Podcast #128: We chat with Kent C Dodds about why he loves React and discuss what life was like in the dark days before Git. Listen now.

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.

Filter by
Sorted by
Tagged with
0
votes
0answers
16 views

What is difference between a formal system and a model of computation

I don't exactly know the difference--partly because I cannot find a mathematical definition for a model of computation (also why is this)?
1
vote
1answer
26 views

Is “represents” a symmetric relation in the provided answer to TAOCP exercise 1.1.9?

In exercise 1.1.9 of volume 1 of The Art of Computer Programming, the reader is asked to formulate a set-theoretic definition for the concept "$C_2$ is a representation of $C_1$" where $C_1$ and $...
2
votes
0answers
14 views

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 ...
0
votes
1answer
33 views

support vector machine values

Does anybody knows how to calculate w1 and w2 and b . I have the formula but I have no idea where those numbers come from . my question has solution so it is not a home work because the solution of ...
2
votes
1answer
36 views

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 ...
0
votes
0answers
7 views

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 ...
1
vote
0answers
18 views

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 ...
0
votes
0answers
26 views

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 ...
0
votes
1answer
29 views

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. ...
0
votes
0answers
28 views

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 ...
1
vote
1answer
32 views

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 ...
-1
votes
1answer
49 views

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. ...
0
votes
0answers
27 views

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 ...
2
votes
1answer
305 views

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 "...
3
votes
1answer
42 views

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 ...
0
votes
0answers
13 views

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 ...
1
vote
0answers
29 views

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 ...
0
votes
1answer
147 views

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 ...
2
votes
1answer
53 views

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 ...
29
votes
4answers
4k views

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 ...
0
votes
0answers
20 views

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 !
0
votes
0answers
28 views

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 ...
1
vote
0answers
26 views

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 ...
0
votes
0answers
103 views

RAM and Turing machines: time complexity of simulation

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 ...
4
votes
1answer
227 views

Doing matrix multiplication with $\lceil n^3 / \log n \rceil$ processors in $2\log n$ steps by Brent's principle

On a parallel machine with $n$ processors we can compute the sum (or product, or the result of any associative operation) on $n$ numbers in $\log n$ steps. In the first step combine neighbors to get $...
2
votes
1answer
32 views

What is the motivation behind “ Descriptive Complexity ”?

Time and Space are two commons parameters (and also natural parameters) to measure the complexity of the problem. I am not able to understand the motivation behind defining " Descriptive Complexity". ...
2
votes
1answer
39 views

Examples of logic gates using non-standard models

These are the only ones I have been able to find online: Pulley Logic Gates Marble adding machine MARBLE COMPUTER LOGICAL AND GATE I would like to find some more discrete models like these (as ...
1
vote
2answers
67 views

Would any continuous model of the universe have/be based on hypercomputational laws?

I've read that when Turing-Church thesis is applied to the universe and physics, one of the three interpretations that we can use and is defended by some important physicists is that: "The universe ...
0
votes
1answer
147 views

Is arithmetic turing complete?

Maybe my question doesn't make sense, because I lack some more thorough understanding, but I was curious if arithmetic was Turing complete? As I understand it, a "model of computation" is a mechanism ...
7
votes
0answers
82 views

Automata that is Turing complete if you add a nondeterminism

Pushdown automata have an interesting property: non-deterministic ones belong to a different computational class than deterministic ones. This is in contrast to finite state and turing machines, for ...
0
votes
0answers
37 views

What is “Phrase structure grammar”?

I'm undertaking Theory of Computation Classes. I came across this sentence while studying Recursively Enumerable Grammar: Type-0 grammars generate recursively enumerable languages. The ...
0
votes
1answer
23 views

Numbering of vertices in RAM model

I have read few research papers in which given a graph $G$ where $V$ denotes its vertex set and $E$ denotes its edge set. Model of computation is word RAM. "Without loss of generality assume that ...
1
vote
1answer
35 views

What is the motivation behind restore model of computation?

