Accelerating Activation Function for 3-Satisfiability Logic Programming

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Mohd Asyraf Mansor 1,* Saratha Sathasivam 1

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

* Corresponding author.


Received: 6 Feb. 2016 / Revised: 17 Jun. 2016 / Accepted: 1 Aug. 2016 / Published: 8 Oct. 2016

Index Terms

3-Satisfiability, Hyperbolic tangent activation function, Elliot symmetric activation function, McCulloch-Pitts function, Logic programming, Hopfield neural network


This paper presents the technique for accelerating 3-Satisfiability (3-SAT) logic programming in Hopfield neural network. The core impetus for this work is to integrate activation function for doing 3-SAT logic programming in Hopfield neural network as a single hybrid network. In logic programming, the activation function can be used as a dynamic post optimization paradigm to transform the activation level of a unit (neuron) into an output signal. In this paper, we proposed Hyperbolic tangent activation function and Elliot symmetric activation function. Next, we compare the performance of proposed activation functions with a conventional function, namely McCulloch-Pitts function. In this study, we evaluate the performances between these functions through computer simulations. Microsoft Visual C++ 2013 was used as a platform for training, validating and testing of the network. We restrict our analysis to 3-Satisfiability (3-SAT) clauses. Moreover, evaluations are made between these activation functions to see the robustness via aspects of global solutions, global Hamming distance, and CPU time.

Cite This Paper

Mohd Asyraf Mansor, Saratha Sathasivam, "Accelerating Activation Function for 3-Satisfiability Logic Programming", International Journal of Intelligent Systems and Applications (IJISA), Vol.8, No.10, pp.44-50, 2016. DOI:10.5815/ijisa.2016.10.05


[1]S. Sathasivam, P. F. Ng, and N. Hamadneh, Developing agent based modelling for reverse analysis method, Journal of Applied Sciences, Engineering and Technology 6 (2013) 4281-4288.
[2]R. Rojas, Neural Networks: A Systematic Introduction, Berlin: Springer, 1996.
[3]J. J. Hopfield and D. W. Tank, Neural computation of decisions in optimization problems, Biological Cybernatics 52 (1985) 141-151.
[4]U. Aiman and N. Asrar, Genetic algorithm based solution to SAT-3 problem, Journal of Computer Sciences and Applications 3 (2015) 33-39.
[5]S. Haykin, Neural Networks: A Comprehensive Foundation, New York: Macmillan College Publishing, 1999.
[6]G. Pinkas, and R. Dechter, Improving energy connectionist energy minimization, Journal of Artificial Intelligence Research 3 (1995) 223-237.
[7]W. A. T. Wan Abdullah, The logic of neural networks. Physics Letters A 176 (1993) 202-206.
[8]K. Bekir and A. O. Vehbi, Performance analysis of various activation functions in generalized MLP architectures of neural network. International Journal of Artificial Intelligence and Expert Systems 1(4) (2010) 111-122.
[9]P. Sibi, S. A. Jones and P. Siddarth, Analysis of different activation functions using back propagation neural networks. Journal of Theoretical and Applied Information Technology 47 (2013) 1264-1268.
[10]R. A. Kowalski, Logic for problem solving, New York: Elsevier Science Publishing Co, 1979.
[11]Y. L. Xou and T. C. Bao, Novel global stability criteria for high-order Hopfield-type neural networks with time-varying delays, Journal of Mathematical Analysis and Applications 330 (2007) 144-15.
[12]N. Siddique and H. Adeli, Computational Intelligence Synergies of Fuzzy Logic, Neural Network and Evolutionary Computing, United Kingdom: John Wiley and Sons, 2013.
[13]B. Sebastian, H. Pascal and H. Steffen, Connectionist model generation: A first-order approach, Neurocomputing 71(13) (2008) 2420-2432.
[14]S. Sathasivam, Upgrading Logic Programming in Hopfield Network, Sains Malaysiana, 39 (2010) 115-118.
[15]B. Tobias and K. Walter, An improved deterministic local search algorithm for 3-SAT, Theoretical Computer Science 329 (2004) 303-313.
[16]D. Vilhelm, J. Peter and W. Magnus, Counting models for 2SAT and 3SAT formulae, Theoretical Computer Science, 332 (2005) 265-291.
[17]L. J. James, A neural network approach to the 3-Satisfiability problem, Journal of Parallel and Distributed Computing 6(2) (1989) 435-449.
[18]H. Asgari, Y. S. Kavian, and A. Mahani, A Systolic Architecture for Hopfield Neural Networks. Procedia Technology, 17 (2014) 736-741.
[19]P. Steven, SAT problems with chains of dependent variables, Discrete Applied Mathematics 130(2) (2003) 329-22.
[20]K. Ernst, B. Tatiana and C. W. Donald, Neural Networks and Micromechanics, New York: Springer Science & Business Media, 2009.
[21]C. Rene and L. Daniel, Mathematical Logic: Propositional Calculus, Boolean Algebras, Predicate Calculus, United Kingdom: Oxford University Press, 2000.
[22]M. Kaushik. Comparative analysis of exhaustive search algorithm with ARPS algorithm for motion estimation. International Journal of Applied Information Systems 1(6) (2012) 16-19.