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Problem Detail: How to approach to solve this question and the likes of it? Let $L$ be the set of strings $langle Mrangle$ such that $M$ accepts all strings of even length and does not accept any strings of odd length. Read More …

Problem Detail: In my CS course, we are covering things from one topic to another in sort of a sensible manner. For example, binary search tree -> 234-tree -> red-black tree -> heap -> greedy algorithms -> dynamic programming. And all Read More …

Problem Detail: I am trying to get a good grasp on Monte Carlo (MC) algorithms, but I feel I am missing something fundamental. What I don’t understand is how MC improves its confidence of giving the correct solution by running more Read More …

Problem Detail: I have the following CFG which I suspect cannot be rewritten to one which is LL(1): $S rightarrow epsilon | aSbS | bSaS | cSdS | dScS$ I’ve thought about it for a while, and can’t seem to make Read More …

Problem Detail: Consider the following 3-SAT variant defined over the variables $x_1,ldots,x_n$. In the $k$P$k$N-3SAT problem each variable $x_j$, $j in [n]$, occurs exactly $k$ times as a positive literal in $phi$, and exactly $k$ times as a negative literal in Read More …

Problem Detail: I’m reading through the HoTT book and I have a hard time with path induction. When I look at the type in the section 1.12.1: $$text{ind}_{=_A}:prod_{C:prodlimits_{x,y:A}(x=_Ay)to mathcal{U}} left( left(prod_{x:A}C(x,x,text{refl}_x)right) to prod_{x,y:A}prod_{p:x=_Ay} C(x,y,p) right),$$ I have no issue understanding what Read More …

Problem Detail: A multiplication table is symmetric over a diagonal, so only about $n^2/2$ of the elements in an $n times n$ multiplication table contain unique information. Same goes for addition tables. In fact, the same is true for any table Read More …

Problem Detail: We know that the $polyL$-hierarchy doesn’t have complete problems, as it would conflict with the space hierarchy theorem. But: Are there complete problems for each level of this hierarchy? To be precise: Does the class $DSPACE(log(n)^k)$ have complete problems Read More …

Problem Detail: Suppose I give you an undirected graph with weighted edges, and tell you that each node corresponds to a point in 3d space. Whenever there’s an edge between two nodes, the weight of the edge is the distance between Read More …

Problem Detail: An algorithm in Artificial Intelligence: A Modern Approach for planning in stochastic, fully observable environments is called And-Or-Graph-Search, implying that it’s a search algorithm. However, I don’t see how it is one. Wikipedia defines search algorithms as, “an algorithm Read More …