8 Lecture - Examples of TGs: accepting all strings, accepting none, starting with b, not ending in b, containing aa, containing aa or bb.

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8 Lecture

CS402

Midterm & Final Term Short Notes

Examples of TGs: accepting all strings, accepting none, starting with b, not ending in b, containing aa, containing aa or bb.

A Turing Machine (TM) is a mathematical model of a computer that can recognize various types of languages. Some examples of TMs include accepting all strings, accepting none, starting with b, not ending in b, containing aa, and containing aa or


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  1. What is the language accepted by a Turing machine that accepts all strings? a) The empty string b) The null language c) The universal language d) All possible strings Solution: d) All possible strings Which of the following is not a Turing machine that accepts none of the languages? a) A machine with no accepting state b) A machine that rejects all strings c) A machine that never halts d) A machine with an infinite tape Solution: d) A machine with an infinite tape What is the language accepted by a Turing machine that starts with the letter 'b'? a) All strings starting with 'b' b) All strings ending with 'b' c) All strings containing 'b' d) None of the above Solution: a) All strings starting with 'b' What is the language accepted by a Turing machine that does not end with the letter 'b'? a) All strings not ending with 'b' b) All strings ending with 'b' c) All strings containing 'b' d) None of the above Solution: a) All strings not ending with 'b' What is the language accepted by a Turing machine that contains the substring 'aa'? a) All strings containing 'aa' b) All strings not containing 'aa' c) All strings starting with 'aa' d) None of the above Solution: a) All strings containing 'aa' What is the language accepted by a Turing machine that contains either the substring 'aa' or 'bb'? a) All strings containing 'aa' or 'bb' b) All strings not containing 'aa' or 'bb' c) All strings starting with 'aa' or 'bb' d) None of the above Solution: a) All strings containing 'aa' or 'bb' Which of the following is a Turing machine that accepts none of the languages? a) A machine that accepts all strings b) A machine that accepts only the empty string c) A machine that accepts only one specific string d) A machine that never halts Solution: a) A machine that accepts all strings Which of the following is a Turing machine that accepts all strings? a) A machine with no accepting state b) A machine that rejects all strings c) A machine that never halts d) None of the above Solution: d) None of the above Which of the following is a Turing machine that starts with the letter 'a'? a) A machine that starts with any letter b) A machine that starts with the letter 'b' c) A machine that starts with the letter 'a' d) None of the above Solution: d) None of the above Which of the following is a Turing machine that does not contain the substring 'ab'? a) A machine that contains only the substring 'ab' b) A machine that contains any substring except 'ab' c) A machine that contains no substrings d) None of the above Solution: b) A machine that contains any substring except 'ab'


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  1. What is a Turing machine that accepts all strings? Answer: A Turing machine that accepts all strings is one that transitions to an accepting state for any input string. What is a Turing machine that accepts none of the languages? Answer: A Turing machine that accepts none of the languages is one that transitions to a rejecting state for any input string. How can a Turing machine be designed to recognize strings that start with the letter 'b'? Answer: A Turing machine that recognizes strings starting with 'b' can be designed to transition to an accepting state if it reads 'b' as the first character of the input string and to a rejecting state for all other characters. How can a Turing machine be designed to recognize strings that do not end with the letter 'b'? Answer: A Turing machine that recognizes strings not ending with 'b' can be designed to transition to an accepting state for all input strings except those that end with 'b'. How can a Turing machine be designed to recognize strings that contain the substring 'aa'? Answer: A Turing machine that recognizes strings containing 'aa' can be designed to transition to an accepting state if it reads 'aa' as a substring of the input string and to a rejecting state for all other characters. How can a Turing machine be designed to recognize strings that contain either the substring 'aa' or 'bb'? Answer: A Turing machine that recognizes strings containing 'aa' or 'bb' can be designed to transition to an accepting state if it reads either 'aa' or 'bb' as a substring of the input string and to a rejecting state for all other characters. What is the difference between a Turing machine that accepts all strings and one that accepts none of the languages? Answer: The difference between a Turing machine that accepts all strings and one that accepts none of the languages is that the former transitions to an accepting state for any input string, while the latter transitions to a rejecting state for any input string. Can a Turing machine recognize a language that contains an infinite number of strings? Answer: Yes, a Turing machine can recognize a language that contains an infinite number of strings, as long as the machine is able to process the input strings in a finite amount of time. How can a Turing machine be designed to recognize strings that start with the letter 'a'? Answer: A Turing machine that recognizes strings starting with 'a' can be designed to transition to an accepting state if it reads 'a' as the first character of the input string and to a rejecting state for all other characters. How can a Turing machine be designed to recognize strings that do not contain the substring 'ab'? Answer: A Turing machine that recognizes strings not containing 'ab' can be designed to transition to an accepting state for all input strings except those that contain 'ab' as a substring.

A Turing machine (TM) is a mathematical model used to study the properties of computation. It consists of a tape that extends infinitely in both directions, a head that moves back and forth across the tape, and a control unit that determines the machine's behavior. Examples of TMs include those that accept all strings, accept none, start with 'b', don't end with 'b', contain 'aa', and contain either 'aa' or 'bb'. A TM that accepts all strings transitions to an accepting state for any input string. This means that the machine will continue to read the input string until it reaches the end and then transition to an accepting state. A TM that accepts none transitions to a rejecting state for any input string. This means that the machine will continue to read the input string until it reaches the end and then transition to a rejecting state. A TM that starts with 'b' transitions to an accepting state if it reads 'b' as the first character of the input string and transitions to a rejecting state for all other characters. A TM that doesn't end with 'b' transitions to an accepting state for all input strings except those that end with 'b'. For those input strings that end with 'b', the machine transitions to a rejecting state. A TM that contains 'aa' transitions to an accepting state if it reads 'aa' as a substring of the input string and transitions to a rejecting state for all other characters. A TM that contains either 'aa' or 'bb' transitions to an accepting state if it reads either 'aa' or 'bb' as a substring of the input string and transitions to a rejecting state for all other characters. In summary, Turing machines provide a formal framework for studying the fundamental properties of computation, and these examples illustrate the basic concepts of acceptance and rejection of input strings.

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