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Chapter 0: Q17E (page 1)

a. Give an NFA recognizing the language (01鈭�001鈭�010)*.

b. Convert this to an equivalent DFA. Give only the portion of theDFAthat is reachable from the start state.

Short Answer

Expert verified

The equivalent DFA for NFA the Language L=01U001U010* is as follows:

Step by step solution

01

To Consider Recognizing the Language

Here, we can say L=01U001U010*.

Consider M to be the NFA which recognises the language L.

02

To Recognizing the language

NFA M for something like the language in question L=01U001U010*is following:


For Number/Character 001,

For Number/Character 010,

This complete NFA for the is created by connecting all of the aforementioned strings. L=(01|01|010)is shown below.:

03

To Change the NFA to a DFA

The change from NFA to DFA.

Initially, delete all 系 Various changes that seem to be present in using the symbols inside the NFA are illustrated.

The equivalent DFA for NFA in the Language L=01U001U010*is as follows:

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Most popular questions from this chapter

a). Let C be a context-free language and R be a regular language. Prove that the languageC鈭�Ris context free.

b). Let A= { w|w鈭�{a,b,c}*andwcontains equal numbers of a鈥�s,b鈥�s,andc鈥�s}. Use part(a) to show that A is not a CFL

Let
fx=3x+1foroddxx/2forevenx

for any natural number x . If you start with an integer x and iterate f , you obtain a sequence, x,fx,ffx,......Stop if you ever hit 1. For example, if x=17 , you get the sequence 17,52,26,13,40,20,10,5,16,8,4,2,1 .Extensive computer tests have shown that every starting point between 1 and a large positive integer gives a sequence that ends in 1 . But the question of whether all positive starting points end up at 1 is unsolved; it is called the 3x+1 problem. Suppose that ATMwere decidable by a TM H. Use H to describe a TM that is guaranteed to state the answer to the 3x+1 problem.

Use the procedure described in Lemma 1.60to convert the following finite automata to regular expressions.

Show that A is Turing-recognizable Am鈮�ATM

Show how to compute the descriptive complexity of strings K(x) with an oracle for ATM.
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