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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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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Prove that a language is decidable iff there is a counter that counts the language in dictionary order

How can I prove that a language is decidable if and only if there is a counter that counts the language in dictionary order ? NOTE: Dictionary order here is an agreement that will fix before counting ...
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18 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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1answer
36 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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1answer
88 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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1answer
69 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, ...
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24 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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52 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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1answer
64 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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30 views

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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53 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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1answer
36 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 ...
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2answers
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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 ...
4
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31 views

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 ...
5
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73 views

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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2answers
88 views

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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1answer
33 views

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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2answers
121 views

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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1answer
54 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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1answer
22 views

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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1answer
9 views

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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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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1answer
64 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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40 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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102 views

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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1answer
45 views

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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3answers
134 views

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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63 views

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 ...
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1answer
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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1answer
260 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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1answer
49 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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194 views

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 ...
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Is infinitely fast computer fundamentally impossible even theoretically?

This may get slightly philosophical, but consider the following program: ...
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1answer
315 views

Is non-determinism in a non-deterministic turing machine different from that of finite automata and push down automata?

Let a input string be given as $w_1w_2...w_n$. Then if a NFA is currently in state $r$ ( and has read the input upto alphabet $w_i$ ) then before reading the next input symbol the NFA splits into two ...
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Generative power and classification of matrix grammars

[Edited] I am reading about matrix grammars from several sources and got confused about its generative power and classification to the Chomsky hierarchy. In here it is stated that: A matrix ...
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3answers
269 views

What specifically makes quantum computers useful?

I know that quantum computers are able to process a superposition of all possible states with a single pass through the logic. That seems to be what people point to as being what makes quantum ...
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2answers
61 views

How Cellular Automata is related to Automata Theory?

I have read about Automata Theory where it is about the study of abstract machines and automata. And i know that an abstract machine takes the input, process it and create the output, just like ...
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3answers
92 views

Computational problem - definition

How should I understand the definition of computational problem? A computational problem is a mathematical object representing a collection of questions that computers might be able to solve. ...
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Computational complexity of emulating (untyped) λ-calculus with a queue machine

I am looking for bounds - both lower and upper - on the time, spacial, and state/symbol (i.e. number of states and symbols required) complexity of simulating the (untyped) λ-calculus with a queue ...
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Complexity bounds for Turing equivalence [closed]

I am looking for bounds - both lower and upper - on the time and spacial complexity of simulating Turing-complete systems with each other. (I am aware that both time and space are ill-defined with ...