Polynomial cellular neural networks for implementing the game of life

Giovanni Egidio Pazienza; Eduardo Gomez-Ramirez; Xavier Vilasís-Cardona

doi:10.1007/978-3-540-74690-4_93

Polynomial cellular neural networks for implementing the game of life

Giovanni Egidio Pazienza, Eduardo Gomez-Ramirez, Xavier Vilasís-Cardona

La Salle International School of Commerce and Digital Economy

Research output: Book chapter › Conference contribution › peer-review

6 Citations (Scopus)

Abstract

One-layer space-invariant Cellular Neural Networks (CNNs) are widely appreciated for their simplicity and versatility; however, such structures are not able to solve non-linearly separable problems. In this paper we show that a polynomial CNN - that has with a direct VLSI implementation - is capable of dealing with the 'Game of Life', a Cellular Automaton with the same computational complexity as a Turing machine. Furthermore, we describe a simple design algorithm that allows to convert the rules of a Cellular Automaton into the weights of a polynomial CNN.

Original language	English
Title of host publication	Artificial Neural Networks - ICANN 2007 - 17th International Conference, Proceedings
Publisher	Springer Verlag
Pages	914-923
Number of pages	10
Edition	PART 1
ISBN (Print)	9783540746898
DOIs	https://doi.org/10.1007/978-3-540-74690-4_93
Publication status	Published - 2007
Event	17th International Conference on Artificial Neural Networks, ICANN 2007 - Porto, Portugal Duration: 9 Sept 2007 → 13 Sept 2007

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Number	PART 1
Volume	4668 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	17th International Conference on Artificial Neural Networks, ICANN 2007
Country/Territory	Portugal
City	Porto
Period	9/09/07 → 13/09/07

Access to Document

10.1007/978-3-540-74690-4_93

Cite this

Pazienza, G. E., Gomez-Ramirez, E., & Vilasís-Cardona, X. (2007). Polynomial cellular neural networks for implementing the game of life. In Artificial Neural Networks - ICANN 2007 - 17th International Conference, Proceedings (PART 1 ed., pp. 914-923). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4668 LNCS, No. PART 1). Springer Verlag. https://doi.org/10.1007/978-3-540-74690-4_93

Pazienza, Giovanni Egidio ; Gomez-Ramirez, Eduardo ; Vilasís-Cardona, Xavier. / Polynomial cellular neural networks for implementing the game of life. Artificial Neural Networks - ICANN 2007 - 17th International Conference, Proceedings. PART 1. ed. Springer Verlag, 2007. pp. 914-923 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 1).

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title = "Polynomial cellular neural networks for implementing the game of life",

abstract = "One-layer space-invariant Cellular Neural Networks (CNNs) are widely appreciated for their simplicity and versatility; however, such structures are not able to solve non-linearly separable problems. In this paper we show that a polynomial CNN - that has with a direct VLSI implementation - is capable of dealing with the 'Game of Life', a Cellular Automaton with the same computational complexity as a Turing machine. Furthermore, we describe a simple design algorithm that allows to convert the rules of a Cellular Automaton into the weights of a polynomial CNN.",

author = "Pazienza, {Giovanni Egidio} and Eduardo Gomez-Ramirez and Xavier Vilas{\'i}s-Cardona",

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Pazienza, GE, Gomez-Ramirez, E & Vilasís-Cardona, X 2007, Polynomial cellular neural networks for implementing the game of life. in Artificial Neural Networks - ICANN 2007 - 17th International Conference, Proceedings. PART 1 edn, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 1, vol. 4668 LNCS, Springer Verlag, pp. 914-923, 17th International Conference on Artificial Neural Networks, ICANN 2007, Porto, Portugal, 9/09/07. https://doi.org/10.1007/978-3-540-74690-4_93

Polynomial cellular neural networks for implementing the game of life. / Pazienza, Giovanni Egidio; Gomez-Ramirez, Eduardo; Vilasís-Cardona, Xavier.
Artificial Neural Networks - ICANN 2007 - 17th International Conference, Proceedings. PART 1. ed. Springer Verlag, 2007. p. 914-923 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4668 LNCS, No. PART 1).

Research output: Book chapter › Conference contribution › peer-review

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N2 - One-layer space-invariant Cellular Neural Networks (CNNs) are widely appreciated for their simplicity and versatility; however, such structures are not able to solve non-linearly separable problems. In this paper we show that a polynomial CNN - that has with a direct VLSI implementation - is capable of dealing with the 'Game of Life', a Cellular Automaton with the same computational complexity as a Turing machine. Furthermore, we describe a simple design algorithm that allows to convert the rules of a Cellular Automaton into the weights of a polynomial CNN.

AB - One-layer space-invariant Cellular Neural Networks (CNNs) are widely appreciated for their simplicity and versatility; however, such structures are not able to solve non-linearly separable problems. In this paper we show that a polynomial CNN - that has with a direct VLSI implementation - is capable of dealing with the 'Game of Life', a Cellular Automaton with the same computational complexity as a Turing machine. Furthermore, we describe a simple design algorithm that allows to convert the rules of a Cellular Automaton into the weights of a polynomial CNN.

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Pazienza GE, Gomez-Ramirez E, Vilasís-Cardona X. Polynomial cellular neural networks for implementing the game of life. In Artificial Neural Networks - ICANN 2007 - 17th International Conference, Proceedings. PART 1 ed. Springer Verlag. 2007. p. 914-923. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 1). doi: 10.1007/978-3-540-74690-4_93

Polynomial cellular neural networks for implementing the game of life

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