Turing completeness bullshit

http://shebang.ws/turing-completeness-bullshit.html

by fogus • 15 years ago

65 44 15 years ago

cleverjake• 15 years ago

While I agree that it is a bit of a misnomer to say that anything is possible in a turing complete language from a feasibility stand point, I think this response falls back to a common thought process that technical minded people go through - literal answers. Of course it is possible to do it, it may just be incredibly difficult. When most people ask if they can do X in Foo, they are usually asking if it is a good idea to do X in Foo. Should the person being asked tell them no even if it is a possibility that is not easy?

damncabbage• 15 years ago

I think it's also due to some people kinda-sorta understanding what Turing Completeness means, and then applying it to everything to sound smart.

p4wnc64• 15 years ago

I agree. The OP blog post is mistaking. I think the real language misuse is on the behalf of Person A. When asking whether you "can do something in the Foo programming language" this could be a question of theoretical universality or a question of practicality. If it's one of practicality, then it has nothing to do with Turing universality. If it's theoretical, as in "is Foo expressive enough to describe such and such a computation at all", then universality matters.

Also, from a computationalist's perspective in Philosophy, Turing completeness literally does mean being able to do anything that a single-taped Turing machine can do (such as writing a GUI or writing to a screen). If you a priori disconnect your Turing machine from the screen, effectively eliminating the logical possibility to print to it (or, similarly, you use some pared down language where specific functionality is intentionally left out) then it makes no sense at all to bring Turing completeness into it. It seems like the OP either rejects the Extended Church Turing thesis, or mistakenly thinks that other people lump all possible hardware limitations into Turing completeness. If a language is resource bounded, then it is only Turing complete w.r.t. a Turing machine that has the same resource bounds.

5hoom• 15 years ago

Wonderfully put, thank you.

z92• 15 years ago

Needs paragraph break.

andreasvc• 15 years ago

> anything that a single-taped Turing machine can do (such as writing a GUI or writing to a screen).

Wait, those are the things a Turing machine CANNOT do! A Turing machine has no input or output, the computation it defines is purely a function of what's on its tape before and after its work (when it halts).

> If you a priori disconnect your Turing machine from the screen

Again this makes no sense, the ('a priori') defintion of a Turing machine does not include a screen, so there's nothing to disconnect. It's really just the tape.

And no, it's quite a stretch to claim that person A could be talking about universality, the blog post says he was asking about GUIs so that's squarely a practical question.

> or [...] thinks that other people lump all possible hardware limitations into Turing completeness.

I have no idea how you arrive at this from the blog post.

podperson• 15 years ago

Agreed (also agree with another post at this level).

It seems like a clever "nit" to pick but the only thing you need to add to "turing complete" is "able to address memory in a reasonable way" (or "not sandboxed from memory") and you get everything the author is complaining about and you're back to square one (i.e. the language is "turing complete and has memory access".

How do I print? I stick stuff in the right places in memory and set the program counter. How do I draw graphics? I stick stuff in the right place in memory and set the program counter.

wyuenho2• 15 years ago

Ahhhh no I disagree. I think this is one of those 140 char limit short sound bite problems that often makes the people listening hard to understand.

Turing Completeness is about computability, but also implies the functions in that class are able to simulate each other. So "theoretically", you COULD write an interpreter in Brainfuck without "," and "." that simulates language L by doing output using some other means, or representing it differently besides printing it out onto the screen. All it has to do is to leave an output state on a Turing Machine.

Now the question, when people talk about "Foo is Turing complete so you can do everything.", is this really what they mean? Probably not, most of them only say this half-jokingly. It's theoretically possible, it's just very unpractical in reality. I'm nonetheless equally annoyed by the term "general purpose language" for the reasons pointed in the post tho.

phillmv• 15 years ago

You could presumably write a "Limited Brainfuck" compiler and then write an interpreter for any language you want into that :P.

If it's complete, it's turtles all the way down.

wyuenho2• 15 years ago

Exactly, that's why my mind screams "BS" every time I hear the term "general purpose language".

cyrus_• 15 years ago

Alan Perlis coined the term "Turing tarpit" for this in one of his Epigrams on Programming.

http://en.wikipedia.org/wiki/Turing_tarpit

RockyMcNuts2• 15 years ago

If you can do a test, a loop, and a write, you're Turing complete IIRC. Hell, the DOS shell is Turing complete, your HP-12C is Turing complete.

So ANSI SQL with selects only may not be Turing complete, but pretty much all SQL implementations are, since they added loops, not to mention stored procedures etc.

All languages are Turing complete and equivalent from a computability standpoint. That's the sense in which it means nothing for a language to be Turing complete - they all are.

They are different in terms of expressive power, computational efficiency for different problems.

Can you do closures in HP-12C assembler? Of course! just write a Lisp interpreter in assembler, and there you go.

xyzzyz5• 15 years ago

The posts like yours are the ones that actually create confusion around this term, because their authors are confused on what the Turing completeness is themselves, and so they spread their confusion on the others.

