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.

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Regularity of a language constructed from a know regular language

I'm working through so textbook questions on regular languages, and came across a problem that amounts to showing the following language is regular, given that $A$ is a regular language: $$ \{x|\...
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What motivates the RAM model?

It looks like most of today's algorithm analysis is done in models with constant-time random access, such as the word RAM model. I don't know much about physics but from popular sources I've heard ...
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In an NFA, what if there are no transitions out of an accept state but there are symbols left in the string?

Let's say I have a string 0110 and after 011 I reach an accept state (let's call the accept state "q") in an NFA. However, there is no transition mentioned in the diagram from q for the ...
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If $A\in RE $ then $f(A)\in RE$

Let $A\in RE$, and define$f(A) = \{y |\ y= f(x),\ x\in A\}$ for some computable function $f$. Then $f(A)\in RE$. I can't figure out why this is true. Since $f$ is computable there is a Turing machine ...
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How design a Deterministic finite automata which accept string starting with 101 and how to draw transition table for it if there is a dead state

I’m trying to design a DFA which accept string starting with 101 if the string start with 0 then it goes to dead state.Is my design is correct or wrong? And I don’t know how to draw transition table ...
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Every decidable language $L$ has an infinite decidable subset $S \subset L$ such that $L \setminus S$ is infinite

Given an infinite decidable language $L$, then if $S \subset L$ such that $L \setminus S$ is finite, then $S$ must be decidable. This is true since given a decider of $L$ we contruct a decider for $S$:...
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Do we have to calculate time for declaring statement in RAM model?

Do we have to calculate time for declaring statement, in my case int num3 statement. The following question was asked by professor as a post-lecture quiz. I ...
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turing machine accepting language {ww} has ω($n^2$)

prove or disprove that any turing machine which accepts language $l=\{ww | w ∈ \{0, 1\}∗ \}$ has time complexity $ω(n^2)$
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Convert PDA by final state in to cfg

Hope you all are doing well. I want your assistance. I have a PDA which is accepted by the final state. I need to convert it into cfg. So I want to ask, If I want to first convert this into ...
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Mealy machine and moore machine

Can we compute the number of machine of two kind of transducers (mealy and moore) with $n$ states, and lenght of input symbols $m$, and lenght of output symbols $p$.
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Equivalence between a TM and a changing TM

Let a changing TM be a TM which is not able to write the same symbol which is being read. Formal: $M^*=(Q,\Sigma,\Gamma,\delta,q_{accept},q_{reject})$,$\delta(q,a)=(q^*,a^*,c),a \neq a^*$ with $q,q^...
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Expressing functions using the arithmetic dictionary

i have seen in the "logic to cs" class i take - a theorem that states: "every recursive (computable) function $f$ can be expressed using the arithmetic dictionary {$C_0, C_1, f_+(,), f_x(,), R_\le(,)$}...
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What does Lambda Calculus teach us about data?

In Lambda Calculus, the distinction between data and code doesn't seem to exist. Is there something fundamental about this, or purely Lambda Calculus's thing? Some context: as a software developer, I ...
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How to find optimal partition subsets

Given a partition $[0,1]$,there are 5000 partition subsets $P_i=[a_{i1},a_{i2}]\in[0,1], 0≤a_{i1}\leq a_{i2} \leq 1, i \in \{1,2,...,5000\}$. I want to analyze these subsets and find 10 subsets to ...
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Over the alphabet {a,b,c,d}, how would i construct a NFA that only accepts strings that end with a letter that is already part of the string?

I've been trying to create a NFA that accepts strings that end with a letter that exists in the string. For example abcdb, cbdd, acac etc. while strings like abc aacd etc are not accepted since the ...
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Are there non-quantum, (potentially) realizable in the real world models of computation that allow a polynomial speedup over RAM?

I hear a lot about how quantum computers are a big thing because they allow solving some problems in polynomial time which we don't know how to do classically. As far as I understand it still isn't ...
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Proof that uniform circuit families can efficiently simulate a Turing Machine

Can someone explain (or provide a reference for) how to show that uniform circuit families can efficiently simulate Turing machines? I have only seen them discussed in terms of specific complexity ...
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Is it semidecidable to test whether a Turing decidable language is empty?

