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Problem Detail: I read that most scientists don’t believe that P=NP. It might be subjective but can you simplify why not? I’m not informed enough to have an opinion but I’d like to know the definitions and some “pretty simple” explanation Read More …

Problem Detail: In the step of removing unit productions when converting a grammar to Chomsky normal form, I sometimes found that the variables may end up having the same production bodies. Is this possible? If so, can we consider these variables Read More …

Problem Detail: Can every linear grammar be converted to a linear Greibach normal form, a form in which all productions look like $A rightarrow ax$ where $a in T$ and $x in V cup {lambda}$? ($T$ is the set of terminals, Read More …

Problem Detail: Let $Sigma$ be the set of terminal and $N$ the set of non-terminal symbols of some context-free grammar $G$. Say I have a string $a in (Sigma cup N)^+$ such that $x a y in mathcal{S}(G)$ where $x,yin (Sigma Read More …

Problem Detail: From the book The Nature of Computation by Moore and Mertens, exercise 8.9: Consider the problem ACYCLIC GRAPH of telling whether a directed graph is acyclic. Show that the problem is in NL, and then show that the problem Read More …

Problem Detail: Given a Turing machine $M$, we say that $L(M) in P$ if the language decided by the machine can be decided by some machine in polynomial time. We say that $M in P$ if the machine runs in polynomial Read More …

Problem Detail: I realize non-deterministic pushdown automata can be an improvement over deterministic ones as they can “choose” among several states and there are some context-free languages which cannot be accepted by a deterministic pushdown. Still, I do not understand how Read More …

Problem Detail: Doing the following exercise: Let $overline{HALT(x,y)}$ be defined as $overline {HALT(x,y)} iff text{program number y never halts on input x}$ Show that it is not computable. Just want to make sure I have understood the concept correctly. We had Read More …

Problem Detail: Consider the language over the alphabet $sum= {a}$ containing strings whose length is either a multiple of 2 or 3 (including the empty strings). Writing a regular expression for this language Asked By : Leroy Kayanda Answered By : Yuval Filmus Read More …

Problem Detail: DISCLAIMER: I understand that I might not be posting in the right part of StackExchange, or this question might have been asked before (I haven’t found it). If this offends anybody, I apologize. I’m 15 and a sophomore in Read More …