Problem Detail: Assume that we want to develop a warehouse management system, which picks up plastic boxes and stacks them on a pallet. A pallet has a maximum of 5 vertical box stacks and the maximum height of a box stack Read More …
Category: Uncategorized
[Solved]: Minimal size of contracting a DAG into a new DAG
Problem Detail: We have a DAG. We have a function on the nodes $Fcolon Vto mathbb N$ (loosely speaking, we number the nodes). We would like to create a new directed graph with these rules: Only nodes with the same number Read More …
[Solved]: Is it possible to decide if a given algorithm is asymptotically optimal?
Problem Detail: Is there an algorithm for the following problem: Given a Turing machine $M_1$ that decides a language $L$, Is there a Turing machine $M_2$ deciding $L$ such that $t_2(n) = o(t_1(n))$? The functions $t_1$ and $t_2$ are the worst-case Read More …
[Solved]: Is it allowed to do a binary search with an oracle when proving NP-completeness?
Problem Detail: In http://cs.stackexchange.com/a/45524/28999, they do a binary search using an oracle for an NP-Complete problem. They show that the original problem can be reduced to that NP-Complete problem, implying that the original problem is in NP. Why is that allowed? Read More …
[Solved]: What is the difference between a problem and an algorithm?
Problem Detail: I can say that $x * y$ is a problem, but also I can say that $x * y$ is an algorithm for finding the area of rectangle. I been reading Wikipedia about an algorithm and a problem, but Read More …
[Solved]: Partition an infinite regular language into 2 disjoint infinite regular languages
Problem Detail: Given any infinite regular language $L$, how can I prove that $L$ can be partitioned into 2 disjoint infinite regular languages $L_1, L_2$? That is: $L_1 cup L_2 = L$, $L_1 cap L_2 = varnothing$, and $L_1$ and $L_2$ Read More …
[Solved]: Name of Bomberman algorithm?
Problem Detail: Last couple of days I’ve been pulling my hair trying to find the name of a bomberman-esque algorithm which finds solutions to the question of where to place a single bomb so as to blow all targets up, either Read More …
[Solved]: Synchronizing sequence and Synchronizable DFA
Problem Detail: I am trying to prove problem 1.59 in Sipser’s book: Introduction to the theory of computation , 2nd Edition. Let $M=(Q,Sigma,delta,q_0,A)$ be a DFA and let $q’$ be a state of $M$ called its “home”. A Synchronizing sequence for Read More …
[Solved]: Decremental reachability in a grid graph
Problem Detail: Consider an $n$ by $n$ grid graph. For example, the following. You can of course reach the top left corner from the bottom right. Now consider the graph dynamically with an arbitrary number of edges deleted at each step. Read More …
[Solved]: Program synthesis, decidability and the halting problem
Problem Detail: I was reading an answer to a recent question, and sort of a strange, ephemeral thought came to mind. My asking this might betray either that my theory chops are seriously lacking (mostly true) or that it’s just too Read More …
