# 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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### Is there way to compare computing power used in two blockchains when every one of them is using different mathematical function as a Proof-of-Work?

If I am a Bitcoin node, I can evaluate two blockchains in terms of each one consisting of more Terahashes than the other and thus deduct which one is the "correct" one. There is impartial source of ...
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### Why is the tape not part of the definition of a Turing Machine?

I've wondered why the tape/tapes are not part of the formal definition of a Turing Machine. Consider, for example, the formal definition of a Turing machine on Wikipedia page. The definition, ...
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### Why no DPDA can accept Palindrome? (according to this proof)

This proof is from the book "Introduction to Languages and the Theory of Computation" by John C. Martin. My question is from the pink part at the second page: It follows in particular that no ...
29 views

### Would models of computation in other conceivable universes be Turing complete?

I'm interested in gathering some references that discuss the topic of the relationship between computation and physics. Specifically, I'm interested in investigating two points of view: our current ...
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### How does one program in a tag system?

I've played with 2-tag systems a bit and read all about tag/lag systems. They're great for experimenting with computation, and obviously useful as intermediaries in various proofs. My question is: ...
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### How to model most optimized encoding of string data

Sorry if this question isn't super well defined, I am just struggling currently with figuring out what an "ideal solution" looks like to the following problem, and haven't pinned down an equation. I ...
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### Can differennt computation model lead to different complexity?

There are many examples where someone replaces a CPU with a GPU or an FPGA and get a performance boost of $\times 100$ or more, but is it possible for a change in the architecture of computational ...
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### Similarities between Babbage's difference engine and the Turing machine

What would you consider similarities between the difference engine and the Turing machine? At this point I feel I know how they both function, yet I can't point out any worthwhile similarities between ...
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### Why do pushdown automata use a stack?

I'm taking a computer theory class and my professor told us that a pushdown automaton cannot use data structures other than a stack (like a queue or multiple stacks). Why is that?
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### Showing the following language is decidable

Let $BAL_{DFA} = \{<M> \mid M \text{ is a DFA that accepts some string containing an equal number of 0's and 1's } \}$ Show that $BAL_{DFA}$ is decidable. Generally such questions seem to be ...
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### Turing: Are the “m-configurations” in his original paper the same as the “means” in his definition of his “computable”?

Are Turing's "m-configurations" the same as the "means" in his original definition of "computable"? In the first line of Turing's paper "On Computable Numbers...", he defines a "computable" number as ...
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### Complexity classes for various models of computation

The various complexity classes usually taught and studied ($P$, $NP$ $co-NP$, EXP, NSPACE etc) are usually defined using Turing Machines as the preferred model of computation. Are these sets of ...
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### Manage event programming under a stack-oriented language

I wonder how events, or more broadly reactive programming, could be managed in a simple stack-oriented language. For example, let's imagine a context where there is a button that displays a small ...
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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 ...
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### Is the graph symbol used in dask a general notation?

Dask is a flexible library for parallel computing in Python. This piece of code define some simple functions. ...
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### Differences between programming model and programming paradigm?

What is the relation and difference between a programming model and a programming paradigm? (especially when talking about the programming model and the programming paradigm for a programming language....
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### Computational power of machine learning

In a nut shell, machine learning is a class of algorithms that can "train" data-structures. You provide a trainer with partial information, and it will produce some entity which can be queried on ...
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### What is the difference between Babbage's analytical and difference engine?

What is the difference between Babbage's analytical and difference engine? Can they even be compared?
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### Injectivity verification in o(n) space and O(n) time

The problem I want to solve is this: Given a list $A$ of $n$ elements, I want to verify that they are all distinct. If I were to do this "myself", I would need $O(n)$ space and $O(n\log n)$ time to ...
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### If the human brain is a Turing machine then how is it able to ascertain that certain problems are undecidable? [closed]

I recently read about the idea that the human brain might be a Turing machine (or Turing complete). If that is true then how is the brain able to reason that a certain problem is undecidable for e.g. ...
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### why does the pumping lemma want us to only consider the first repitition of states?

