Questions tagged [simulation]

Questions about simulating one model in another. This includes simulating reality in any model, or simulating a machine model with Turing machines.

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Make a tag system simulate a finite automaton?

Tag systems are Turing-complete. I was wondering if there is any easy way to create tag systems that simulate finite automata. So create tag systems that recognize languages, e.g. by having at the end ...
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1k views

Oblivious Universal Turing Machine in O(T log(T)) time

I'm currently reading Computational Complexity: A Modern Approach. In this book, they give a proof of a universal Turing machine $U$ such that if $M(x)$ runs in $T$ steps, then $U(\lfloor M \rfloor, x)...
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1answer
749 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}...
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2k views

Prove that turing machines and the lambda calculus are equivalent

It is known that a turing machine and the lambda calculus are equivalent in power. I now want to try to prove this myself. I think proving that the lambda calculus is at least as powerful as a turing ...
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249 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 ...
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29 views

Avoiding collisions in space and time

Say I have an image, represented as a 2D array of pixel values. Also, say I have a set of points on that image where each has a current (x, y) position and a Destination (x, y) associated with it. I ...
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103 views

Simulating QC using nondeterministic Turing machine

Is it more efficient to simulate Quantum Computer using a non-deterministic Turing machine? Would it be more efficient than simulation using a deterministic Turing machine or probabilistic Turing ...
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29 views

Advantages of block-based simulator versus equation-based simulator

I am mostly using Modelica, an equation-based simulator. I assume that block-based simulators like Simulink have their strengths and are better at some tasks, but I am wondering what those are. It ...
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208 views

Context free grammar as minimal solution of a system of equations

It is a well-known fact that language generated by a context-free grammar is the minimal solution of a particular system of equations, for example: $$\begin{align*} X &=\{{\epsilon}\} \cup Y\\ X ...
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148 views

Proving weak simulation

I want to prove something but I am not sure if it is the right way to do it. I have two LTS that define different semantics. A=($Q_a,Λ,\to)$, and B=$(Q_b,Λ\cup\{\beta\},\leadsto)$, where $\beta$ is ...
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64 views

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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How to improve convergence to an equilibrium value, & damp oscillation?

I am developing a program which seeks strategies for the players A, B in any of a family of simple 2-player gambling-games. The program iterates, using a genetic algorithm to determine, from the ...
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95 views

MAX-CUT: are there any algorithms or codes for classical computers, that cater to this specific case?

A paper was published recently in Science where the authors minimized the following function: $$E_{\text{Ising}}(s) = -\dfrac{1}{2} \Sigma_{i=1}^{N} \Sigma_{j=1}^{N} J_{i,j} s_i s_j,$$ where $...
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87 views

How can an arbitrary Turing machine running for $t$ steps be simulated in $O(n \log(n))$ steps?

I'm confused about a point regarding the Time Hierarchy Theorem. In order to establish the upper bound for this theorem it's necessary to show the following: We're given $(\langle M \rangle, t)$ ...
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61 views

How to Optimise Each Multithreading Technique? (Cooperative/Preemptive/Simultaneous)

I am currently in the process of writing an IB Extended Essay on the efficacy of multithreading on increasing the performance of applications. So far, I have been able to deduce that there are three ...
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30 views

How to Simulate Nested Parallelism on a Sequential Machine

So I have sets of functions $A$, $B$, $C$, $D$, $E$, and $F$. I want to run them in a nested way. I also want to run some of them in parallel, and some of them in sequence. Here is how that might look:...
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19 views

Strategy / Technique for Proving Equivalence between Multiple Program Forms

Wondering how to prove different compiled forms of a program to be "effectively the same" or "equivalent". For example, you can have a program represented as your normal nested function calls, or ...
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68 views

MATLAB script to model biological branching process

I took an introductory MATLAB course a couple of years ago (and since then have only taken a basic C++ course) and am presently stumped as to how to start with a project I am undertaking. As part of ...
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82 views

Bisimulation, bisimulation equivalence and simulation equivalence?

