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Chapter 4: 13P (page 211)

Let A={R,S|R and S are regular expressions and LR⊆LS}. Show that A is decidable.

Short Answer

Expert verified

A is decidable.

Step by step solution

01

Explain Decidable Language

A problem is decidable if a Turing machine halts in finite amount of time for every input and gives the answers as “yes” or “no.”A decidable problem has an algorithm to determine the answer for a given input.

02

Show that A is decidable

A language is decidable if a Turing machine accepts the input of a language. Consider that Rand Sare regular expressions.

Consider a Turing machine M that decides the language AOn input string W

  1. Consider that the input has two possibilities.
  2. If the input decodes a pair of regular expressions, then it takes finite time.
  3. If it doesn’t decode a pair of regular expressions, then it stops rejecting.

Therefore, the language given is decidable and has been proved.

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Most popular questions from this chapter

Let ∑={0,1}.Show that the problem of determining whether a CFG generates some string in 1*is decidable. In other words, show that

{G|G  is  a  CFG over 0,1 and 1*∩LG≠∅}is a decidable language.

Question:LetINFINITEDFA={(A)|AisaDFAandLAisaninfinitelanguage}.Show thatINFINITEDFA is decidable.

Say that an NFA is ambiguous if it accepts some string along two different computation branches

LetAMBIGNFA={(N)|NisanambiguousNFA}.Show thatAMBIGNFA is decidable. (Suggestion: One elegant way to solve this problem is to construct a suitable DFA and then run EDFAon it.)

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LetBALDFA={(M)|Mis a DFA that accepts some string containing an equal number of 0s and 1s}. Show that BALDFA is decidable.

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