Yuri Matiyasevich (St Petersburg)
Turing Machines vs Diophantine Machines

Allan Turing introduced his celebrated machines by analyzing elementary steps of computational devices, real physical and abstract imaginary ones. Diophantine machines were introduced by Leonard Adleman and Kennet Manders from quite different considerations - on the base of DPRM theorem about sets defined by Diophantine equations. The talk will be devoted to comparison and interplay of these two kinds of machines.