Difference between revisions of "Computability"
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| − | An [[algorithm]] is called '''computable''' if it can be encoded into a set of instructions, which can be input into | + | 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]]. | The definition of computability is largely a consequence of the [[Church-Turing thesis]]. | ||
| − | [[ | + | [[Category:Logic]] |
[[Category:Computer Science]] | [[Category:Computer Science]] | ||
Latest revision as of 18:10, June 27, 2016
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.