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Problem Detail: For an L2 cache that is strictly inclusive of the L1 cache, if a block to be evicted is also present in L1, then back invalidation is required to maintain the inclusion property. I am interested in some details Read More …

Problem Detail: Suppose I have a graph $G$ with $M(G)$ the (unknown) set of perfect matchings of $G$. Suppose this set is non-empty, then how difficult is it to sample uniformly at random from $M(G)$? What if I am okay with Read More …

Problem Detail: In Michael Sipser’s Theory of Computation on page 270 he writes: P = the class of languages for which membership can be decided quickly. NP = the class of languages for which membership can be verified quickly. What is Read More …

Problem Detail: I am unable to find a clear definition of term “size of the instance” when considering some algorithmic problem. I came accross a definition that said, that “Size of the instance corresponds to the size of the input array Read More …

Problem Detail: is there any difference between transition systems and finite automata? Is it that transition systems consist of both NFA (nondeterministic finite automata) and DFA (deterministic finite automata)? Asked By : ishaarora95 Answered By : Luke Mathieson Yes, did you try wikipedia? Read More …

Problem Detail: Consider the following grammar with starting symbol of $S$. $$S rightarrow 0S11;|;S1;|;0$$ Let $L = {0^i1^j:; ge 1; and; j ge2i-2}$ . Give a formal proof of the following claim : For all $n;ge0$, every string of length $n$ Read More …

Problem Detail: I asked a (seed) question about sums of Landau terms before, trying to gauge the dangers of abusing asymptotics notation in arithmetics, with mixed success. Now, over here our recurrence guru JeffE does essentially this: $qquad displaystyle sum_{i=1}^n Thetaleft(frac{1}{i}right) Read More …

Problem Detail: Let $T$ be a Turing machine whose accepted language is $L(T)$. Let $X$ be another language. How do you approach a proof like $L(T)subseteq X?$ Asked By : And Answered By : Hendrik Jan In order to prove that any machine, Read More …

Problem Detail: My intuition is telling me that this is untrue. But I am having trouble formulating a proof for this. Can anyone point me in the right direction? I’ve seen a proof by contradiction involving the union of all singletons Read More …

Problem Detail: Is there an NP complete language having no polytime decidable superset (apart from the set of all strings)? Asked By : ARi Answered By : David Richerby No, assuming P$,neq,$NP. Let $L$ be any NP-complete language over alphabet $Sigma$ and let $N Read More …