Problem Detail: What is the most efficient way to find all paths of length M to N in a large sparse graph? Some general information: Graph has 30,000 to 50,000 nodes Average number of edges per node ~ 10 M=4, N=7 Read More …
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[Solved]: How many languages exist with input alphabet {0,1} and all strings in the language have length less than or equal to 5?
Problem Detail: I’m trying to write a formal proof in automata theory to show a few properties of DFAs but I am having some trouble with this that I am trying to incorporate into my proof. I want to show how Read More …
[Solved]: Best pathfinding algorithm for undirected unweighted graph
Problem Detail: I have an unweighted undirected graph with every node connected with an average of two hundred other nodes (nodes are people from social network). What will be the fastest algorithm to find the shortest path from one node to Read More …
[Solved]: design of self-loops and final states in fsm
Problem Detail: I am learning about automata and finite state machines. Consider the following automaton, that accepts the word ‘ab’, does not have to be infinite, just once: alphabet: ‘a’,’b’ states: 1,2, 3 (3 is the final state and 1 is Read More …
[Solved]: Finding a way out of a polygon
Problem Detail: There is a simply-connected polygon $C$. It contains $n$ pairwise-interior-disjoint simply-connected polygons, $D_1,dots,D_n$: The goal is to select one of the polygons, say $D_i$, and attach to it a polygon $E_i$ such that: $D_icup E_i$ is still simply-connected. $E_i$ Read More …
[Solved]: Reduce the following problem to SAT
Problem Detail: Here is the problem. Given $k, n, T_1, ldots, T_m$, where each $T_i subseteq {1, ldots, n}$. Is there a subset $S subseteq {1, ldots, n}$ with size at most $k$ such that $S cap T_i neq emptyset$ for Read More …
[Solved]: Does Reverse Polish Notation have an LL grammar?
Problem Detail: Let L be the language of all arithmetic expressions written in Reverse Polish Notation, containing only binary operators. $Sigma(L) = {n, o}$, n := number, o := operator. Is there an LL grammar G so that L(G) = L? Read More …
[Solved]: Advantages of amortized analysis
Problem Detail: I understood what amortized analysis does, but can anyone tell me what is the main purpose of this kind of analysis? What I understood: Let say we have 3 three operations a,b,c used 1,2 and 3 times to achieve Read More …
[Solved]: execises in computational complexity
Problem Detail: I am trying to get better in proofs and deep understanding of concept of computational complexity. Unfortunately, so far, with no success. In order to get more intuition, I decided to do more exercises, but most of them are Read More …
[Solved]: Are the Before and After sets for context-free grammars always context-free?
Problem Detail: Let $G$ be a context-free grammar. A string of terminals and nonterminals of $G$ is said to be a sentential form of $G$ if you can obtain it by applying productions of $G$ zero or more times to the Read More …
