Problem Detail: I learned from this post that ${sf DTIME}^{text{EXP}}(n^k) neq text{EXP}$ for a fixed $k$ for otherwise the Time Hierarchy Theorem would fail in that relativized world. However, is it possible to prove that no oracles exist in which the Read More …
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[Solved]: In principle, what is the relation between Artifical Intelligence and Turing machine?
Problem Detail: I am working on my cs project about AI & Turing machines, so i know that Artifical Intelligence is meant to implement different algorithms into the machine {the computer} to solve a problem or a set of problems together Read More …
[Solved]: Upper bound on the number of edges relative to the height of a DFS tree
Problem Detail: Let $T$ be a depth-first search tree of a connected undirected graph $G$ and $h$ be the height of $T$. How do you show that $G$ has no more than $h times |V|$ edges where $|V|$ is the number Read More …
[Solved]: Late and Early Bisimulation
Problem Detail: This is a follow up to my earlier questions on coinduction and bisimulation. A relation $R subseteq S times S$ on the states of an LTS is a bisimulation iff $forall (p,q)in R,$ $$ begin{array}{l} text{ if } p Read More …
[Solved]: Can a Boolean circuit be considered an algorithm?
Problem Detail: Can a Boolean circuit by itself be considered an algorithm (a single step algorithm if you like)? For instance say you have a simple tree circuit with two AND gates as the input gates feeding a single OR gate Read More …
[Solved]: Maximimal Independent Set on Ring and Path
Problem Detail: Let’s consider distributed version of algorithm for finding MIS of any graph $A$. For details, MIS – Maximimal Independent Set. Slow version of distributed algorithm for MIS, page 2 – Distributed algorithms. Maximal Independent Set In worst case, time Read More …
[Solved]: Extra space of MergeSort
Problem Detail: Here is my implementation of mergeSort. I need n extra space for the helper array. But what about recursive calls? I call sort log n times. mergeRoutine is a tail call, and it doesn’t add to the call stack. Read More …
[Solved]: Schedule two trains whose tracks overlap so they don’t crash
Problem Detail: I’ve encountered scheduling problems in my algorithms class before like the type we use vertex cover to solve. Recently I was asked this question and did not even know what algorithmic technique to use to answer it! There are Read More …
[Solved]: Showing that DNF VALID is coNP-hard
Problem Detail: I’m trying to understand/show that DNF VALID is coNP-hard. I have given an algorithm for the complement of DNF VALID and shown that this is in NP (since the complement of a language in NP is in coNP), but Read More …
[Solved]: First-order logic arity defines decidability?
Problem Detail: I’ve read first-order logic is in general undecidable, and that could be decidable only when working with unary operators. (I think that’s propositional logic, correct me if I am wrong) The question is why arity leads to undecidable problems? Read More …
