Problem Detail: Let $mathrm{MIN}_{mathrm{DFA}}$ collection of all the codings of DFAs such that they are minimal regarding their states number. I mean if $langle A rangle in mathrm{MIN}_{mathrm{DFA}}$ then for every other DFA $B$ with less states than $A$, $L(A)ne L(B)$ Read More …
Category: Uncategorized
[Solved]: Context-free grammar for $L = {a^n : nleq2^{20}}$
Problem Detail: I want to find a context-free grammar for $L = {a^n : nleq2^{20}}$. There’s one for sure. I approached it by two ways and both seemed dead end. One was to set a limit during the production of the Read More …
[Solved]: Type inference + overloading
Problem Detail: I’m looking for a type inference algorithm for a language I’m developing, but I couldn’t find one that suits my needs because they usually are either: à la Haskell, with polymorphism but no ad-hoc overloading à la C++ (auto) Read More …
[Solved]: What if block sizes are not equal among caches?
Problem Detail: In all the books, packets of slides and similar I read, cache miss is always explained by assuming that blocks of different caches (or cache and RAM) are always of the same size. It’s pretty clear how it’s works Read More …
[Solved]: Is Post’s Correspondence Problem decidable with fixed word size?
Problem Detail: So, it’s known that PCP is undecidable even when we fix the number of tiles to $n geq 7$. I’m wondering, can anything similar be said for when there is a fixed word length? To be precise, here’s the Read More …
[Solved]: Log-Space Reduction $CO-2Col le_L USTCON$
Problem Detail: I want to show that $CO-2Col le_L USTCON$ (Log-Space reduction) $USTCON$ The $s-t$ connectivity problem for undirected graphs is called $USTCON$. [Input]: An undirected graph $G=(V,E)$, $s,t in V$. [Output]: 1 iff $s$ is connected to $t$ in $G$. Read More …
[Solved]: Meyniel’s theorem + finding a Hamiltonian path for a specific graph family
Problem Detail: Let’s say we have a directed graph $G = (V, E)$ for which $(v, w) in E$ and/or $(w,v) in E$ holds true for all $v, w in V$. My feeling is that this graph most definitely is Hamiltonian, Read More …
[Solved]: Is it axiomatic that the Time Hierarchy Theorem holds true in all relativized worlds?
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 …
[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 …
