Lenore Blum: “Alan Turing and the other Theory of Computation”

Abstract:

Most theoretical computer scientists are familiar with Alan Turing’s 1936 seminal paper setting the stage for the foundational (discrete) theory of computation. Most however remain unaware of Turing’s 1948 seminal paper, notwithstanding its many references in the modern literature of numerical analysis and computational mathematics. The 1948 paper, introducing the notion of condition, sets the stage for a natural theory of complexity for the “other theory of computation” emanating from the classical tradition of equation solving and the continuous mathematics of calculus.

This talk will recognize Alan Turing’s work in the foundations of numerical computation (in particular, his 1948 paper “Rounding-Off Errors in Matrix Processes”), its influence in complexity theory today, and how it provides a unifying concept for the two major traditions of the Theory of Computation.