Questions tagged [check-my-answer]

Questions asking us to check whether your solution is correct are considered off-topic (per http://meta.cs.stackexchange.com/questions/597/) and should not be posted on this site.

2
votes
2answers
42 views

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 ...
-1
votes
1answer
49 views

Show that the Language L is not regular (pumping lemma) [closed]

$L = \{cda^nb^n\mid n\in \Bbb N\} \cup \{a,b,d\}^*$ Assuming $L$ is regular then there exist a pumping length $n$ for $L$. Lets use w = $cda^nb^n$. Thus $w \in L$ and $|w| = 2n+2$ $\implies$ $|w| \...
0
votes
1answer
49 views

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 ...
3
votes
2answers
3k views

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[...
0
votes
0answers
25 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 ...
2
votes
1answer
37 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 ...
0
votes
1answer
35 views

$ L = \{xyyz\in\{0,1,2\}^{*} : y \neq \epsilon \wedge \exists_{a \in \{0,1,2\}} |y|_a \equiv 0 \}$

$ L = \{xyyz\in\{0,1,2\}^{*} : y \neq \epsilon \wedge \exists_{a \in \{0,1,2\}} |y|_a \equiv 0 \}$ I think this languages is regular. I write regular expression: $(1 + 2 + 0) ^ {*} (11 + ...
0
votes
1answer
56 views

Is complement $L = \{ w : |w|_{a} \equiv |w|_{b} \vee |w|_{c} \equiv |w|_{d} \}$ context-free

$L = \{ w : |w|_{a} \equiv |w|_{b} \vee |w|_{c} \equiv |w|_{d} \}$ In my opinion complement of the L language is $L^{C} = \{ w : |w|_{a} \neq |w|_{b} \wedge |w|_{c} \neq |w|_{d} \}$ I choose to ...
1
vote
0answers
78 views

Proof that G is a Tree After DFS and BFS form the same tree T [closed]

Let G be a connected, undirected graph containing some vertex s. let's say that BFS and DFS are both run on G starting at s and that the breadth first search and depth first search ...
9
votes
0answers
95 views

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 ...
2
votes
1answer
242 views

Proof of NP Completeness of set-partition problem

I have reduced subset sum problem to set partition problem but do not know whether it is correct and so I need your help. MY METHOD In subset sum problem we have to find a subset $S_1$ of set $S$ so ...
-1
votes
1answer
53 views

Proving a language is non-regular using the Pumping Lemma for non-binary strings [duplicate]

I am unsure of how to prove this language is non-regular. I do not even know where to start to develop a string that would prove the language is non-regular by contradiction. Any help would be ...
2
votes
1answer
48 views

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{...
3
votes
1answer
42 views

Any finite Graph G with all V have at least degree of 2, is it true that every vertex is necessarily contained IN a cycle?

As title, (note: this questions is asking weather or not all vertices are contained IN a cycle not asking if the G contains a cycle. My attempt is that: So this graph would be an counter example ...
1
vote
3answers
73 views

Optimizing coin splitting - Is this algorithm as fast as I think?

In a recent exam, I've been asked to solve the following problem: The problem Two players play the following game: Given a sequence of coin values $v_1,\ldots,v_n (n \vert 2)$ the players ...
0
votes
0answers
317 views

Show that P is a subset of NP

Okay, before I start with the question I would like to point out that I am aware that there are many proofs of this question online. However, I am interested in showing this with the definitions of my ...
0
votes
0answers
230 views

Prove DFA constructed by subset construction has exactly the states and transitions of NFA plus transitions to new dead state

Prompt: if $N$ is NFA that has at most one choice of state for any state and input symbol, then the DFA constructed from $N$ by subset construction has exactly the state and transitions of $N$ plus ...
4
votes
1answer
96 views

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 ...
2
votes
1answer
62 views

Question about proving that Rado's function is non-computable

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 ...
1
vote
1answer
36 views

Solving Recurrence relation with master method?

I have to solve the following recurrence equation and I thought to solve it with case #3 of the master theorem. Can I do that? $$T(1) = c>0 $$ $$T(n) = 9T(n/3) + f(n)$$ $$f(n) = n^2\cdot lg^3 (n) +...
1
vote
1answer
106 views

Maximum value of LOOP-Program turing-computable

Lets consider the class of "simple" LOOP-Programs. A LOOP-Program P is inducively defined as: $P_1: x_i = x_j$ and $P_2:x_i = x_i +1$ are LOOP-Programs. We also define a length property $l(P)$ ...
1
vote
1answer
201 views

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 ...
0
votes
1answer
190 views

Universal Lossless Compression? [closed]

It is not possible to losslessly compress all files of size $n$ using a single algorithm, as there are more files of size $n (2^n)$ than of size $p, p: p < n ( 2^n-1)$. Via the pigeon hole ...
0
votes
1answer
196 views

How to prove this language is not regular (via Fooling Set)

By using this fooling set, I am able to prove that the concatenation of bz is in the language L, but I still need to prove that az is not in the language to complete the proof. This is also the ...
1
vote
3answers
149 views

Is Goedel's 1st theorem not algorithmically derivable?

