# Questions tagged [computation-models]

The definition of the set of allowable operations used for computation and their respective costs. Some examples of models include Turing machines, recursive functions, lambda calculus, and production systems.

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### Differences and relationships between randomized and nondeterministic algorithms?

What differences and relationships are between randomized algorithms and nondeterministic algorithms? From Wikipedia A randomized algorithm is an algorithm which employs a degree of randomness ...
3answers
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### How to show two models of computation are equivalent?

I'm seeking explanation on how one could prove that two models of computation are equivalent. I have been reading books on the subject except that equivalence proofs are omitted. I have a basic idea ...
1answer
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### Universal simulation of Turing machines

Let $f$ be a fixed time-constructable function. The classical universal simulation result for TMs (Hennie and Stearns, 1966) states that there is a two-tape TM $U$ such that given the description of ...
5answers
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### Are if statements unnecessary if a program is represented as an explicit state machine?

This question occurred to me some time ago when I was thinking about whether or not if statements are fundamental in computation. Consider a program that manages a ...
2answers
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### Classfication of randomized algorithms

From Wikipedia about randomized algorithms One has to distinguish between algorithms that use the random input to reduce the expected running time or memory usage, but always terminate with a ...
1answer
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### Expressiveness of modern regular expressions

I recently discussed with a friend about a website that proposed regex challenges, mainly matching a group a of words with a special property. He was looking for a regex that matches strings like <...
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### Is a Turing Machine “by definition” the most powerful machine?

I agree that a Turing Machine can do "all possible mathematical problems". But that is because it is just a machine representation of an algorithm: first do this, then do that, finally output that. ...
2answers
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### How to define quantum Turing machines?

In quantum computation, what is the equivalent model of a Turing machine? It is quite clear to me how quantum circuits can be constructed out of quantum gates, but how can we define a quantum Turing ...
2answers
910 views

### How is the computational power of a human brain comparing to a turing machine?

This seems related to these questions at a glance: What are some problems which are easily solved by human brain but which would take more time computers? What would show a human mind is/is not ...
1answer
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### 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, ...
1answer
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### How can one simulate a PDA with a FIFO queue PDA?

I'm trying to figure out how a pushdown automata (PDA), which we know uses a stack (LIFO) can be simulated by a queue (FIFO). I understand that in a regular PDA, we only have access to the top most ...
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### Right moving turing machine

I am interested in simulating any turing machine with a turing machine that is allowed only to move right. I guess that it should be pretty standard material and likely it is trivial (or known to be ...
2answers
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### Is there an always-halting, limited model of computation accepting $R$ but not $RE$?

So, I know that the halting problem is undecidable for Turing machines. The trick is that TMs can decide recursive languages, and can accept Recursively Enumerable (RE) languages. I'm wondering, is ...
3answers
247 views

### Splicing squares on a Turing Machine finite tape

Trying to explain a problem, I thought of a variant of Turing Machines. It is unlikely to be new, but I do not recall ever seing it before, and I wonder whether it has been used or has a name. The ...
2answers
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### Quantum lambda calculus

Classically, there are 3 popular ways to think about computation: Turing machine, circuits, and lambda-calculus (I use this as a catch all for most functional views). All 3 have been fruitful ways to ...
1answer
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### Algorithm Complexity Analysis on functional programming language implementations

I've learned today that algorithm analysis differs based on computational model. It is something I've never thought about or heard of. An example given to me, that illustrated it further, by User @...
1answer
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### Is non-determinism in a non-deterministic turing machine different from that of finite automata and push down automata?

Let a input string be given as $w_1w_2...w_n$. Then if a NFA is currently in state $r$ ( and has read the input upto alphabet $w_i$ ) then before reading the next input symbol the NFA splits into two ...
2answers
421 views

### How do nondeterministic Turing machines compute general function problems?

(Hope this hasn't been asked before, but I didn't find anything.) In my understanding, nondeterminism applies to decision problems only, due to the requirement of the existence of an accepting path. ...
4answers
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### 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: ...
6answers
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### Do Turing machines assume something infinite at some point?

In a previous question What exactly is an algorithm?, I asked whether having an "algorithm" that returns the value of a function based on an array of precomputed values was an algorithm. One of the ...
2answers
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### Is there any data structure that can't be represented or described inside a computer?

We all know that, at least theoretically, there are several possible models of computation, varying in structure. Strictly speaking, there are several (not just one) models of computation that exist ...
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### Can a Turing machine have infinite states?

Does it make sense for a Turing machine to have infinite number of states ? I had previously asked a question Can Turing machines have infinite length input. From which I came to know about Type-2 ...
2answers
719 views

### $L(M) = L$ where $M$ is a $TM$ that moves only to the right side so $L$ is regular

Suppose that $L(M) = L$ where $M$ is a $TM$ that moves only to the right side. I need to Show that $L$ is regular. I'd relly like some help, I tried to think of any way to prove it but I didn't ...
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### Variant of Turing machine

How to prove that standard Turing machine is equivalent to a variant model where a string is accepted if the machine enters an accept state during computation? However, the machine may leave the ...
3answers
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### Where does the need for conditionals (if, switch, jump tables, etc…) truly arise? [duplicate]

I know that this question is a bit out-of-the-box, yet i would be glad if someone could help with a good answers for my question because it is something that is troubling my curious mind. When we ...