Problem Detail: In a course of computer science it is common to study the hierarchy of formal languages, grammars, automata and Turing machines. I wonder what is the relationship of these objects with formal systems. For example, lambda calculus is said Read More …
Author: ignougroup
[Solved]: Algorithm to search substring in a circular string?
Problem Detail: I need an algorithm to search for substrings. I checked different resources, and it seems that the most known algorithms are the Boyer–Moore and the Knuth–Morris–Pratt. However, as far as I understand, these operate on “regular” strings, but what Read More …
[Solved]: Induction proof, base case not working but induction step works?
Problem Detail: $1+3+5+…+(2n+3)=n^2+4n$ For this series using induction proof. Base case 1,2,3,.. not working. But induction step works well. Base case is not given in question. Asked By : user5507 Answered By : yuanshang First of all, the right hand side should be 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]: 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]: 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]: 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]: Finding all paths with lengths in a fixed interval in sparse graphs
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 …
[Solved]: Confluence proof for a simple rewriting system
Problem Detail: Assume we have a simple language that consists of the terms: $mathtt{true}$ $mathtt{false}$ if $t_1,t_2,t_3$ are terms then so is $mathtt{if}: t_1 :mathtt{then}: t_2 :mathtt{else}: t_3$ Now assume the following logical evaluation rules: $$ begin{gather*} dfrac{} {mathtt{if}: mathtt{true} :mathtt{then}: Read More …
[Solved]: Intersection of Turing-recognizable language and regular language
Problem Detail: True or false: An intersection of a Turing-recognizable and a regular language is always Turing-decidable. This was asked on a practice test and the answer is False. Why? I thought regular languages were a subset of decidable languages. So Read More …
