Friday, May 30, 2014

Being Turing Complete Ain't All That and a Bag of Chips

I was talking to someone the other day. He said that given two Turing Complete programming languages, A and B, if you can write a program in A, you can write a similar program in B. Is that true? I suspect not.

I never took a class on computability theory, but I suspect it only works for a limited subset of programs--ones that only require the features provided by a Turing machine. Let me provide a counterexample. Let's suppose that language A has networking APIs and language B doesn't. Nor does language B have any way to access networking APIs. It's entirely possible for language B to be Turing Complete without actually providing such APIs. In such a case, you can write a program in language A that you can't write in language B.

Of course, I could be completely wrong because I don't even understand the definitions fully. Like I said, I've never studied computability theory.

4 comments:

Ewa Janikowska said...

I think you should have stopped on "I never took a class on computability theory". This statement is true and there is a mathematical proof of that. You have to correctly understand what is Turing Complete Language and how Turing Machine is defined. It's really far from any of programming languages that are being used.

Ewa Janikowska said...

BTW, you can always write your own Networking API in language B and then use it.

Shannon Behrens said...

Ewa,

> I think you should have stopped on "I never took a class on computability theory".

There's no need to be mean ;)

> It's really far from any of programming languages that are being used.

Yeah, my buddy John Chee just enlightened me with (https://twitter.com/chee1bot/status/472585589045207042). All this time, people have just been throwing around that most programming languages are Turing Complete, whereas, as you said, "It's really far from any of programming languages that are being used."

> BTW, you can always write your own Networking API in language B and then use it.

I'm not sure how that would work if the language doesn't have APIs for accessing hardware or other processes. Hence, you certainly couldn't write Chrome in such a language.

Matthew Good said...

To simplify the networking example think about a program that sends a "ping" message and waits for the response "pong".

If you take Python and throw away the standard library, and even the built in functions, you're left with a language with no network or even file access. Can you still write "ping"?

You can if you think outside the "box" (bad pun) and consider both machines as part of a bigger program. In this stripped down Python you can define classes representing the two machines, the ping and pong programs, and the network connection between them. Even though your program has no physical network, you can still compute the same result.

All the Turing theory says, is that you can write a program in the other language to compute the same result. Networking adds a way to distribute the computation across multiple physical computers, but you can achieve the same result with one computer, given enough time and sufficient memory.

So to write Chrome, you just have to write a simulation of the Internet :)