On the Power of Real Turing Machines Over Binary Inputs

In recent years the study of the complexity of computational problems involving real numbers has been an increasing research area. A founda-tional paper has been 4] where a computational model |the real Turing machine| for dealing with the above problems was developed. One research direction that has been studied intensively during the last two years is the computational power of real Turing machines over binary inputs. The general problem can be roughly stated in the following way. Let us consider a class C of real Turing machines that work under some resource bound (for instance polynomial time, branching only on equality, etc.). If we restrict these machines to work on binary inputs (i.e. nite words over f0; 1g) they deene a class of binary languages D. The question is, what can we say about D depending on C? More formally, let us denote by IR 1 the direct sum of countably many copies of IR and let P(IR 1) be the set of its subsets. Also, let us denote by the subset f0; 1g of IR and |as usual| by the subset of IR 1 consisting Partially supported by DGICyT PB 920498, the ESPRIT BRA Program of the EC under contracts no. 7141 and 8556, projects ALCOM II and NeuroCOLT. y Partially supported by Volkswagen{Stiftung.