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.

3
votes
1answer
36 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 ...
12
votes
1answer
303 views

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 ...
5
votes
3answers
207 views

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 ...
2
votes
4answers
184 views

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 ...
0
votes
1answer
76 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 ...
0
votes
1answer
16 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
10 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
1answer
66 views

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 ...
3
votes
2answers
519 views

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 ...
1
vote
0answers
26 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 ...
2
votes
1answer
96 views

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 ...
2
votes
1answer
41 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 ...
28
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 ...
3
votes
1answer
842 views

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 ...
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 !
19
votes
3answers
3k views

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 ...
4
votes
1answer
646 views

How to simulate a bidirectional TM on a regular one with time factor four?

In Computational Complexity A Modern Approach, one claim says that if $f$ is computable in time $T(n)$ by a bidirectional TM $M$, then it is computable in time $4T(n)$ by a unidirectional TM $\tilde{M}...
0
votes
0answers
26 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
24 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 ...
1
vote
2answers
98 views

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....
0
votes
0answers
71 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 ...
0
votes
1answer
97 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 ...
4
votes
1answer
211 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
30 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
38 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 ...
3
votes
2answers
6k views

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?
1
vote
2answers
63 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 ...
4
votes
1answer
137 views

Advances in recent time in Von-neumann self replication idea

I have read about Von-neumann self replication from Theory of Self-reproducing automata, which are lecture notes reconstructed from lectures in book of the same name. Theory of Self-reproducing ...
7
votes
0answers
80 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
28 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
21 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 ...
6
votes
3answers
3k views

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?
0
votes
1answer
74 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 ...
1
vote
1answer
33 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
61 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 ...
2
votes
0answers
96 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 ...
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
37 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 ...
3
votes
1answer
195 views

Is the system of measuring length in the US Turing complete?

The author here writes: Little known fact, the system of measuring length in the US is Turing complete My question is: Is the system of measuring length in the US Turing complete?
1
vote
0answers
48 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 ...
2
votes
2answers
74 views

Is this system Turing complete?

I want to develop a genetic program that can solve generic problems like surviving in a computer game. Since this is for fun/education I do not want to use existing libraries. I came up with the ...
0
votes
0answers
19 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
0answers
39 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
412 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
157 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 ...
2
votes
1answer
39 views

Potential General Model of Computation with Physics?

I posted a question about a month back regarding the significance of Turing machines (relative to other models of computation). In that post, I mentioned vaguely some conversion between an input ...
5
votes
2answers
179 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 ...
50
votes
7answers
19k views

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. ...
5
votes
2answers
114 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
51 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 ...