# Tagged Questions

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### Basic Question about ambiguity of Grammar

I saw one book in Computation Course. I take a picture from this book, and in this book say why (or not) the following grammar is ambiguous? I couldn't find any solution to prove it's ambiguous. ...
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### Countable Set & Formal Grammar

We know set A is countable if A is finite or in a one-to-one mapping to natural numbers. I try to summarize my though. I think the following proposition is true. suppose $\Sigma$ is arbitrary ...
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### Formulating the Twin Prime Conjecture as a Language Recognition problem.

I'm trying to figure out how to formulate the Twin Prime Conjecture as a language recognition problem. I've got: A = {p: p is the largest prime such that p + 2 is prime} B = {p: p and p+2 are both ...
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### Are there known patterns among minimal expressions?

Let $R = F[z_1, z_2, \dots]$ be the finite-degree polynomials in a countable number of variables. Let $\mathcal{E}(R)$ be the set of all expressions of polynomials. Note that there could be an ...
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### My notes on $\Bbb{Z}/p\Bbb{Z}$-theoretic computational complexity

(Question at the very bottom) Def 1. Let $F = \Bbb{Z}_p$ be a finite field. Then an $F^k$-machine is a machine with $k$ input / output memory slots. All computations are done in the field $F$ and ...
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### If $P=NP$, prove that $L' \in NP$

I think I'm overthinking this problem and need some hints in the right direction. The goal of this question is to show that if $P=NP$ then for every language $L \in NP$ via a polynomial time verifier ...
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### Prove 2-HamiltonianCycle $\in \textbf{NP}$

Just want to verify that I have the right idea here with this hamiltonian cycle question. $HC$ = $\{\langle G \rangle$ | $G=(V,E)$ is an undirected graph such that there is a simple cycle (no vertex ...
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### Prove that RE is closed under reduction

Prove that the class RE is closed under reduction. Definitions: A language $A \subseteq \Sigma^*$ is called reducible to $B \subseteq \Gamma^*$ ( denoted by $A \leq B$) if there is a computable ...
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### Why every regular language is in $\text{TIME}(n)$?

How can I prove that every regular language $R$ has linear time complexity, i.e. every regular language satisfies $$R \in \text{TIME}(n)$$
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### A computer's memory is finite, so how can there be languages more powerful than regular?

A computer has a finite memory. There are no computers with infinite memory. Therefore the only languages that a computer can process are those whose member strings are finite. As I recall, the ...
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### Sequences and Languages

Let $U$ be the following language. A string $s$ is in $U$ if it can be written as: $s = 1^{a_1}01^{a_2}0 ... 1^{a_n}01^b$, where $a_1,..., a_n$ are positive integers such that there is a 0-1 ...
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### Function problem vs. decision problem

Take the set $FP$ of number-theoretic functions that are computable in polynomial time. Let us restrict to those functions with range in $\{0,1\}$, $FP_{0,1}$. Is there any correspondence with ...