AF: Small: Collaborative Research: Studies in Nonuniformity, Completeness, and Reachability

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Computational complexity theory classifies computational problems into various complexity classes based on the amount of resources needed to solve them. This classification is done by measuring various resources such as time, space, nonuniformity, nondeterminism, and randomness. A better understanding of the relationships among these various resources shed light on the computational difficulty of the problems that are encountered in practice. This project explores several central questions regarding nonuniformity, complete problems, and space bounded computations. This project attempts to discover improved upper bounds for problems with high circuit complexity. Regarding complete sets, non-relativizing properties of complete sets will be explored. Space bounded computations will be investigated in the context of planar graph reachability problems. This project addresses several basic questions in computational complexity theory. The results from this project will further our understanding of computational resources such as nonuniformity, nondeterminism, and space. Research results will be published in peer-reviewed journals and will be presented at national and international conferences, thus enabling broad dissemination of the the results to enhance scientific understanding. New courses will be created and taught along the themes of this project, thus integrating teaching and research. The project supports various human resource development activities such as supporting and mentoring graduate students and inviting visitors.