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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A modified version of two way DFA

Following an exercise from Hopcroft-Ullman's Introduction to automata theory: Let's define $k-MDFA$ as two way deterministic finite automaton with $k$ markers, similarly to two way $DFA$ but with ...
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27 views

ORAM: Is it generic?

Recently, plenty of researchers are looking at designing efficient data-oblivious algorithms. Roughly speaking, an algorithm is said to be data-oblivious if its data access patterns are independent of ...
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61 views

CFG Equivalent of regular expressions

So I was wondering something about the Chomsky hierarchy. DFAs (and NFAs) accept regular languages, while NPDAs accept context-free languages. Right-regular or left-regular grammars produce regular ...
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34 views

Context-free and context-sensitive grammars in FSM with counters

Consider an extension of finite-state machines that utilizes a finite set $C$ of counters. Let's call them counter automata. Before execution, each counter $c\in C$ is set to zero. Every transition, ...
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Polynomial reduction ,RE and R

Are there any languages L1,L2 such that: L1 is decidable (in R) L2 is Recursively enumerable (in RE) and there is a polynomial reduction between L2 and L1? Thanks.
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35 views

Is it always possible to convert a k-tape Turing machine to a single-tape one without increasing its running time complexity exponentially?

I am studying the past exam paper of course Theory of Computation. I know it is always possible to convert a k-tape Turing machine to a single-tape one, but how will the running time complexity be ...
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82 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. ...
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57 views

runtime of problems vs algorithms

I know that a solving a specific problem can have different runtimes on different models of computation. But can a specific algorithm have different runtimes on different models of computation? Also, ...
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27 views

Is there a broader class of total functions than $PR$? [duplicate]

In total functional programming programs are restricted to total computable functions. A well-known class of total functions are the primitive recursive functions ($PR$). However the Ackermann ...
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inclusion relation or equality of languages

Draw a bull's eye diagram that shows inclusion relation or equality between the following sets-Give an example in each case:  The set of regular expressions REX  The set of all regular languages ...
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21 views

Primitive Recursion equipped with an evaluator function

The wikipedia article for primitive recursion mentions a limitation that primitive recursive function can't compute the function $ ev(i,j) $ which computes the $ i $th primitive recursive function on ...
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38 views

Theoretical justification of “halting problem avoidance”

The wikipedia page for the Halting problem mentioned practical solutions to avoiding the halting problem such as avoiding infinite loops. And there is a mention that "by restricting the capabilities ...
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113 views

Is the system of measuring length in the US is 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 is Turing complete?
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77 views

Turing Machine with additional finite memory of size $n$

The question itself: Let us define a generalization of Turing Machines to include a finite memory of >size $n$. We denote such a Turing Machine formally as: $M_{mem} = (Q, Σ, γ, δ_{...
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27 views

Generate a graph to exact size using Kronecker product graph model

In network science, we can take sample a complex system and derive from this sampling a representative network (or graph) that describes the system to some extent. A model of a network, is a powerful ...
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1answer
35 views

Is there any count-preserving cellular automata which tends do “10101010…”?

Suppose that I have a bit string of finite length. Is there any bit rewriting rule rewrire :: (Bit,Bit,Bit) -> (Bit,Bit,Bit), that doesn't change the total count ...
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56 views

Construct DFA given oracle access to the language

I was given the following question. Given a minimal DFA $A$ with $m$ states over some alphabet $\Sigma$ which is a "black box" (you can only run words to it and it tells you if it accepts or not): ...
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65 views

How can a Turing machine accept infinite number of inputs? [closed]

How it is possible for a turing machine to process an infinitely long input ?
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A linear code, what is that?

I have been trying to understand the polytope model used for loop nest optimizations. Now while going through some of the thesis written on this, i came across the term/phrase "linear code" a number ...
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2answers
87 views

Turing machine states, lost in the jungle

There is a lengthy discussion going on at the English Language & Usage StackExchange site suggesting various synonyms for dead code, and it got me wondering about an angle that wasn't covered -- ...
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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....
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What does the “Lambda” in “Lambda calculus” stand for?

I've been reading about Lambda calculus recently but strangely I can't find an explanation for why it is called "Lambda" or where the expression comes from. Can anyone explain the origins of the term?...
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Why does using an encoding trick like Gödel numbers make a register machine universal?

Here the author describes the Random Access Stored Program machine and the problem of indirect addressing. The author states: But this does not solve the problem (unless one resorts to Gödel ...
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What theorem are these? (from Scott Aaronson's blog)

Browsing Scott Anderson's blog, I found this list of theorem. Among them are: If every second or so your computer’s memory were wiped completely clean, except for the input data; the clock; a ...
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Can one consider living (biological) cell to be Turing Complete?