I got a little confused with these 3 concepts. Is there a difference between bisimulation and bisimulation equivalence and if yes, then what is it? Also, if we say that the LTS's X and Y are bisimilar,...
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502 views

Constructing a turing machine from a PDA - dealing with non-determinism

Given a PDA $P$, I believe we can simulate it with a turing machine with 2 tapes - one for keep reading the input and one for the stack. But, a PDA transition function may have multiple transitions ...
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61 views

Formal definition of simulation

Assume that the model of computation is a standard Turing machine model with input alphabet $\Sigma = \{0,1\}$, work alphabet $\Gamma = \{0,1,\_\}$, 1 input tape, 1 work tape and 1 output tape. We ...
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34 views

Particles-based models - Discrete or Continuous, why?

I have a theoritical question about particles-based simulator (Reeves,83). I don't know if my question is relevant and I apologize if not. On each frame, the system generate particles and attribute ...
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121 views

generic technique to build LTL/CTL formula that satisfy specific inputs to a model

I have an automaton, for example the below automaton and would like to generate a single formula (LTL or CTL, or some other representation) that satisfy exactly the traces provided. e.g., $t_1 = i^*...
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35 views

How to make logical inference from simulated data

I have data collected from a computer simulation of football games which seem to have recurring patterns of the following form. if madrid plays arsernal and the match ends under 3 goal, then on ...
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551 views

K -> 2 tape reduction for nondeterministic Turing machines

How to I show that any language in NTIME(T(n)) can be accepted by a non-deterministic 2-tape O(T(n)) time-bounded Turing machine, with modifiable input tape? I've seen the k to 2 tape reduction for ...
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38 views

Regular grammars

I am fairly new to automata, regular expressions and regular grammar. I am struggling to understand how to define the regular expression (abc)* into one or several regular grammar expressions. ...
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35 views

Is there defined limits on, how a Turing Machine can emulate itself / another one?

Meaning for example lower or upper bounds of any kind, possibly concerning time or space complexity?
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13 views

Using FFT in the following convolution in a simulation

I have the following convolution as part of a numerical simulation. $$T(r)=\int d^3r_2 p(r_2)f(r_2)\alpha(r-r_2)$$ My problem is that the analytical expressions for $f$ and $p$ do exist but, I have ...
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50 views

Hierarchical Parallel Processing Machines

Introduction I am wondering if there is a generalization of parallel processing / asynchronous communication that explains/models how to deal with a hierarchy of parallel processes. Mainly looking ...
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71 views

Is it possible for a [futuristic] computer to contain the information of the whole universe?

(This is a question of information theory, data compression and entropy, so I believe it fits CS forum) Does the fact that the computer itself is a part of the universe make it logically impossible ...
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45 views

Is it possible to simulate oracle machines on 1-dimensional cellular automata?

My instinctual response is that it is possible, but I can't see how to simulate the oracle tape on a 1-d CA. If not, are they able to be simulated on n-dimensional CA? My thought is that the oracle ...
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68 views

Metropolis algorithm Simulated annealing

Someone could explain me in a simple way why Bruce Hayek theorem guarantee an optimal schedule for Metropolis algorithm? For me is enough an informal explanation. Thanks.
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433 views

Converting a CFG with epsilons into a DPDA

I have a CFG: S -> $T$ T -> T+T|T-T|T/T|(T)|CX|I X -> XX |C|N|_|@ C -> a|b|c|....|z|A|B|C|...|Z|_ N -> 0|1|2|....|9 I -> NI|N Here @ means epsilon. The above is a valid arithmetic expression ...
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165 views

Stepping through a sequence of grouped logic gates

I'm performing a simulation of protein-protein interactions. I'm using Python to code logic gates as functions to model protein interactions. My model is basically a series of groups (...
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32 views

Name for a Type of Simulation

I have come up with a type of simulation "game" but I cannot find anything describing it online. The simulation has a 2D "world" with a number of automatons on a discrete grid, similar to the game ...