Are there minimum criteria for a programming language being Turing complete?
Does there exist a set of programming language constructs in a programming language in order for it to be considered Turing Complete?
From what I can tell from wikipedia, the language needs to support recursion, or, seemingly, must be able to run without halting. Is this all there is to it?
Asked By : Khanzor
Best Answer from StackOverflow
Question Source : http://cs.stackexchange.com/questions/991
Answered By : Raphael
I always though that $\mu$-recursive functions nailed it. Here is what defines the whole set of computable functions; it is the smallest set of functions containing resp. closed against:
- The constant $0$ function
- The successor function
- Selecting parameters
- Function composition
- Primitive Recursion
- The $\mu$-operator (look for the smallest $x$ such that...)
Check above link for details; you see that it makes for a very compact programming language. It is also horrible to program in -- no free lunch. If you drop any of those, you will lose full power, so it is a minimal set of axioms.
You can translate those quite literally into basic syntactical elements for WHILE programs, namely
- The constant
0
- Incrementation
_ + 1
- Variable access
x
- Program/statement concatenation
_; _
- Countdown loops
for ( x to 0 ) do _ end
- While loops
while ( x != 0 ) do _ end
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