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### Proof by padding: $\textsf{TIME}(t_1(n)) = \textsf{TIME}(t_2(n)) \implies \textsf{TIME}(t_1(f(n))) = \textsf{TIME}(t_2(f(n)))$

I've been given the task of proving the statement in the title, which I found out it should be called the translational lemma by means of a padding argument; $f$, $t_1$ and $t_2$ are three ...
16 views

### If there is no negative path or cycle for a maximum matching $M$, $M$ is a minimum cost matching

I'm stuck at a proof about maximum matchings in graphs: If there is no negative path or cycle for a maximum matching $M$, $M$ is a minimum cost matching. A negative path is defined as an alternating ...
91 views

### Prove $\epsilon(S\cap T)\subseteq S \cap T$

Suppose there are sets $S\subseteq Q, T\subseteq Q$ such that $T=\epsilon (T),S=\epsilon (S)$. Prove $\epsilon(S\cap T)\subseteq S \cap T$ Definition of $\epsilon$- closure for epsilon NFA is: ...
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### Minimal paths as solution of a linear program of a special network flow

Let $G= (V,E)$ be a given directed weighted graph, and $s,t$ two specified nodes, so that there is no negative cycle reachable from $s$, and $t$ is reachable from $s$. We're looking for the shortest ...
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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 < A[...
31 views

### Search operation in hash table

Suppose that we have a hash table of some size $s$ and we have a set of keys $K$. We decide to hash the keys using chaining. Now assume that we randomly select $k \in \mathbb{N}$ keys from $K$ and ...
117 views

### 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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255 views

### Proving that $L=\lbrace{ab^{n}ba^{n}|n\geq1}\rbrace$ is not regular with pumping lemma

I'm trying to understand the pumping lemma for regular languages and would like to prove that $L=\lbrace{ab^{n}ba^{n}|n\geq1}\rbrace$ is not regular. My suggestion is as follows: Assuming $L\in{}REG$...
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### Algorithm to recognize Strongly Regular Graph (SRG)

I am looking for an algorithm to determine whether a graph is Strongly Regular Graph (SRG) or not.
228 views

### If $f$ and $g$ are increasing functions, are we guaranteed that $f=O(g)$ or $g=O(f)$? [duplicate]

Given two increasing functions $f$ and $g$ with values in the natural numbers, is it always the case that either $f\in O(g)$ or $g\in O(f)$. If the statement is true, then can anyone provide a ...
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### Multiprocessor Scheduling is NP-Complete [closed]

Consider this version of MS where we have set $A$ of tasks, $l(a)$, length of each task in $A$ and $m$ number of processors and also a deadline $D$. The question is where we can partition A into m ...
A) Solve this recurrence where $T(0)=0$ and write it in O-notation: $T(n)= {2 \over n} (T(0)+T(1)+...+T(n-1))+c$ So, I started to calculate: $T(1)=2(0)+c=c$ $T(2)=1(0+c)+c=2c$ and so on, ...