I'm not sure how to go about solving this. I tried this: Suppose L is a Turing decidable language. Turing Machine M1 is a decider of L and M2 is a decider of the complement L We construct a TM U ...
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Is there a recursive problem encoding the Turing completeness of a model of computation?

Suppose we have a model of computation $C$ we want to show to be Turing complete. The usual strategy would be to emulate within $C$ any model of computation we already know to be Turing complete (e.g. ...
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Closure on regular languages

A) Let $L$ be a regular language. according to the theorem there is an DFA which accepts the language. Describe shortly how to change the DFA to NFA which Accepts $L^R$, where R is reverse. There is ...
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Is there an abstract architecture equivalent to Von Neumann's for Lambda expressions?

In other words, was a physical implementation modelling lambda calculus (so not built on top of a Von Neumann machine) ever devised? Even if just on paper? If there was, what was it? Did we make use ...
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Computational complexity of counting symbols

Consider the counting function $\{x\}^* \rightarrow \mathbb N$ that counts the number of occurrences of the symbol $x$. I am confused about the (asymptotic) complexity of computing this function, ...
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Does Turing machine have no shift?

In a Turing machine I read that it can go only right or to left. But in my book [elements of theory of computation, Book by Christos Papadimitriou and Harry R. Lewis ] it says that Turing machine ...
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Parallel programming models: Why do OpenMP and MPI dominate?

In a lecture on HPC parallel programming (for CPUs) we discussed various models available from Pthreads to OpenMP to MPI and others like Charm++, X10, UPC, Chapel…. The main focus was clearly on the ...
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If L = {xy | |x| = |y|, x=y} is not Context Free, then what about L = {xy | |x| = |y|, x!=y}?

I know that, when x = y, then it's not Context Free. This is because, the first letter of y cannot be matched with first letter of x, which is at the bottom of the stack. But, a link of Show that { ...
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Are weakly polynomial time algorithms truly polynomial?

I've been looking through a ton of sources to try and understand the definitions of strongly and weakly polynomial time algorithms. Wikipedia states an algorithm runs in strongly polynomial time if ...
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trace vs. computation vs. run vs. execution vs. walk

Many folks use the terms "trace", "execution", "computation", "run", "walk" ... interchangeably when they speak about state machines with labeled transitions. Does any work distinguish between these ...
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Convert CFG to CNF Arithmatic Expression

Convert CFG to CNF The Grammar E→E+T E→T T→T*F T→F F→(E) F→x Step 1 Assign variables to terminals A→ + B→ * C→( D→ ) F→x ...
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Which machine learning should I choose for a one->list relation

I'm trying to write machine learning software that will predict a list of 3 values from a given number input (reverse grayscale). There is a function determining values of the list to the grayscale, ...
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Would models of computation in other conceivable universes be Turing complete?

I'm interested in gathering some references that discuss the topic of the relationship between computation and physics. Specifically, I'm interested in investigating two points of view: our current ...
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How does one program in a tag system?

I've played with 2-tag systems a bit and read all about tag/lag systems. They're great for experimenting with computation, and obviously useful as intermediaries in various proofs. My question is: ...
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How to model most optimized encoding of string data

Sorry if this question isn't super well defined, I am just struggling currently with figuring out what an "ideal solution" looks like to the following problem, and haven't pinned down an equation. I ...
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134 views

Why no DPDA can accept Palindrome? (according to this proof)

This proof is from the book "Introduction to Languages and the Theory of Computation" by John C. Martin. My question is from the pink part at the second page: It follows in particular that no ...
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Can differennt computation model lead to different complexity?

There are many examples where someone replaces a CPU with a GPU or an FPGA and get a performance boost of $\times 100$ or more, but is it possible for a change in the architecture of computational ...
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Formal definiton of RAM model with D disks of blocks B, fast memory M and P processors

In some articles I've read of RAM model with D disks of blocks B, fast memory M and P processors. Is there a formal deifition of that model?
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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)?
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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 $...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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. ...
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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 ...
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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. ...
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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 ...
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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 "...
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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 ...
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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 ...

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