Problem Detail: We know that A(TM) is undecidable, what if we reduce A(TM) to A(DFA) which is decidable? How will we prove that A(DFA) is decidable? I couldn’t find an example or theory. Thanks Asked By : Abdussami Tayyab Answered By : Patrick87 Read More …
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[Solved]: Is it decidable whether a Turing machine will ever leave the start state on any input?
Problem Detail: Is $L={ M | Mtext{ leaves the start state on every input}}$ decidable? I have an intuition that the following language is undecidable, since the complement $L^C$ seems to not be recursively enumerable. Some TM might remain on the Read More …
[Solved]: Cost of partitioning in quicksort
Problem Detail: I’m reading “Algorithms Fourth Edition” by Sedgewick & Wayne and am wondering if I have spotted an error in the book or if I just can’t wrap my head around something so simple. When talking about the complexity of Read More …
[Solved]: Does NP-completeness require to find the solution?
Problem Detail: In the paper “Computing Equilibria:A Computational Complexity Perspective” by Tim Roughgarden, they consider the problem: Problem 2.1 (Clique). Given a graph $G = (V, E)$ and an integer $k$: if there is a set $K ⊆ V$ with $|K| Read More …
[Solved]: Number of digits in a binary product
Problem Detail: Assume i have 2 numbers in binary form (or, more precisely, assume to know the number of their digits, DF1, DF2): 101010101001010101010101010111111111111111111111010101 10101111111111111111010101 Is there a formula for the exact number of binary digits (DP) of the product? DP Read More …
[Solved]: Where in the Chomsky Hierarchy are Regular Expressions as a language?
Problem Detail: I’m referring to regular expressions as language: begin{equation*} Sigma = { “a”, “b”, “(“, “)”, “*”, … } end{equation*} and begin{equation*} L = Sigma^* text{, which form a legal regular expression} end{equation*} I am not referring to their computational Read More …
[Solved]: Exercise on Divide&Conquer’s technique
Problem Detail: I need help on this exercise: You are given an array of n elements, and you notice that some of the elements are duplicates; that is, they appear more than once in the array. Show how to remove all Read More …
[Solved]: What is the difference between “definition” and “inductive” in Coq?
Problem Detail: In Coq, you can use two different kinds of keywords to do definitions–Inductive and Definition. I do not understand the difference between an inductive and a definition, or when it is appropriate to use one instead of the other. Read More …
[Solved]: Is there a generalization of Huffman Coding to Arithmetic coding
Problem Detail: In trying to understand the relationships between Huffman Coding, Arithmetic Coding, and Range Coding, I began to think of the shortcomings of fuffman coding to be related to the problem of fractional bit-packing. That is, suppose you have 240 Read More …
[Solved]: What is the formal description of a Turing machine?
Problem Detail: I was asked to give a formal description of a Turing machine I have no experience with this, and was wondering what “formal description” entails. Asked By : Mark Answered By : Yuval Filmus In class you must have seen a Read More …