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Questions tagged [turing-completeness]

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52
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6answers
11k views

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 ...
38
votes
9answers
7k views

Is C actually Turing-complete?

I was trying to explain to someone that C is Turing-complete, and realized that I don't actually know if it is, indeed, technically Turing-complete. (C as in the abstract semantics, not as in an ...
17
votes
2answers
6k views

How is the rule 110 Turing complete?

I've read the wikipedia page for rule 110 in cellular automata, and I more or less know how they work (a set of rules decides where to draw the next 1 or 0). I've just read they're Turing complete, ...
19
votes
2answers
4k views

Universality of the Toffoli gate

Regarding the quantum Toffoli gate: is it classicaly universal, and if so, why? is it quantumly universal, and why?
42
votes
9answers
14k views

Why are some programming languages Turing complete but lack some abilities of other languages?

I came across an odd problem when writing an interpreter that (should) hooks to external programs/functions: Functions in 'C' and 'C++' can't hook variadic functions, e.g. I can't make a function that ...
21
votes
5answers
5k views

Why are functional languages Turing complete?

Perhaps my limited understanding of the subject is incorrect, but this is what I understand so far: Functional programming is based off of Lambda Calculus, formulated by Alonzo Church. Imperative ...
5
votes
4answers
1k views

Do we need recursion in programming language to solve any problem?

My question is simple: If we want to be able to solve every problem, that we can solve using recursions, do we need programming language to allow us use recursions? Assuming we are allowed to use: ...
5
votes
1answer
682 views

Is a LBA with stack more powerful than a LBA without?

Even so a linear bounded automata (LBA) is strictly more powerful than a pushdown automata (PDA), adding a stack to a LBA might make it more powerful. A LBA with stack should not be Turing complete, ...
6
votes
4answers
2k views

Can we write algorithms without conditional statements?

Regarding turing completeness, i read that for a language/machine to be turing complete it is required that it has some sort of conditional. Consider the factorial problem, we would typically define ...
15
votes
2answers
3k views

What makes PROLOG Turing-complete?

I know that it can be proven PROLOG is Turing-complete by constructing a program that simulates a Turing machine like this: ...
4
votes
3answers
706 views

Rice's theorem vs Turing completeness

I would like to clarify this because I see some kind of contradiction between Rice's theorem and Turing completeness. This is the problem: In building an Universal Turing Machine to emulate another ...
6
votes
4answers
497 views

Is the halting problem always decidable for non-universal programs?

For every non-universal computable program $P$ that takes input of type $D$ does there exist some total computable function $g$ that takes an input $I$ of type $D$ and decides successfully whether $P$ ...
5
votes
5answers
611 views

Is there any example of automatas (or similar) systems that emerge complex internal structures on its own?

Automatas are turing-complete grid-based systems with progression rules on which we can encode arbitrarily complex structures. For example, this is a "glider gun" on Conway's Game of Life: Due to ...
5
votes
1answer
264 views

How rule 110 would be proven to be universal if the tag system did not exist?

I was reading about Cellular Automata and I read in this question that Matthew Cook proved that rule 110 is universal, and that his proof relied upon showing how rule 110 can simulate a tag system. ...
7
votes
1answer
960 views

How close are common programming languages to not being Turing complete?

The term "Turing completeness" has been discussed in several of the Computer Science classes that I've taken. However, I've never gotten an intuitive feel for what Turing completeness actually ...
7
votes
2answers
719 views

Is a stack machine with a forward read iterator Turing complete?

It is well known that a machine with a single stack as only unlimited storage is not Turing complete, if it can only read from the top of the stack. I want a machine which is (slightly) more powerful ...
6
votes
2answers
675 views

Looping and branching with Algorithmic Differentiation

Algorithmic (aka Automatic) Differentiation is a wonderful technique for numerical computation of derivatives. I understand how it relates to the fact that we know how to deal with every elementary ...
4
votes
1answer
239 views

Natural RE undecidable problems but not Turing-complete

The Halting problem is a natural undecidable language which is complete for the set of recursivly enumrable sets. I am interested in undecidable but not Turing-complete language such that we can not ...
2
votes
1answer
346 views

Would adding recursive named functions to Simply typed lambda calculus make it Turing complete?

Say I have Simply typed lambda calculus, and add an assignment rule: <identifier> : <type> = <abstraction> Where ...
2
votes
1answer
302 views

Explanation for indirect addressing

While reading about minimal instruction set computer I found out that one needs at least (for example) the ability to increment or decrement the value stored in register, a test for zero and a jump. ...
5
votes
3answers
2k views

Is there an algorithm for converting Turing machines into equivalent Lambda expressions?

We know that Turing machines and Lambda Calculus are equivalent in power. And There are proofs for that, I'm sure. But is there an algorithm, a systematic way for us to convert a Turing machine into ...
3
votes
1answer
287 views

Is a Turing Machine that only takes strings of the form $0^*$ Turing Complete?

You have a Turing machine that only processes input on the form $0^*$. If it is given an input without 0's, it will simply halt without accepting or do anything else. Is it Turing Complete? The set $...
2
votes
2answers
264 views

If a DFA can be simulated by a real program, can it be simulated by a TM

In proofs of decidability, we often want to simulate another model of computation by a Turing machine. But if I can simulate a $\mathsf{DFA}$ by, say, a C program, then is there some result which says ...