Universal Turing Machine can be boiled down to two components. Infinite tape of input and an action table, a finite state machine that moves read/write head along the tape and writes to it depending ...
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Prove that the Kolmogorov complexity function cannot be approached from below

How would one go about proving that Kolmogorov function $K(x)$ cannot be approached from below by any computable function? After some research it seems I must show the function $K(x)$ is not lower ...
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Why classification represents all computations?

I'm a computer science student taking a theory of computation class. Recently we were taught about what is computable and what is not and about the Turing machine. As I understood (please correct me ...
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55 views

Non deterministic turing machine

Does a non deterministic turing machine which is a decider halt on all branches for all inputs?? I know it must halt on all branches for a string not in language but for a string in language ,NDTM ...
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Maximal class for which function equivalence is decidable

I previously asked if it's decidable whether two primitive recursive functions are equivalent: "primitive recursive functional equivalence". The answer was no. Here is my followup. What is the most ...
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Relation of deterministic push down automata and lower elementary recursion

Deterministic context free languages are the context free languages that can be accepted by a deterministic push down automata. Deterministic context free languages can be recognized by a ...
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Is there anything that MUST be done on a multi-core CPU?

When considering how multi-thread-friendly our program must be, my team puzzled about whether there's anything that absolutely cannot be done on a single-core CPU. I posited that graphics processing ...
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About the SOS degree of a function and optimization algorithms for the function

Given a non-negative function on the hypercube $f : \{0,1\}^n \rightarrow \mathbb{R}_{\geq 0}$ one says that it is of "SOS-degree" of $d$ (denoted as $deg_{SOS}(f) =d$) if $d$ is the minimum $k$ such ...
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50 views

Turing machine that can tell if it ends in standard position?

Suppose we have a TM $M$ with alphabet $\{0, 1 \}$ with n states. Say $M$ halts in standard position if it is scanning the left-most $1$ of a non-broken string of $1$s (and everything else on the tape ...
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66 views

Why is universal turing machine considered with only one head?

While defining the following time hierarchy theorem (for deterministic case ) : If $f(n)\log{f(n)}=o(g(n))$ then there are languages decidable in $O(g(n))$ which cannot be decided in $O(f(n))$ ...
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Explanation for indirect addressing

While reading about minimal instruction set computer I found out that one needs at least (for example) the ability to increment or decrement the value stored in register, a test for zero and a jump. ...
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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 ...
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246 views

Turing machine - infinite tape - does that thing exist?

Can we use a Turing machine with infinite tape as a basis to prove anything disregarding the fact that such a thing can never exist? Do we have the right to regard a machine (a construct) in the same ...
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43 views

What can be said about the Halting Problem if we can include the halting status to the input?

I was reading about Turing Machines and the Halting Problem, i understand that you need an oracle to decide whether given input will halt or loop forever. But why do we need an oracle if we can ...
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Computational power of Actor Model

In the question below, let TM be Turing machine, NTM be nondeterministic Turing machine and PTM be probabilistic Turing machine. In his paper "Actor Model of Computation: Scalable Robust Information ...
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Can computation models be categorized in terms of efficiency?

It is widely accepted that turing-complete systems are equivalent in terms of computability - i.e., whatever a turing-machine can do, can be emulated by automatas, the lambda calculus and other ...
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Can a Turing Machine have infinite accept states?

I'm still fairly new to Turing Machines, but I've been doing some research. I know that a Turing Machine can have an infinite tape and that it requires a finite number of states, but does it ...
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What does it mean to be “independent of machine model”?

I have often heard people mention off-hand that the class $\mathsf{P}$ is "machine-independent", or "independent of machine model", or "invariant under change of machine model" - something to do with ...
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Expressing classic automata in modern terms

This semester I was introduced to finite automata (FSM), then pushdown automata (PDA), and now the Turing machine (TM). Granted that there're many possible implementations of these abstractions (...
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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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67 views

A model of computation vs an abstract machine

Wikipedia says A model of computation is a formal description of a particular type of computational process. The description often takes the form of an abstract machine that is meant to perform ...
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281 views

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 ...
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Programming language where every expression makes sense

Per recommendation I am reposting this from Stack Overflow. Recently I have been thinking about following issue. Consider the code for a standard "Hello world!" program: ...
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1answer
37 views

Is modulus capable of universal computation?

I heard once that you could translate any digital circuit into a modulus operation, perhaps modulusing against different numbers? It was a long while ago though and don't remember where I heard it. ...
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50 views

Are Cellular Automata always computers?

I was reading on Complex Systems journal and found a paper where the author states that a cellular automaton can be viewed as a computer. In the introduction part: Cellular automata can be ...
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In principle, what is the relation between Artifical Intelligence and Turing machine?

I am working on my cs project about AI & Turing machines, so i know that Artifical Intelligence is meant to implement different algorithms into the machine {the computer} to solve a problem or a ...