During his PhD, Buss worked in bounded arithmetic. He received his PhD in 1985. He introduced bounded arithmetic in his thesis and gave a nice proof theoretic characterization of polynomial time computation. His thesis is one of the main references in the area of bounded arithmetic.[2] He is also author/editor of several books in mathematical logic and computer science.[3]
Buss proved in 1983 that the Boolean Formula Evaluation problem is in ALogTime, a major result in complexity theory.