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Category: Uncategorized

[Solved]: 2 cases for P = NP

February 8, 2017March 27, 2017 ignougroup

Problem Detail: As we all know the million dollar question in Computer Science P=NP or not. I was trying to understand it and got some doubts please tell me whether I’m right or wrong N=NP in two cases Case 1: We Read More …

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[Solved]: Sorting numbers in $O(1)$

February 8, 2017March 27, 2017 ignougroup

Problem Detail: Here is an experiment I came up with (I don’t have sufficient material to make it): Say that, you have a list of $n$ numbers $L = {l_1, l_2, …, l_n}$. And you have bars representing those numbers like Read More …

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[Solved]: Proof of big theta using induction

February 8, 2017March 27, 2017 ignougroup

Problem Detail: Here is a recursive definition for the runtime of some unspecified function. $a$ and $c$ are positive constants. $T(n) = a$, if $n = 2$ $T(n) = 2T(n/2) + cn$ if $n > 2$ Use induction to prove that Read More …

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[Solved]: Optimal upper bound on the number of states in the complement of an NFA

February 8, 2017March 27, 2017 ignougroup

Problem Detail: I have my own version of lex and I would like to add the complement operation. Derived from that I can then add the intersection and difference also. My version also supports the generation of NFAs (Non-deterministic Finite Automaton) Read More …

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[Solved]: 3 Colorability reduction to SAT

February 8, 2017 ignougroup

Problem Detail: I’d like to reduce 3 colorability to SAT. I’ve stuffed up somewhere because I’ve shown it’s equivalent to 2 SAT. Given some graph $G = (V,E)$ and three colors, red, blue, green. For every vertex $i$, let the boolean Read More …

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[Solved]: What is it called when two problems are similar?

February 8, 2017March 27, 2017 ignougroup

Problem Detail: Suppose that there are two problems $P$ and $Q$. How can I say that “solving $P$ is same thing with solving $Q$”? For instance, if $P$ is NP-Hard, then we can say “$P$ can be solved in polynomial time Read More …

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[Solved]: Confusion about the Time Hierarchy Theorem and relativization

February 8, 2017March 27, 2017 ignougroup

Problem Detail: I know that $mathsf{P}^A = mathsf{EXP}$ for any $mathsf{EXPTIME}$-complete language $A$. Is it true that $mathsf{DTIME}^A(n^k) = mathsf{EXP}$ for any fixed $k$ and any $mathsf{EXPTIME}$-complete oracle $A$? If not, what do these complexity classes equal and why? I am Read More …

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[Solved]: How Is a Computer Able to Store and Quickly Manipulate All the Data Required For A Computer Display?

February 8, 2017March 27, 2017 ignougroup

Problem Detail: I did some quick math on how much data is contained on a screen at any given instant and I ended up with a number well beyond what I thought was possible. 256 colors for Red, Green, and Blue Read More …

Uncategorized

[Solved]: Is the set of CFGs that contain all odd and even length words Turing-decidable?

February 8, 2017March 27, 2017 ignougroup

Problem Detail: $ALLEVEN_{CFG}$ = {M is a grammar, and L(M) includes all strings of even length in $Sigma^*$} = {(M): ($SigmaSigma$)* ⊆ L(M)} $ALLODD_{CFG}$ = {M is a grammar, and L(M) includes all strings of odd length in $Sigma^*$} = {(M): Read More …

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[Solved]: Converting context-free grammar to Chomsky/Greibach Normal Form

February 8, 2017March 27, 2017 ignougroup

Problem Detail: Is it necessary to remove all lambda productions, unit productions and useless productions from a context free grammar(CFG) before converting to Chomsky Normal Form(CNF) or Greibach normal form (GNF). If so why is it required? Also my Professor said Read More …

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