<p><span style="font-size:11pt"><span style="font-family:Calibri,sans-serif">One of the main goals of artificial intelligence is to develop learning algorithms that can be implemented on computers using simulations of the human brain. In this paper, we review methods for solving Turing machine problems using experiment based artificial intelligence algorithms. The paper also presents critical concepts of the NTM method based on a comprehensive review of the research made in this domain. Experimental results of applying the NTM method to memory data and problem solving are being presented. The paper presents scientific discussions ongoing in this domain and solutions to future challenges.</span></span></p>