Entry for 2012 HUMIES 1. Title of the paper:"Evolving the Best Known Approximation to the Q Function" 2. List of authors: Dao Ngoc Phong Address: Dept of Information & Communication, Hanoi City Government, 186 Giang Vo, Dong Da, Hanoi, Vietnam Email: phongaptech@yahoo.com Nguyen Xuan Hoai Address: IT Research & Development Center, Hanoi University, 9th Km, Nguyen Trai, Thanh Xuan, Hanoi, Vietnam E-mail: nxhoai@hanu.edu.vn R.I. (Bob) McKay Address: Structural Complexity Laboratory, Gwanak-gu, Gwanangno 599, Seoul National University 302-427, Seoul 151744, Korea E-mail: rimsnucse@gmail.com Constantin Siriteanu Address: Information Processing and Communications Laboratory, Department of Electrical and Computer Engineering, Queen's University, 9 Union Street, Walter Light Hall, Rm. 504 Kingston, Ontario, Canada, K7L 3N6 Email: sircosti@gmail.com Nguyen Quang Uy Address: Faculty of Information Technology Military Technical Academy, 100 Hoang Quoc Viet, Hanoi, Vietnam E-mail: quanguyhn@gmail.com Namyong Park Address: Structural Complexity Laboratory, Gwanak-gu, Gwanangno 599, Seoul National University 302-427, Seoul 151744, Korea E-mail: zest159@naver.com@gmail.com 3. Corresponding Author: Nguyen Xuan Hoai 4. Paper's Abtract "The Gaussian Q-function is the integral of the tail of the Gaussian distribution; as such, it is important across a vast range of fields requiring stochastic analysis. No elementary closed form is possible, so a number of approximations have been proposed. We use a Genetic Programming (GP) system, Tree Adjoining Grammar Guided GP (TAG3P) with local search operators to evolve approximations of the Qfunction in the form given by Benitez [1]. We found more accurate approximations than any previously published. This confirms the practical importance of local search in TAG3P." 5. [B,D,E] 6 Statetements Good and closed form approximations to Q-function are immensely important in the field of communications as it appears in many calculations. Since the work of P. Borjesson and C. Sundberg in IEEE Transactions on Communications (IEEE TC) in 1979 detailing the first acurate and closed form approximation of the Q-function, there has been a number of work (mainly in IEEE TEC) on improving the accuracy and ease of computation of approximations to the Q-function. These solutions was designed by human experts in the field of communications. In the paper, we use a Genetic Programming system to discover a new approximation that is more acurate than any previously published results by Human experts while maintaining the form of approximation that ease the computation. The new approximation is publishable and benefitial to researchers and practioners in the field of communications who could use it in their calculations related to the Q-function. 7. Full citation of the paper: Dao Ngoc Phong, Nguyen Xuan Hoai, Constantin Siriteanu, R.I. McKay,and Nguyen Quang Uy, Namyong Park, Evolving a Best Known Approximation to the Q Function, To appear in the Proceedings of ACM-SIGEVO Genetic and Evolutionary Computation Conference (GECCO'2012) 8. any prize money, if any, is to be divided equally among the first five authors (20%-20%-20%-20%-20%-0%) 9. Very acuarate approximations to the Q-function (and its inverse) are immensely important in the field of communications. The optimal approximation in closed and simple form is not known. Human's solutions based on mathematical theories are often etremely good (going to optimal) if only the complexity of the function (usually number of serie terms) goes to infinite. Therefore, the problem of finding short, simple, and in-closed-form approximations to the Q-function is a potentially good application for Evolutionary Computation. Our paper is the first to detail an approach using a Genetic Programming system to solve the problem. The result obtained is better than any previously known/published solutions (in terms of accuracy). It not only provides a good and practical solution to the problem but also demonstrate the usefulness of Evolutionary Computation techniques.