Whit Tabor (UConn)
Apr 15, 2pm, LH 302
Consider an iterated map f on a connected space X. A proper subset, A, of X, is said to be asymptotically stable if, when the system is perturbed slightly away from A, it converges back on to A, under continued iteration of f. When one is working in the realm of logic, or classical computation more broadly, stability is not an issue and does not really make sense. There is no possibility of being slightly off—formulas are either well-formed and have precise meaning, or they are ill-formed and they have no meaning at all. Interestingly, in recent decades, a number of people have discovered ways of doing complex computation on connected spaces. This raises the question of whether there could be “stable computation” in such systems. In this talk, I define asymptotic stability for a particular type of connected space computer and show that at least one interesting class of languages (the mirror recursion languages) has a realization which exhibits asymptotic stability of certain fractal sets. One interesting outcome is an answer to the question: Why is there grammaticality?