Surreal Blum-Shub-Smale Machines Lorenzo Galeotti Abstract: Blum-Shub-Smale machines are a classical model of com- putability over the real line. In [9], Koepke and Seyfferth generalised Blum-Shub-Smale machines to a transfinite model of computability by allowing them to run for a transfinite amount of time. The model of Koepke and Seyfferth is asymmetric in the following sense: while their machines can run for a transfinite number of steps, they use real num- bers rather than their transfinite analogues. In this paper we will use the surreal numbers in order to define a generalisation of Blum-Shub-Smale machines in which both time and register content are transfinite.