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Chapter 0: Q1E (page 1)

Question: Answer all parts for the following DFA and give reasons for your answers.

a.Is<M,0100>鈭�ADFA?b. Is<M,011>鈭�ADFA?c. Is<M>鈭�ADFA?d. Is<M,0100>鈭�AREX?e. Is<M>鈭�EDFA?f. Is<M,M>鈭�EQDFA?

Short Answer

Expert verified

Answer

  1. Yes
  2. No
  3. No
  4. No
  5. No
  6. Yes

Step by step solution

01

Explain Deterministic Finite Automata 

A Deterministic Finite Automata is the computational model that determines the state of the input symbol provided.

02

Step 2: Is  <M,0100>∈ADFA

a.

Consider the given diagram, assume that the states are named as follows,

M,0100, represents the inputs of the machine. Symbol 0 starts with the state S , the next input 1 takes to the state A . The input symbol 0 moves to the state B and the next input 0 is the last symbol of the string that ends in the state S ,which accepts the input.

Therefore, Yes, M,0100鈭�ADFA.

03

Step 3: Is  M,011∈ADFA

b.

Consider the given diagram, assume that the states are named as follows,

M,011, represents the inputs of the machine. Symbol 0 starts with the state S , the next input 1 takes to the state A . The input symbol 0 is the last symbol of the string that ends in the state B ,which doesnot accepts the input.

Therefore, No, M,011鈭�ADFA.

04

Step 4: Is <M>∈ADFA

c.

Consider the given diagram, assume that the states are named as follows,

M, represents the inputs of the machine. The input symbol empty is not accepted by the given automata.

Therefore, No,role="math" M鈭�ADFA .

05

Step 5: Is  <M,0100>∈AREX

d.

Consider the given diagram, assume that the states are named as follows,

M,0100, represents the inputs of the machine. The input symbol is belongs to DFA not the regular language inputs.

Therefore, No,M,0100鈭�AREX

06

Step 6: Is  <M>∈EDFA

e.

Consider the given diagram, assume that the states are named as follows,

M, represents the empty input of the machine. The input symbol is belongs to DFA not the regular language inputs.

Therefore, No,M鈭�EDFA.

07

Step 7: Is  <M,M>∈EQDFA

e.

Consider the given diagram, assume that the states are named as follows,

M,M, represents the same language of the machine. The input symbol belongs to the DFA.

Therefore, Yes,M,M鈭�EQDFA.

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Most popular questions from this chapter

Give a counter example to show that the following construction fails to prove that the class of context-free languages is closed under star. Let A be a CFL that is generated by the CFG G=(V,鈭�,R,S). Add the new ruleS鈫�SS and call the resulting grammar. This grammar is supposed to generate A*.

Show that P is closed under homomorphism iff P = NP.

Read the informal definition of the finite state transducer given in Exercise 1.24. Give the state diagram of an FST with the following behaviour. Its input and output alphabets are 0,1 . Its output string is identical to the input string on the even positions but inverted on the odd positions. For example, on input 0000111 it should output 1010010 .

Show that the function K(x) is not a computable function.

Write formal descriptions of the following sets.

  1. The set containing the numbers1,10, and100
  2. The set containing all integers that are greater than5
  3. The set containing all natural numbers that are less than5
  4. The set containing the string aba
  5. The set containing the empty string
  6. The set containing nothing at all
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