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### 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 ...
6k views

### 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 ...
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### 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 ...
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### 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 $C$ ...
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### Can we say McCarthy and Hoare had the same objective in the 60s regarding a mathematical theory of computation?

I don't think there's any way to ask a very precise question here, so this might be considered opinion based. Nevertheless, it seems the question is clear enough because I'm asking whether these two ...
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### Maximise sum of “non-overlapping” numbers in square array - help with proof

A question was posted on Stack Overflow asking for an algorithm to solve this problem: I have a matrix (call it A) which is nxn. I wish to select a subset (call it B) of points from matrix A. The ...
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### 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 ...
325 views

### What is the complexity of this subset merge algorithm?

Updated Algorithm: There was a major flaw in my original presentation of the algorithm which could have impacted the results. I apologize for the same. The correction has been posted underneath. The ...
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### Prove: if $\delta_D(q0, w) = p$ then $\delta_N(q0, w) = {p}$

In my textbook, it presents the theorem, "A language L is accepted by some DFA if and only if l is accepted by some NFA". My textbook explains that the "if" portion of the proof is given by the subset ...
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### Why is this a proof by contradiction for this algorithm? Isn't this a direct proof instead?

First Slide: Find Max(A) // INPUT: A[1..n] - an array of integers // OUTPUT: an element m of A such that m >= A[j], for all 1 <= j <= A.length max = A[j==1] for j = 2 to A.length if max < ...
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### If $L$ is a regular language, how to prove $L_1 = \{ uv \mid u \in L, |v| =2 \}$ is also regular?

If $L$ is a regular language, prove that the language $L_1 = \{ uv \mid u \in L, |v| =2 \}$ is also regular. My idea: $L$ can be represented as a DFA and then you could add 2 consecutive ...
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### $\Phi_1=1$ or $\Phi_1=2$ for the dynamic $\text{Table-Insert}$ , where $\Phi_i$ is the potential function after $i$ th operation, as per CLRS

The following comes from section Dynamic Tables, Introduction to Algorithms by Cormen. et. al. In the following pseudocode, we assume that $T$ is an object representing the table. The field $table[T]$...
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### Number of possible heaps on $\{1,…,2^h-1\}$

Let $C_h$ be the number of possible heaps for the set of keys $\{1,...,2^h-1\}$. Determine a recurrence relation for $C_h$ via the substitution method and prove it. Definition A binary tree is ordered ...
880 views

### Proving the loop invariant for a simple program in Hoare logic

I was studying loop invariant and came across Tomas Petricek's example. Here's the equivalent(I believe) program after I revised it a bit for proof in Hoare logic: ...
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### Is this proof for showing that $EQ_{CFG}$ is co-Turing-recognizable incorrect?

I have been searching for proofs that show that $EQ_{CFG}$ is co-Turing-recognizable. When searching for proofs I can only find proofs on the following form: Construct a TM $M$ which recognizes the ...
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I am currently following the proof, found here, that Rado's function $$\Sigma (n) = \max \{ \text{# of 1's that may be written to a tape by an n-state turing machine} \}$$ is non-computable. Within ...
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### 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 ...
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### How to Apply Elementary Axioms from Kleene Star to an Inequality

Axioms For * \begin{align} 1 + aa^* &\leq a^* \\ 1 + a^*a &\leq a^* \\ b + ax &\leq x \to a^*b \leq x \\ b + xa &\leq x \to ba^* \leq x \\ \end{align} Elementary Results \begin{...
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### Show that function is not turing-computable?

We have two functions: $f_1: \mathbb{N}\rightarrow \mathbb{N} \quad$ $f_2: \mathbb{N}\rightarrow \mathbb{N}$ By definition $f_1$ is turing-computable while $f_2$ is not. Then we define a third ...
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### For selection in worst-case linear time ambiguity in consideration of $n$ for which $T(n) =O(1)$ and $T(n)\leq cn$
This was given as a homework problem but I have already submitted the assignment. I'd like to resolve it at this point for my own satisfaction. Given that $L_1$ is a linear language and $L_2$ is a ...