",

year = "2025",

month = apr,

day = "17",

doi = "10.1007/978-3-031-90062-4\_4",

language = "English",

isbn = "9783031900617",

series = "Lecture Notes in Computer Science",

publisher = "Springer",

pages = "52--67",

editor = "Pablo Garc{\'i}a-S{\'a}nchez and Emma Hart and Thomson, \{Sarah L.\}",

booktitle = "Applications of Evolutionary Computation - 28th European Conference, EvoApplications 2025, Held as Part of EvoStar 2025, Proceedings",

address = "Germany",

}

Carlet, C, Đurasević, M, Jakobovic, D, Mariot, L & Picek, S 2025, The More the Merrier: On Evolving Five-Valued Spectra Boolean Functions. in P García-Sánchez, E Hart & SL Thomson (eds), Applications of Evolutionary Computation - 28th European Conference, EvoApplications 2025, Held as Part of EvoStar 2025, Proceedings. Lecture Notes in Computer Science, vol. 15612 LNCS, Springer, pp. 52-67, 28th European Conference on Applications of Evolutionary Computation, EvoApplications 2025, Trieste, Italy, 23/04/25. https://doi.org/10.1007/978-3-031-90062-4_4

The More the Merrier: On Evolving Five-Valued Spectra Boolean Functions. / Carlet, Claude; Đurasević, Marko; Jakobovic, Domagoj et al.
Applications of Evolutionary Computation - 28th European Conference, EvoApplications 2025, Held as Part of EvoStar 2025, Proceedings. ed. / Pablo García-Sánchez; Emma Hart; Sarah L. Thomson. Springer, 2025. p. 52-67 (Lecture Notes in Computer Science; Vol. 15612 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - The More the Merrier

T2 - 28th European Conference on Applications of Evolutionary Computation, EvoApplications 2025

AU - Carlet, Claude

AU - Đurasević, Marko

AU - Jakobovic, Domagoj

AU - Mariot, Luca

AU - Picek, Stjepan

N1 - Conference code: 28

PY - 2025/4/17

Y1 - 2025/4/17

N2 - Evolving Boolean functions with specific properties is an interesting optimization problem since, depending on the combination of properties and Boolean function size, the problem can range from very simple to (almost) impossible to solve. Some problems are more interesting as there may be only a few options for generating the required Boolean functions. This paper investigates one such problem: evolving five-valued spectra Boolean functions, the functions whose Walsh-Hadamard coefficients can only take five distinct values. We experimented with three solution encodings, two fitness functions, and 12 Boolean function sizes and showed that the tree encoding is superior to other choices, as we can obtain five-valued Boolean functions with high nonlinearity.

AB - Evolving Boolean functions with specific properties is an interesting optimization problem since, depending on the combination of properties and Boolean function size, the problem can range from very simple to (almost) impossible to solve. Some problems are more interesting as there may be only a few options for generating the required Boolean functions. This paper investigates one such problem: evolving five-valued spectra Boolean functions, the functions whose Walsh-Hadamard coefficients can only take five distinct values. We experimented with three solution encodings, two fitness functions, and 12 Boolean function sizes and showed that the tree encoding is superior to other choices, as we can obtain five-valued Boolean functions with high nonlinearity.

KW - 2025 OA procedure

KW - Evolutionary Algorithms

KW - Five-valued Functions

KW - Plateaudness

KW - Boolean Functions

UR - https://www.scopus.com/pages/publications/105003904301

U2 - 10.1007/978-3-031-90062-4_4

DO - 10.1007/978-3-031-90062-4_4

M3 - Conference contribution

AN - SCOPUS:105003904301

SN - 9783031900617

T3 - Lecture Notes in Computer Science

SP - 52

EP - 67

BT - Applications of Evolutionary Computation - 28th European Conference, EvoApplications 2025, Held as Part of EvoStar 2025, Proceedings

A2 - García-Sánchez, Pablo

A2 - Hart, Emma

A2 - Thomson, Sarah L.

PB - Springer

Y2 - 23 April 2025 through 25 April 2025

ER -

Carlet C, Đurasević M, Jakobovic D, Mariot L, Picek S. The More the Merrier: On Evolving Five-Valued Spectra Boolean Functions. In García-Sánchez P, Hart E, Thomson SL, editors, Applications of Evolutionary Computation - 28th European Conference, EvoApplications 2025, Held as Part of EvoStar 2025, Proceedings. Springer. 2025. p. 52-67. (Lecture Notes in Computer Science). doi: 10.1007/978-3-031-90062-4_4