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Questions tagged [check-my-proof]

Questions which also contain a proof or a solution that needs to be checked for correctness and completeness.

20 questions
19
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1 answer

Number of Hamiltonian cycles on a Sierpiński graph

I am new to this forum and just a physicist who does this to keep his brain in shape, so please show grace if I do not use the most elegant language. Also please leave a comment, if you think other tags would be more appropriate. I am trying to…
flonk
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16
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2 answers

Is Karp Reduction identical to Levin Reduction

Definition: Karp Reduction A language $A$ is Karp reducible to a language $B$ if there is a polynomial-time computable function $f:\{0,1\}^*\rightarrow\{0,1\}^*$ such that for every $x$, $x\in A$ if and only if $f(x)\in B$. Definition: Levin…
c c
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14
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5 answers

Flaw in my NP = CoNP Proof?

I have this very simple "proof" for NP = CoNP and I think I did something wrongly somewhere, but I cannot find what is wrong. Can someone help me out? Let A be some problem in NP, and let M be the decider for A. Let B be the complement, i.e. B is in…
simpleton
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11
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1 answer

subsets of infinite recursive sets

A recent exam question went as follows: $A$ is an infinite recursively enumerable set. Prove that $A$ has an infinite recursive subset. Let $C$ be an infinite recursive subset of $A$. Must $C$ have a subset that is not recursively enumerable? I…
user1435
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7
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1 answer

Proving NP is a subset of the union of exponential DTIME

I need to prove that $\mathsf{NP}$ is a subset of the union of $\mathsf{DTIME}(2^{n^c})$ for all $c > 1$. Let $L$ be a language/decision problem in $\mathsf{NP}$. Then $L$ can be decided given a polynomial-size certificate in polynomial time with a…
Michael Studebaker
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6
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1 answer

Generalizing the Comparison Sorting Lower Bound Proof

Let's start with the comparison sorting lower bound proof, which I'll summarize as follows: For $n$ distinct numbers, there are $n!$ possible orderings. There is only one correct sorted sequence of the $n$ numbers. We are given that comparison…
ShyPerson
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6
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1 answer

Show that the halting problem is decidable for one-pass Turing machines

$L=\{<\!M,x\!>\, \mid M's \text{ transition function can only move right and } M\text{ halts on } x \}$. I need to show that $L$ is recursive/decidable. I thought of checking the encoding of $M$ first and determine whether its transition function…
Numerator
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5
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1 answer

Proving that a language is not in P using diagonalization

Pardon me if i'm missing something which is very obvious here but i cant seem to figure it out. $E=\{ \langle M, w \rangle \mid \text{ Turing Machine encoded by $M$ accepts input $w$ after at most $ 2^{|w|}$ steps}\}$ We have to prove $E\notin…
swarnim_narayan
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5
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1 answer

Lower bound for sorting n arrays of size k each

Given $n$ arrays of size $k$ each, we want to show that at least $\Omega(nk \log k)$ comparisons are needed to sort all arrays (indepentent of each other). My proof is a simple modification of the decision tree argument used to obtain the lower…
Cornelius Brand
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4
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1 answer

Quasigroups, congruences and recognizable subsets

My question refers to the draft of Mathematical Foundations of Automata Theory, IV.2.1 (pages 89ff in the pdf). I will repeat everything necessary nevertheless: Let $M,N$ be monoids and $\varphi: M \rightarrow N $ a monoid morphism. We say that a…
Cornelius Brand
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3
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2 answers

Show $x^y$ is a primitive recursive function

As this thread title gives away I need to prove $x^y$ to be a primitive recursive function. So mathematically speaking, I think the following are the recursion equations, well aware that I am assigning to $0^0$ the value $1$, which shouldn't be,…
haunted85
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3
votes
1 answer

Error in Generating Function Solution

I am currently working my way through An Introduction to Analysis of Algorithms to stay sharp with recurrences as well as learn generating function techniques. However my analyses and the books analyses for the first few sample problems on ordinary…
Nicholas Mancuso
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3
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3 answers

Show $B= \{z \mid (\exists x)\; P(x,z)\}$ is a recursive enumerable set

Let $B = \{z \mid (\exists x)\; P(x,z)\}$ and $P$ be a computable predicate. Show $B$ is a recursive enumerable set. My attempt As $P$ is a computable predicate then there is a program that computes it, therefore $B= \{z \mid (\exists x)(\exists…
haunted85
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2
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1 answer

Prove $\varphi(x)$ to be primitive recursive

Let $\varphi(x)=2x$ if $x$ is a perfect square, $\varphi(x) = 2x+1$ otherwise. Show $\varphi$ is primitive recursive. In proving $\varphi$ to be a p.r. function I think it could come in handy the following theorem: Let $\mathcal C$ be a PRC class.…
haunted85
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2
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0 answers

Single machine job scheduling (Greedy heuristic)

Here is a variation of a job-scheduling Problem. Let $J = \{j_1,...j_n\}$ be a set of Jobs for $1 \leq i \leq n$. Given Job length $|j_i|\in \mathbb{N}$, deadline $f_i \in \mathbb{N}$, profit $p_i \ge 0$ and starting-time $s_i \in \mathbb{N}$. I am…
heliodromus
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