Problem Detail: I know that maximum independent set on cubic triangle-free graphs is NP-complete. Is it still NP-complete in case we require the independent set to be of size exactly $|V|/2$? Basiclly, YES instance of independent set problem on cubic triangle-free Read More …
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[Solved]: Why does SAT not reduce to QBF?
Problem Detail: So, I remember the professor saying that SAT does not reduce to QBF (Quantifier Boolean Formula) $QBF ::= prop|-QBF|(QBFoQBF)|exists pQBF |forall pQBF$ So, I guess this is not NP, since solving a QBF could grow exponentially. However, $P subseteq Read More …
[Solved]: Algorithm exercise
Problem Detail: making exercises to prepare a test I’m having problems to understand 2 questions, the questions are: how many are the leafs of a decisional tree associated to any algorithm for the search problem in a ordered set? for this Read More …
[Solved]: Can you have a binary search tree with O(logn + M) property for the following case
Problem Detail: Let $n$ be the number of strings which are sorted in lexicographical order and stored in a balanced binary search tree. You are provided with a prefix $x$ of which $M$ strings have the prefix $x$. I have devised Read More …
[Solved]: What is the difference between formal language, regular language and regular expression?
Problem Detail: I want to know the difference between these three languages and it would be great if you would give some examples as well, thank you. 🙂 Asked By : hackhan Answered By : Yuval Filmus An alphabet $Sigma$ is a finite Read More …
[Solved]: No need to rename a free variable in substitution?
Problem Detail: I wonder if the following two substitutions are correct: $$(x,y)[x:=y] = (y,y)$$ $$ lambda y. (x,y) [x:=y] = lambda z.(y,z)$$ They are what I understand from http://en.wikipedia.org/wiki/Lambda_calculus#Substitution. Although I can follow the rules there mechanically, I wonder why there Read More …
[Solved]: Mapping reducibility vs. Turing reducibility
Problem Detail: Let $A$ and $B$ be two languages. If $A le_{m} B$ ( reducible by mapping ) then I know that if $B$ is decidable so is $A$ and if $B$ is recognizable so is $A$. And if $A le_{T} Read More …
[Solved]: Visualization of Lamport’s three-dimensional “space-time diagram” with introduced “tick lines”
Problem Detail: In the third page (the third paragraph in the right column) of the paper “Time, Clocks, and the Ordering of Events in a Distributed System” by Leslie Lamport, it says that The reader may find it helpful to visualize Read More …
[Solved]: Relationship of algorithm complexity and automata class
Problem Detail: I have been unable to find a graph depicting or text answering the following question: Is there a direct relationship between the complexity of an algorithm (such as best / worst case of quick sort), and class of automata Read More …
[Solved]: Space(n) not closed under Karp reductions – what about NTime(n)?
Problem Detail: In the book on complexity by Arora and Barak, there is an exercise to show $Space(n)neq NP$, the proof of which goes by showing that $NP$ is closed under Karp reductions, while $Space(n)$ isn’t. To show that $Space(n)$ isn’t Read More …
