Sains Malaysiana 49(11)(2020): 2847-2857

http://dx.doi.org/10.17576/jsm-2020-4911-23

Novel Random k Satisfiability for k ≤ 2 in Hopfield Neural Network

(Novel Rawak k Kepuasan untuk k ≤ 2 dalam Rangkaian Neural Hopfield)

SARATHA SATHASIVAM¹, MOHD. ASYRAF MANSOR²*, AHMAD IZANI MD ISMAIL¹, SITI ZULAIKHA MOHD JAMALUDIN¹, MOHD SHAREDUWAN MOHD KASIHMUDDIN¹ & MUSTAFA MAMAT³

¹School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Pulau Pinang, Malaysia

²School of Distance Education, Universiti Sains Malaysia, 11800 USM, Pulau Pinang, Malaysia

³Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, 21300 UniSZA Kuala Terengganu, Terengganu Darul Iman, Malaysia

Received: 23 March 2020/Accepted: 18 May 2020

ABSTRACT

The k Satisfiability logic representation (kSAT) contains valuable information that can be represented in terms of variables. This paper investigates the use of a particular non-systematic logical rule namely Random k Satisfiability (RANkSAT). RANkSAT contains a series of satisfiable clauses but the structure of the formula is determined randomly by the user. In the present study, RANkSAT representation is successfully implemented in Hopfield Neural Network (HNN) by obtaining the optimal synaptic weights. We focus on the different regimes for k ≤ 2 by taking advantage of the non-redundant logical structure, thus obtaining the final neuron state that minimizes the cost function. We also simulate the performances of RANkSAT logical rule using several performance metrics. The simulated results suggest that the RANkSAT representation can be embedded optimally in HNN and that the proposed method can retrieve the optimal final state.

Keywords: Artificial neural network; Hopfield neural network; logic programming; random satisfiability

ABSTRAK

Perwakilan logik k Kepuasan mengandungi maklumat berguna yang diwakilkan dalam sebutan pemboleh ubah. Kajian ini mengkaji penggunaan suatu peraturan logik yang tidak sistematik iaitu logik k Kepuasan Rawak (RANkSAT). RANkSAT mengandungi siri klausa penuh tetapi struktur rumusnya ditentukan secara rawak oleh pengguna. Dalam kajian ini, perwakilan RANkSAT berjaya dilaksanakan untuk Rangkaian Neural Hopfield (HNN) dengan memperoleh pemberat sinapsis yang optimum. Fokus diberikan kepada rejim berbeza bagi k ≤ 2 dengan menggunakan struktur logik yang tidak berulang dan justeru memperoleh secara optimal keadaan neuron akhir yang meminimumkan fungsi kos. Prestasi logik k Kepuasan Rawak disimulasi dengan menggunakan beberapa indikator prestasi tertentu. Keputusan simulasi menunjukkan perwakilan RANkSAT boleh dimasukkan secara optimum dalam HNN dan teknik yang telah dicadangkan berupaya memperoleh semula perwakilan neuron akhir yang optimum.

Kata kunci: Kepuasan rawak; rangkaian neural buatan; rangkaian neural Hopfield; pengaturcaraan logik

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*Corresponding author; email: asyrafman@usm.my