Computability

An algorithm is called computable if it can be encoded into a set of instructions, which can be input into a universal Turing machine for processing, and the universal Turing machine eventually halts. How to decide if an arbitrary algorithm is actually computable is called the halting problem. Alan Turing proved that the halting problem itself is uncomputable.

The definition of computability is largely a consequence of the Church-Turing thesis.