Foundations and Frontiers in Theoretical Computer Science: A Review of Key Concepts and Open Problems

Abstract

The survey looks into the foundations and the frontiers of Theoretical Computer Science (TCS) which is a central bit of computing to understand capabilities, limitations, and models of computation. Its concentration areas are the automata theory, computability, complexity theory, logic, and algorithms, along with the multidisciplinary overlap with quantum computing, cryptography and geometry, and machine learning. The new advances--in interactive proofs and zero-knowledge protocols and in quantum complexity--all indicate that the field still has its youthful vitality. Such important open issues as P vs NP and circuit lower bounds still exist to make the study. First-order effects include allowing TCS to provide leverage to secure communication, efficient algorithms, formal verification and theory of artificial intelligence. Looking to the future, it can be said that there are several possible issues on the horizon in the sphere in the sense of both quantum computing and ethical AI and biological computing, respectively. The design, analysis and development of computer science is still centered on TCS, and it is important to consider theory and practice through the integration of the two.