The memory that stores the input is called the input memory. The memory that an algorithm additionally occupies during the computation is called the working memory. $\textit{Model of Computations}$ ...
0
votes
0answers
90 views

Correctness proof: induction on sequence of steps, need a stronger claim?

Im trying to prove the correctness of the construction proposed in this site answer: a two stack PDA that simulates a Turing Machine. By "correctness" i mean to prove more or less formally that we can ...
0
votes
1answer
83 views

Why a TM with infinite states can decide the halting problem?

Assuming we have a model of TM with an infinite number of states. The domain and range of the transition function are also infinite. Given a description of a TM $M$ and a string $w$ how can we use the ...
0
votes
1answer
23 views

Can all Turing-computable problems be solved with a machine with finite tape and infinite controls?

We know all computer computable problems can be solved using the infinite tape and finite control system of the turing machine. Now think something different, let the tape is finite but the control ...
2
votes
0answers
161 views

Equivalence between different Turing Machines and a definition of simulation

Im having some difficulty understanding how the following two concepts could be related. Equivalence between TMs as is commonly tought According to this site answer, to prove a standard TM model to ...
2
votes
0answers
38 views

Is the language $L$ of coded CFG's Turing decidable?

Consider the following language $L$ = {$<G><w>$ | $G$ is a CFG and $w\in L(G)$} Now, I wish to prove that $L$ is Turing decidable. My gut tells me to construct a Turing machine that ...
1
vote
0answers
65 views

RO turing machine with finite memory

Consider the following: A weak TM is a TM with finite tape in size $k$ which can only read its input values. note: the tape size does not include the input length. I need to determine whether if the ...
0
votes
0answers
20 views

How to prove that models of indirect and direct RAM machines are equivalent?

as in the title, I am looking for a formal proof how to show that models of indirect and direct RAM (random-access) machines are equivalent. I would really appreciate your help.
0
votes
1answer
18 views

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 ...
0
votes
0answers
41 views

Is there a common unit of measurement for comparison of computing power used to solve mathematical puzzles?

I just wanted to make sure if I'm reasoning correctly. So, if two computers are solving the same mathematical puzzle i.e. SHA-256 function of Bitcoin (finding nonce that satisfies difficulty target), ...
-1
votes
3answers
936 views

why can not NPDA is equal to DPDA?

I have recently read that turing machine can be remodeled to perform as PDA now, i have a question that since DTM = NDTM ( non deterministic Turing machine) then every DTM can remodeled to be NDTM ...
2
votes
0answers
264 views

What is the relationship between “model of computation” and “algorithm”?

Traditionally, the usual definition you find for model of computation is "an abstract description of how an output is computed given an input" (Wikipedia and my TCS course are my sources, but the ...
5
votes
2answers
254 views

Why do DFAs with a single final state have less power?

I came across this question in a test and I had to answer whether it is true or false. DFA with single final state has the same powers as DFA with more than one final state. I was confused by what ...
5
votes
2answers
120 views

Is there any other computation theory besides the one in automata theory?

I'm a bit confused at a fundamental level. In Computer Science, maybe some of us mostly use discrete mathematics since our computer is digital (like during studying operating system, algorithms, ...
3
votes
2answers
55 views

Weaker, but similar conditions to Turing completeness?

A model of computation is called Turing complete if it can simulate any Turing machine. This rules out for example a combinational logic circuit. However, there is a sense in which combinational ...
3
votes
2answers
73 views

Primitive recursive plus Ackermann

Let us consider the class $\cal F$ of functions that contains all constant functions all projections the successor function the Ackermann function as basic functions, and that is closed under ...
1
vote
2answers
171 views

Can I program a universal Turing machine to accept arbitrary input encodings?

I've been reading about building Turing machines for specific purposes, and some sources talk about input encodings and some talk about programming specific machines, but I've been unable to find ...
1
vote
1answer
87 views

SIMD computational model

Flynn's taxonomy contains three interesting computer architectures: SISD, SIMD, MIMD. For the SISD architecture, we have RAM computational model that simulate real SISD systems very well; For the ...