No, tests and loops are not what make computational stuff Turing complete -- nondeterministic finite automatons have both of them, and yet they're very weak computationally. I/O (assuming that's what you mean by write) is not even relevant. What matters the most is _memory_, and more importantly, _infinite, easily accessible_ memory. Nondeterministic finite automata have only finite amount of memory available, and thus they are very constrained on what they can compute. Nondeterministic pushdown automata, in spite of having infinite amount of memory available, don't have an easy access to it, and so, being stronger than finite automata, they're still weaker than Turing machines. But as soon as you add a second stack to a pushdown automaton, it suddenly becomes Turing complete. Hell, you can do it even with 6 integer variables instead of 2 stacks (I recall from my computation theory course that 3 integer variables are enough to encode a stack, so 6 will give you two stacks. Maybe you can go down even to 5 or 4). However, you absolutely require infinite memory, because, for sane definitions of "memory", every device with finite amount of memory (for instance, x86 PC) will not be able to compute anything more than deterministic finite automaton. From this point of view, all our computers are able to do is to match its input to a long and hairy regular expression. I hope that it will help some people realize how irrelevant is Turing completeness notion when it's used with regard to real life stuff.

alok-g3• 15 years ago

This was helpful! I knew most of the pieces but not about the 3 integers encoding a stack. I presume integers here can be of any size (that is not constrained by number of bits) or else it won't be infinite amount of memory. Nevertheless, could you shed some more light? Is a push operation left shifting the integer and adding the pushed value...?

djcapelis2• 15 years ago

You're way off the mark. While it annoys me that computers are constantly modeled as Turing Machines when it's much more appropriate that they be modeled as LBAs (Linear Bounded Automata) it does not have a huge bearing on computational feasibility in practice. While LBAs vs. TMs do have entirely different definitions and notions of what is and what is not undecidable (for instance, the halting problem is decidable for computers since they're LBAs. It's just impractical.) this only really becomes a theoretical difference.

Suggesting that an x86 PC is limited to the level of computational complexity of regular grammars is just wrong. LBAs are capable of context sensitive grammars and are much more capable than a FSM and absolutely can compute more.

In real life, computers can be modeled as turning machines without much issue. Memory is generally Big Enough(tm) that problems undecidable on TMs are terribly infeasible to attempt even though theoretically they are actually decidable.

And as long as the problem has a small enough state space, the computational expressiveness is the same. In practice, this occurs often enough that people still call computers turing machines even though they aren't.

RockyMcNuts2• 15 years ago

fair enough - sufficiently large memory is also necessary. For that reason you couldn't write a Lisp interpreter on the 12C, although you could write one in the 12C language.

The point I was trying to make is that the simplest languages are Turing equivalent (given sufficient memory), because they have the necessary tests and control flow.

The TFA goes a bit astray IMHO when it says Turing completeness is not necessary for a language to be useful. Turing completeness is a low bar and even SQL as generally implemented hurdles it.

sorry, I wasn't incredibly rigorous or clear.

praptak• 15 years ago

"If you can do a test, a loop, and a write, you're Turing complete IIRC."

No. What you got is a while-program. The main limitation of a while-program is the finite number of variables it has. Its computational power therefore depends on the data types it can work on.

Of course if you have stacks, dynamic arrays or equivalent then you're basically Turing-complete. Even if all you have is unbound integer arithmetic, you can emulate the infinite tape on the bits of a large integer.

If you only have finite types, then the while-program obviously has a finite number of states, so it's equivalent to an FSM.

0x123• 15 years ago

Your understanding is limited and confuses rather than enlightens.

A test, loop and write are not the definition of Turing complete.

See:

http://en.wikipedia.org/wiki/Turing_complete

And for a very interesting take on this:

http://en.wikipedia.org/wiki/Rule_110

And

http://en.wikipedia.org/wiki/One_instruction_set_computer

gfodor• 15 years ago

You think that's bad? I'll raise you the "the halting problem proves that you can never prove a program halts" claim.

baddox2• 15 years ago

The two statements aren't really analogous. Yours is simply incorrect, while the one in the article is a correct (factual) response that's just not helpful.

mihaifm• 15 years ago

What's so incorrect about this statement?

InclinedPlane• 15 years ago

Turing completeness concerns itself with the ability of a computer to solve problems that are computable. Modern computers, however, are almost entirely purposed towards interacting with humans and processing data.

Mathematically these "problems" are isomorphic, but the real world concerns itself with issues like correctness, robustness, performance, efficiency, cost, scalability, etc.

The idea of turing completeness compares a 100% perfect program against another 100% perfect program. It does not concern itself at all with efficiency, which is horrific in and of itself, but worse yet it does not concern itself with the difficulty of creating and maintaining the program. Given that this tends to be the overwhelmingly largest factor in the cost of creating software this is a bit of a problem.

0x123• 15 years ago

Turing completeness deals with computability, not with the practicalities of IO and so on.

To say that something is Turing complete simply means that you could implement a universal Turing machine, which can then run any other Turing machine as its program, and so can compute anything that is in theory (without any constraints on time and space) computable.

I understand the authors aggravation with people throwing around the sentence 'x is Turing complete, so you can do anything in x' without any appreciation of the disconnect between the theoretical and the practical sides of this, but I think that it's use is more in jest than serious and that the author should possibly grow a sense of humor.

Typical use:

A: can you do 'x' in Perl

B: Perl is Turing complete, of course you can do 'x'.

Shows that person 'B' has a sense of humor and/or wants to get rid of the questioner without having to answer the question, not that they're clueless about the practicalities of this statement.

It's analogous to 'google it', 'rtfm' or any one of another 100 ways in which people try to show their superiority over others or try to create an 'in' and and 'out' group. Think of it as just another meme and move on.

Flagged.

omaranto• 15 years ago

Flagging a post because you think the author lacks a sense if humor seems harsh to me.

0x123• 15 years ago

No, I've flagged it because this 'Turing Completeness Bullshit' is not bullshit, but the article is. Turing completeness actually has a use and railing against the people that use it in a manner that it was never intended to be used in is a total waste of time.

The article author seems to agree with that assessment, see: http://news.ycombinator.com/item?id=3047002

Turing completeness bullshit

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