Questions tagged [machine-models]

26 questions
42
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5 answers

Difference between a turing machine and a finite state machine?

I am doing a presentation about Turing machines and I wanted to give some background on FSM's before introducing Turing Machines. Problem is, I really don't know what is VERY different from one another. Here's what I know it's different: FSM has…
18
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1 answer

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 a TM $\langle M \rangle$, and an input string…
16
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2 answers

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 correct result in a bounded amount of time, and …
14
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3 answers

Is there an abstract machine that can capture power consumption?

When reporting algorithmic complexity of an algorithm, one assumes the underlying computations are performed on some abstract machine (e.g. RAM) that approximates a modern CPU. Such models allow us to report time and space complexity of algorithms.…
12
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1 answer

Prove that a boolean function computable in T(n) by a RAM machine is in DTIME(T(n)^2)

The question is exercise 1.9 from Arora-Barak's book Computational Complexity — A Modern Approach: Define a RAM Turing machine to be a Turing machine that has random access memory. We formalize this as follows: The machine has an infinite array A…
c c
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Mathematical model on which current computers are built

It is said that "The Turing machine is not intended as practical computing technology, but rather as a hypothetical device representing a computing machine. Turing machines help computer scientists understand the limits of mechanical computation."…
user5507
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Which computational model is used to analyse the runtime of matrix multiplication algorithms?

Although I have already learned something about the asymptotic runtimes of matrix multiplication algorithms (Strassen's algorithm and similar things), I have never found any explicit and satisfactory reference to a model of computation, which is…
042
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Which theoretical parallel model is closest to CUDA?

Which theoretical parallel model is closest to CUDA/OpenCL programming model? For example, it fits at some degree to the generic Parallel Random Access Machine (PRAM) model. However, that is too generic, since it makes abstraction of various memory…
isti_spl
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7
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Does forcing TMs to change all symbols they read change their power?

If we limit a turing machine so that it is not allowed to write the symbol that it reads would it reduce its power? For example: $( State, A, State, Z, DIRECTION)$ $A$ cannot be the same symbol as $Z$.
user3115
7
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3 answers

What piece am I missing to turn this idea into a programming language?

I've been doing some reading (I'll name drop along the way) and have selected a few scattered ideas that I think could be cobbled together into a nifty esoteric programming language. But I'm having some difficulty assembling the parts. Kleene's…
7
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2 answers

Can we represent all computer programs as graphs?

I was thinking the other day, and it occurred to me that computer programs all seem to be representable as a graph (an abstract syntax tree for example), or, once common expressions are combined, an abstract syntax graph. It occured to me that…
gct
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7
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What is the significance of primitive recursive functions?

I was studying the proof of Ackermann function being recursive, but not primitive recursive, and a question hit me: "So what?". Why does it matter? What is the significance of primitive recursive functions?
Untitled
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Can a Multi-Tape Turing Machine have an infinite number of tapes?

So if k is the number of tapes, is a multi-tape Turing machine allowed to have k = ∞ tapes. I'd assume not since this would give an infinite transition function?
Ozal
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7
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Automaton equivalent of the π calculus?

If Turing Machines are the automata equivalent of the $\lambda$ calculus, what is the automaton equivalent of the $\pi$ calculus? I suppose it would be some class of automata that resembled a Turing Machine, but with support for communication…
BlueBomber
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5
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Coq --- non-terminating programs

People usually say Coq does not allow writing non-terminating functions. I have a question regarding that. Does Coq allow writing exactly all terminating functions? In other words, what are the completeness and soundness properties of Coq's…
zpavlinovic
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