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Chapter 1: Q3E (page 83)

Question : The formal description of a DFA M is q1,q2,q3,q4,q5,u,d,未,q3,q3, where 未 is given by the following table. Draw the state diagram of this machine.

Short Answer

Expert verified

Answer:

The state diagram is

Step by step solution

01

Explain the given DFA

The specified DFA M is defined as follows:

M=(Q,鈭�,未,q3,F)Q={q1,q2,q3,q4,q5}a={u,d}未=Transition

The transition of the given DFA is given as follows:

02

Step 2: Draw the state diagram of the given machine

Assume that the initial state and the final state is q3, and represent it by double circle. The transitions are made from one state to another based on the input symbol and the data from the table given. The state diagram for the DFA M is as follows:

Therefore, the state diagram for the machine M has been obtained.

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Most popular questions from this chapter

If A is any language, let A13-13be the set of all strings in A with their middle thirds removed so that

A13-13={xz|forsomey,|x|=|y|=|z|andxyz鈭�A}.

Show that if A is regular, then A13-13is not necessarily regular
  1. Show that ifis a DFA that recognizes languageB, swapping the accept and non accept states inyields a new DFA recognizing the complement ofB. Conclude that the class of regular languages is closed under complement.
  2. Show by giving an example that ifM is an NFA that recognizes language C swapping the accept and non accept states in Mdoesn鈥檛 necessarily yield a new NFA that recognizes the complement of C. Is the class of languages recognized by NFAs closed under complement? Explain your answer.

Question: Prove that the following languages are not regular. You may use the pumping lemma and the closure of the class of regular languages under union, intersection, and complement.

a.{0n1m0n|m,n猢�0}b.{0m1n|m鈮�n}c.{w|w鈭�{0,1}*isnotapalindrome}d.{wtw|w,t鈭�{0,1}+

Recall that string x is a prefix of string y if a string z exists where xz=y, and that x is a proper prefix of y if in addition x6=y. In each of the following parts, we define an operation on a language A. Show that the class of regular languages is closed under that operation.

a)NOPREFIXA={w鈭�A|noproperprefixofwisamemberofA}.b)NOEXTENDA={w鈭�A|wisnottheproperprefixofanystringinA}.

Give regular expressions generating the languages of Exercise 1.6.

a. {begins with a 1 and ends with a 0}

b. { w|wcontains at least three 1s}

c. { w|wcontains the substring 0101 (i.e., w = x0101y for some x and y)}

d. { w|whas length at least 3 and its third symbol is a 0}

e. { w|wstarts with 0 and has odd length, or starts with 1 and has even length}

f. { w|wdoesn鈥檛 contain the substring 110}

g. { w|the length of wis at most 5}

h. { w|wis any string except 11 and 111}

i. { w|every odd position of w is a 1 }

j. { contains at least two 0s and at most one 1}

k. {蔚,0}

l. { w|wcontains an even number of 0 s, or contains exactly two 1s}

m. The empty set

n. All strings except the empty string
See all solutions

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