Technical Report 2013-608 WHAT IS COMPUTATION?

Abstract Three conditions are usually given that must be satisfied by a process in order for it to be called a computation, namely, there must exist a finite length algorithm for the process, the algorithm must terminate in finite time for valid inputs and return a valid output, and finally the algorithm must never return an output for invalid inputs. These three conditions are advanced as being necessary and sufficient for the process to be computable by a universal model of computation. In fact, these conditions are neither necessary, nor sufficient. On the one hand, recently defined paradigms show how certain processes that do not satisfy one or more of the aforementioned properties can indeed be carried out in principle on new, more powerful, types of computers, and hence can be considered as computations. Thus the conditions are not necessary. On the other hand, contemporary work in unconventional computation has demonstrated the existence of processes that satisfy the three stated conditions, yet contradict the Church-Turing Thesis, and more generally, the principle of universality in computer science. Thus the conditions are not sufficient

WHAT IS COMPUTATION?

Three conditions are usually given that must be satisfied by a process in order for it to be called a computation, namely, there must exist a finite length algorithm for the process, the algorithm must terminate in finite time for valid inputs and return a valid output, and finally the algorithm must never return an output for invalid inputs. These three conditions are advanced as being necessary and sufficient for the process to be computable by a universal model of computation. In fact, these conditions are neither necessary, nor sufficient. On the one hand, recently defined paradigms show how certain processes that do not satisfy one or more of the aforementioned properties can indeed be carried out in principle on new, more powerful, types of computers, and hence can be considered as computations. Thus the conditions are not necessary. On the other hand, contemporary work in unconventional computation has demonstrated the existence of processes that satisfy the three stated conditions, yet contradict the Church-Turing Thesis, and more generally, the principle of universality in computer science. Thus the conditions are not sufficient

Technical Report No. 2006-508 EVEN ACCELERATING MACHINES ARE NOT UNIVERSAL

We draw an analogy between Godel's Incompleteness Theorem in mathematics, and the impossibility ofachieving a Universal Computer in computer science. Speci cally, Godel proved that there exist formal systems of mathematics that are consistent but not complete. In the same way, we show that there does not exist a general-purpose computer that is universal in the sense of being able to simulate any computation executable on another computer