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Chapter 13: Q29E (page 898)

Which of the following problems is a decision problem\(?\)

\(a)\)What is the smallest prime greater than \(n\)\(?\)

\(b)\)Is a graph \(G\) bipartite\(?\)

\(c)\)Given a set of strings, is there a finite-state automaton that recognizes this set of strings\(?\)

\(d)\)Given a checkerboard and a particular type of polyomino (see Section \(1.8\)), can this checkerboard be tiled using polyominoes of this type\(?\)

Short Answer

Expert verified

\(a)\)The problem is not a Decision problem.

\(b)\)The problem is a Decision problem.

\(c)\)The problem is a Decision problem.

\(d)\)The problem is a Decision problem.

Step by step solution

01

Definition

The problem is a decision problem, if the answer is yes or no type.

02

Determining the answer yes/no

\(a)\)No, the answer is a number, it is not yes or no.

Therefore, it is Decision problem.

\(b)\)The answer can be yes or no.

Hence, it is Decision problem.

\(c)\)The, the answer can be yes or no.

So, it is Decision problem.

\(d)\)The, the answer can be yes or no.

Accordingly, it is Decision problem.

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Most popular questions from this chapter

Determine whether the string 01001 is in each of these sets.

a){0,1}* b){0}*{10}{1}*

c){010}*{0}*{1} d){010,011} {00,01}

e){00} {0}*{01} f){01}*{01}*

In Exercises 16–22 find the language recognized by the given deterministic finite-state automaton

Describe the set of strings defined by each of these sets of productions in EBNF.

\(\begin{array}{c}\left( {\bf{a}} \right){\bf{string :: = L + D?L + }}\\{\bf{L :: = a }}\left| {{\bf{ b }}} \right|{\bf{ c }}\\{\bf{D :: = 0 | 1}}\\\left( {\bf{b}} \right){\bf{string :: = signD + |D + }}\\{\bf{sign :: = + | - }}\\{\bf{D :: = 0 | 1|2|3|4|5|6|7|8|9}}\\\left( {\bf{c}} \right){\bf{string :: = L*}}\left( {{\bf{D + }}} \right){\bf{?L* }}\\{\bf{L :: = x |y }}\\{\bf{D :: = 0 | 1}}\end{array}\)

What is an unsolvable decision problem? Give an example of such a problem.

let \({{\bf{G}}_{\bf{1}}}\) and \({{\bf{G}}_{\bf{2}}}\) be context-free grammars, generating the language\({\bf{L}}\left( {{{\bf{G}}_{\bf{1}}}} \right)\) and \({\bf{L}}\left( {{{\bf{G}}_{\bf{2}}}} \right)\), respectively. Show that there is a context-free grammar generating each of these sets.

a) \({\bf{L}}\left( {{{\bf{G}}_{\bf{1}}}} \right){\bf{UL}}\left( {{{\bf{G}}_{\bf{2}}}} \right)\)

b) \({\bf{L}}\left( {{{\bf{G}}_{\bf{1}}}} \right){\bf{L}}\left( {{{\bf{G}}_{\bf{2}}}} \right)\)

c) \({\bf{L}}{\left( {{{\bf{G}}_{\bf{1}}}} \right)^{\bf{*}}}\)
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