The talk is centered around the problem of solving a system of Boolean equations in several variables over finite Boolean algebra coefficients. This problem has been addressed in many different communities of engineers and scientists in different ways. However fundamental to all these approaches is the process of elimination of variables and consistency of equations, which arise from what is known as the Boole-Shannon expansion of a Boolean function. This talk will address an attempt by the speaker in generalizing this expansion to derive consistency condition and elimination by arbitrary orthonormal Boolean functions over a finite Boolean algebra. In recent times, due to several applications in Computer Science and Cryptology the problem of solving Boolean systems has gained importance. This is often known as the Boolean satisfiability problem. Many competitive algorithmic heuristics have developed for fast and efficient solution of these problems. The approach being used by the speaker is however algebraic and is aimed at gaining another notion of efficient computation, that of scalability, which is important for solving large problems practically.
Virendra Sule has been teaching in Electrical Engineering departments at IIT Kanpur and then at IIT Bombay since 1990. During 2007-9 he served as the Head of Information Security group at the Computational Research Laboratories, Pune and worked on large scale and parallel computation. During 2009-10 he was instrumental in launching a project sponsored by DRDO on SAT based methods for cryptanalysis at the C. R. Rao Advanced Institute at Hyderabad. His research interests are in Cryptology, Boolean equations and Systems Theory and their applications in Electrical Engineering.