The computational power of self-stabilizing distributed systems is exa
mined. Assuming availability of any number of processors, each with (s
mall) constant size memory we show that any computable problem can be
realized in a self-stabilizing fashion. The result is derived by prese
nting a distributed system which tolerates transient faults and simula
tes the execution of a Turing machine. The total amount of memory requ
ired by the distributed system is equal to the memory used by the Turi
ng machine (up to a constant factor).