In Sipser's Intro to Theory and computation, He writes: I don't understand the constraint on x. Shouldn't it be just y <=p? (Equal bc in the case when machine M runs through all states p) Making ...
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### Random Access Machines with only addition, multiplication, equality

The literature is fairly clear that unit-cost RAMs with primitive multiplication are unreasonable, in that they cannot be simulated by Turing machines in polynomial time can solve PSPACE-complete ...
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### Difference between multi-tape Turing machine and single tape machine

A beginner's question about "fine-grained" computational power. Let $M_k$ be a $k$-tapes turing machine, and let $M$ be a single tape turing machine. We know that $M_k$ and $M$ both have the same "...
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### Can a petri net fire only one transition at a single moment?

After reading several articles about petri nets, I am confused on how firing works. Can Petri net system fire only one transition out of all active (fire-able transitions) at a single moment? Or are ...
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### Uncomputably coded model of computation

There are many different but equivalent models of computation. I assume their equivalence is shown by coding input of one model to the input of the other model and making an argument why should there ...
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### Defining computable functions on arbitrary sets

Turing machines take inputs that are strings of symbols from some alphabet, and they give outputs that are strings of symbols from the same alphabet. To show that a function is computable, we have to ...
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### Is there a name for an inverted state machine?

I recently needed something like a state machine, but with a slightly different use case. In general, I would say a state machine knows about a set of states, and different events. Depending on the ...
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### What's the purpose of the non-deterministic Turing machine?

(*) Acronyms NTDM := non-deterministic Turing machine. TM := deterministic Turing machine. (*) Consider the following idea The NTDM is able to follow, in parallel, all paths of the tree of the ...
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### State-machine semantics of instruction set architectures

An instruction set architecture is an abstraction, a common interface layer between the software and the micro-architecture. The existence of this clearly delineated interface is becoming increasingly ...
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### What mathmatical model shall be used for describing P2P processes interaction?

I am creating a distributed service system. It runs in the cloud on heterogeneous hardware. I am using C# .NET for business logic and C++ for different physics\chemical calculations. Having three ...
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### Theory for programs that are “embedded” in other programs?

We can make the following distinctions: (I will use the term "program" and "machine" as synonyms). A (baseline) machine. This can be formalized by a Turing machine. It receives an input, and computes ...
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### What is the computation model of Prolog?

Several computation models have representative programming language counterparts, as, according to this answer, Snobol for rewriting systems, APL for combinators, Lisp/Scheme for lambda calculus, and ...
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### The order of ε-transitions in NFA

I'm reading 'Introduction to the Theory of Computation' by Michael Sipser. He gives an example of a NFA, stating that this particular automaton accepts $a$ (he lists other strings as well, I just want ...
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### What did Turing mean when saying that “machines cannot give rise to surprises” is due to a fallacy?

I encountered below statement by Alan M. Turing here: "The view that machines cannot give rise to surprises is due, I believe, to a fallacy to which philosophers and mathematicians are ...
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### NP with a parallelism model?

Can we think of NP using a parallelism model instead of using a "checking relation" without loss of generality? From what I understand from the problem statement given by Stephen Cook, The ...
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### Can we use Wifi signals readings to estimate 3D shapes?

I don't know if this is the appropriate SE for this question, but I hope someone would answer !
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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 ...
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### Is the proof for the undecidability of $A_{TM}$ still valid if we change certain parts?

i have a question based on a question i saw exists on the site, but with wrong information in it and no answer there, so i am reposting it with valid information(cited wrong from the book). on page ...
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### General notion of memory for a computational model

I have just started studying Michael Sipser's Theory of Computation, studying various computational models such as FAs, PDAs et cetera. In the book, the term "memory" was often used,as in the case of ...
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### PRAM with no bit operations and P vs NC

I was reading up on something called the PRAM model without bit operations. What exactly does it mean that this PRAM model cannot do bit operations? I can't find a straightforward definition anywhere....
My RAM machine is very simple: it has $k$ tapes, an input tape and one special control tape it has an infinite memory (array called $A$) which can be accessed randomly the control tape is read ...