First let me explain what I mean by algorithmically derivable. An algorithm must be able to come up with the proof without prior knowledge of the proof, in the same way mathematicians and computer ...
1
vote
2answers
134 views

Find an upper bound for $T(n)=T(\sqrt{n})+10\log\log n$

I need to find an upper bound for $T(n)=T(\sqrt{n})+10\log\log n$. I thought first to make a substitution: $m=\log n$. Then: $$ T(2^m)=T(2^{m \over 2})+10\log m $$ Let $S(m)=T(2^m)$: $$ S(m)=S\big({m ...
0
votes
1answer
65 views

Proof Review: Integer Factorization is in NP

I want to prove that integer factorization is in NP I have a general idea of how to prove this, and was wondering if I could get a sanity check: I'll show it's in NP by using a non-deterministic TM ...
2
votes
1answer
771 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: ...
0
votes
1answer
820 views

$ADD = {x=y+z}$ with $x, y, z$ binary integers, and $x$ is the sum of $y$ and $z$. Pumping lemma to show that $ADD$ is not regular

Consider the alphabet $\Sigma = \{0, 1, +, =\}$ and the language $ADD = \{x=y+z|x,y$ are binary integers $x$ is the sum of $y$ and $z$ $\}$. This is the (informal) solution I came up with (not sure ...
0
votes
0answers
38 views

Verification of extendible hashing proof

I have to proof this theorem: "An extendible hashing table always contains at least one bucket where only one pointer points to after an element is added". I made this proof, but I'm not completely ...
1
vote
1answer
1k views

Every AVL tree may be red black tree

I proved by induction that every AVL tree may be colored such that it will be red black tree. The problem is that I can't see an error in my proof. Look at my proof. Induction for height. Let's ...
3
votes
2answers
598 views

Sorting an “almost sorted” array in sub linear time

I am given an "almost sorted" array with the condition that each element is no more than $k$ places away from its position in the sorted array. I need to show that it is impossible to sort this array ...
2
votes
1answer
482 views

Prim's algorithm: difference between brute force and PQ approaches

I'm trying to figure out the different way we obtain an MST with a brute force Prim's algorithm compared to the optimized version based on priority queues. Given a graph $G=(V,E)$, the former can be ...
1
vote
1answer
829 views

Optimal prefix code: full binary tree existence

I'm ok following the passages generally used to prove this theorem, like in this question concerning the same subject. Anyway i've the unpleasant feeling that the proof lacks something to be ...
5
votes
1answer
179 views

Simpler proof of Rabin's Compression Theorem?

I was doing a presentation on Rabin's Compression Theorem, when someone in the audience brought up a point I have no answer to. Rabin's Compression Theorem states that every reasonable complexity ...
0
votes
0answers
138 views

Designing a 2 place function that is not Turing computable

I'm just refreshing my memory on Turing machines and computability, and I was wondering how to design a function of 2 arguments that is guaranteed not to be computable. I've seen the proof (by ...
2
votes
0answers
40 views

How to use homomorphisms to prove irregularity [duplicate]

I'm a bit confused on how to use homomorphims to prove irregularity or to prove that a language is not context free. This is what I'm currently thinking: Example 1: Let $L = \{ a^{i}b^{j}c^{k} : i ...
0
votes
1answer
234 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 $L\in{}REG$...
0
votes
1answer
116 views

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.
4
votes
3answers
200 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 ...
0
votes
1answer
960 views

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 ...
0
votes
2answers
345 views

Hoare Calculus Incorrect Assignment Axiom

I'm currently preparing for an exam and recently came across the following exercise and would like to know whether my solution would be correct. Exercise: Prove that the following axiom is not ...
4
votes
2answers
725 views

Solve recurrence relations

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, ...
6
votes
2answers
531 views

Existence of Efficient Set Difference Algorithm

As a foreword, I'm not asking what the algorithm is, just whether one can possibly exist (though, if it does already exist and someone knows what it is, that'd be great). Basically, given two sets $S$...
3
votes
1answer
186 views

Proof or refute $n^n = \Omega(n!)$ with the help of Stirling's approximation

I'm trying to proof/refute the following equation: $$n^n = \Omega(n!)$$ Generally I would try to use Convergence Criteria and or l'Hôpital's rule to solve such a problem. $$\lim_{n\to \inf}{{f(n)}\...
2
votes
0answers
672 views

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 ...
3
votes
3answers
156 views

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 ...
5
votes
1answer
181 views

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 $ ...
4
votes
1answer
99 views

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 \...
-1
votes
2answers
2k views

Using pumping lemma to show $L = \{a^i b^j a^k \ | \ k > i + j\}$ cannot be accepted by an FA

$L = \{a^i b^j a^k \ | \ k > i + j\}$ Use the pumping lemma to show that this language cannot be accepted by an FA. Proof: Suppose $L$ can be accepted by an FA. Suppose a string $s = xyz \...