# 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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### How to create DFA from regular expression without using NFA?

Objective is to create DFA from a regular expression and using "Regular exp>NFA>DFA conversion" is not an option. How should one go about doing that? I asked this question to our professor but he ...
8k views

### How to show two models of computation are equivalent?

I'm seeking explanation on how one could prove that two models of computation are equivalent. I have been reading books on the subject except that equivalence proofs are omitted. I have a basic idea ...
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### 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 ...
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### Prove Queue Automaton is equivalent to Turing Machine

A deterministic queue automaton (DQA) is like a PDA except the stack is replaced by a queue. A queue is a tape allowing symbols to be written (push) on the left-end and read (pull) on the right-end. ...
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### How can I convert the Turing machine the recognizes language $L$ into an unrestricted grammar?

According to this Wikipedia article, unrestricted grammars are equivalent to Turing machines. The article notes that I can convert any Turing machine into an unrestricted grammar, but it only shows ...
5k views

### Infinite alphabet Turing Machine

Is a Turing Machine that is allowed to read and write symbols from an infinite alphabet more powerful than a regular TM (that is the only difference, the machine still has a finite number of states)? ...
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### Proof that PDA's with different definitions have same expressive power

Let $P$ be a push down automaton $(Q,\Sigma,\Gamma,\delta,q_s,F)$, where $Q$ is the set of states, $\Sigma$ is the input alphabet $\Gamma$ is the stack alphabet $\delta$ is the transition function ...
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### Right moving turing machine

I am interested in simulating any turing machine with a turing machine that is allowed only to move right. I guess that it should be pretty standard material and likely it is trivial (or known to be ...
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### Is every linear-time algorithm a streaming algorithm?

Over at this question about inversion counting, I found a paper that proves a lower bound on space complexity for all (exact) streaming algorithms. I have claimed that this bound extends to all linear ...
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### Convert CFG to PDA

Is there any set of rules or methods to convert any context free grammar to a push down automata? I already found some slides online but I wasn't able to understand them. In slide 10 he speaks ...
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### pda: transformation between acceptance by empty stack and final states

I am stuck with understanding the transformation of final-state acceptance automaton into empty-stack acceptance automaton. From everywhere that I've read, it always says introduce a new start state ...
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### Multitape Turing machines against single tape Turing machines

Introduction: I recently learned that a multi-tape Turing Machine $\text{TM}_k$ is no more "powerful" than a single tape Turing machine $\text{TM}$. The proof that $\text{TM}_k \equiv \text{TM}$ is ...
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### 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 ...
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### Steps to convert regular expressions directly to regular grammars and vice versa

I came across following intuitive rules to convert basic/minimal regular expressions directly to regular grammar (RLG for Right Linear Grammars, LLG for Left Linear Grammars): Then I came across many ...
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### 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 ...
1k views

### Would creating a complete computer simulation of the human brain prove the Church-Turing thesis?

According to Wikipedia, the Church-Turing thesis "states that a function on the natural numbers is computable by a human being ignoring resource limitations if and only if it is computable by a Turing ...
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### Why is simulation by non deterministic Turing machine faster than a deterministic one?

A deterministic universal Turing machine $U_D$ can simulate a deterministic turing machine $M_D$ in $O(T(n)log(T(n)))$ where $M_D$ runs in $O(T(n))$. But I came across an exercise in Sanjeev Arora and ...
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### Does every turing machine have an equivalent, single-state, n-tape turing machine?

Is it the case that every problem computable by a Turing Machine can also be represented by some kind of equivalent n-tape Turing Machine which one has only one state? (We can assume that the accept ...
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437 views

### For the time hierarchy theorem, how is the input translated efficiently?

I'm trying to understand the proof of the time hierarchy theorem appearing in sipser's book. The proof requires a TM M to simulate an arbitrary TM N without too much slowdown. In particular, it is ...
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1 vote
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### Variant of Turing machine

How to prove that standard Turing machine is equivalent to a variant model where a string is accepted if the machine enters an accept state during computation? However, the machine may leave the ...
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1 vote
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### Prove Halting on all Inputs is not in RE simulation

I don't understand why when proving if Halting on all inputs problem si not in RE using the complement of the halting problem, I have to take a turing machine and simulate the machine M(the machine ...
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