Question

Which of the following problems is a decision problem? a) Is the sequence $a_{1}, a_{2}, \ldots, a_{n}$ of positive integers in increasing order? b) Can the vertices of a simple graph $G$ be colored using three colors so that no two adjacent vertices are the same color? c) What is the vertex of highest degree in a graph $G ?$ d) Given two finite-state machines, do these machines recognize the same language?

Name: Problem 30, Chapter 13: Discrete Mathematics and its Applications
Uploaded: 2020-08-27T13:37:48-08:00
Duration: 3 min 8 s
Channel: Chris Trentman
Description: Which of the following problems is a decision problem? a) Is the sequence a1, a2, …, an of positive integers in increasing order? b) Can the vertices of a simple graph G be colored using three colors so that no two adjacent vertices are the same color? c) What is the vertex of highest degree in a graph G ? d) Given two finite-state machines, do these machines recognize the same language?

   Which of the following problems is a decision problem?
a) Is the sequence $a_{1}, a_{2}, \ldots, a_{n}$ of positive integers in increasing order?
b) Can the vertices of a simple graph $G$ be colored using three colors so that no two adjacent vertices are the same color?
c) What is the vertex of highest degree in a graph $G ?$
d) Given two finite-state machines, do these machines recognize the same language?

Discrete Mathematics and its Applications

Kenneth Rosen 8th Edition

Chapter 13, Problem 30

Instant Answer

Solved by Expert Chris Trentman

08/27/2020

Step 1

This problem can be solved by comparing each element $a_{i}$ with the next element $a_{i+1}$ in the sequence. If for all $i$, $a_{i} \leq a_{i+1}$, then the sequence is in increasing order. Otherwise, it is not. Since the answer to this problem is either "yes" Show more…

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Which of the following problems is a decision problem? a) Is the sequence $a_{1}, a_{2}, \ldots, a_{n}$ of positive integers in increasing order? b) Can the vertices of a simple graph $G$ be colored using three colors so that no two adjacent vertices are the same color? c) What is the vertex of highest degree in a graph $G ?$ d) Given two finite-state machines, do these machines recognize the same language?

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Key Concepts

Decision Problem

A decision problem is one where the answer is restricted to a simple 'yes' or 'no'. This type of problem is fundamental in computational theory and complexity analysis because it allows for precise categorization of problems based on the binary nature of their outputs.

Problem Classification

Computational problems can be broadly categorized into decision problems, search problems, and optimization problems. Decision problems, unlike search or optimization problems, require only a binary response, which makes them pivotal in studies of algorithmic efficiency and complexity classes.

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