Emphasizing Foundational Research Challenges and Issues of Theoretical Computer Science and Computing Systems for the Trusted Future Computing Environment

The concepts involving the theoretical aspect of computer science have now become implanted in computing systems that must penetrate the thought process of each and every computer scientist. Theoretical computer science provides a hands-on tool to understand and dive deeper into technology. This theoretical computer science and computing systems will straightaway modify drastically the way of studying science in the future. The extent to which the new technology will be successful in solving the difficult scientific and societal problems depends on the progress in theoretical research in computing. Theoretical, fundamental and unpredictable discoveries and innovation will modify the field of computer science. It addresses risky,unpredictable problems and provides the base for innovations in technology in the future. There is a need for a more basic research that is high risk/high return research. This will give rise to new ideas and methods for new applications development. In our paper we are emphasizing on the challenges existing in theoretical computer science and computing systems that were recorded in its chronological order of significance. The challenges and problems were discussed critically and the loop holes in the research were depicted. The requirement for future research is highlighted for the betterment of future of computing environment. These problems are categorized under cognitive science, bio medicine, polynomial, bioinformatics, application development and many other new age technologies. The primary purpose of this paper is to solve the fundamental theoretical questions and to grow interest that will become the pivot of intellectual pursuits all over the world.The social lifestyle is being changed by the modern sciences. The concepts revolving computers have gained momentum after World War II. There have been many radical changes, products and systems that have immensely affected the business and lifestyle of people for years and it is still doing so. But even today there lies many issues in the computing world. Once these problems are solved the society will be benefited with automated, enhanced and trusted services through the computing world.Computer science is the study of theory, experimentation and engineering that forms the building block for the design and use of computers. Also, it is a science that explores automated algorithmic procedure to perform a particular computation or task. A researcher of computer who is working in this field separates the problems into theoretical and practical subsets. Researchers from all over the world have recorded their challenges and problems. Even after the immense growth of this field the problems remain unsolved. To increase the understanding of the prevailing problems this review has been undertaken. This may come to a help to the researchers who can formulate suitable research projects for the current problems. This paper lists some of the vital challenges tat are prevailing in the field today.There are numerous major closed form problems in computer science, the theoretical computer science problems are such as Computational Complexity theory, Polynomial (P) vs. Non-deterministic Polynomial (NP), Cryptography, Integer Factorization, Clustered Planar, Multiplication Algorithm, Fourier Transform, Tree Rotation, Integer Multiplication and Matrix Multiplication Algorithm. The computing system problems are Big-data Applications and Analysis, Artificial Intelligence and Robotics, System Biology, Computational Biophysics, Computational Cognitive Science, Computational Neuro-biology, Natural Language Processing, Human Computer Interaction, Space Communication and Networking and Internet Security. Hence, if the computing world finds the acceptable solutions for these problems then the society will enjoy a trusted and better computing service.