For the following Turing machine T, ﬁnd the ﬁnal tape when T is run on the following tape, beginning in the initial position (the ﬁrst nonzero entry from the left): \[\begin{array} { l } \begin{array} { l | l | l | l | l | l | l | l | l | l | l | l } \hline \cdots & \mathrm { B } & \mathrm { B } & 0 & 0 & 0 & 1 & \mathrm {~B} & 0 & \mathrm {~B} & \mathrm {~B} & \cdots \\ \hline \end{array} \\ \left( s _ { 0 } , 0 , s _ { 0 } , 1 , R \right) , \left( s _ { 0 } , 1 , s _ { 1 } , 0 , R \right) , \left( s _ { 1 } , 1 , s _ { 2 } , 1 , R \right) , \left( s _ { 1 } , B , s _ { 0 } , 0 , R \right) \\ \end{array}\]

The answer of For the following Turing machine T, ﬁnd...

Exam 13: Modeling Computation

Let G be the phrase-structure grammar with vocabulary V={A, B, 0,1, S} , terminal elements T={0,1} , start symbol S , productions from S ? (1) 000 , (2) 11 , (3) 010 , (4) 0000 , (5) 0001 (6) 110 , (7) 0010 .

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Question 41

Determine if 1101 belongs to the regular set $11 ( 00 ) ^ { * } ( 10 ) ^ { * }$ .

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Question 42

Suppose V={S, A, a, b}, T={a, b} , and S is the start symbol. Find a set of productions that includes $Suppose V={S, A, a, b}, T={a, b} , and S is the start symbol. Find a set of productions that includes and A \rightarrow a and generates the language {a, aa} .$ and $A \rightarrow a$ and generates the language {a, aa} .

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Question 43

$S \rightarrow A 10 , A B \rightarrow 0$

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Question 44

Find a deterministic ﬁnite-state automaton equivalent to the following nondeterministic ﬁnite-state machine.

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Question 45

For the following Turing machine T, ﬁnd the ﬁnal tape when T is run on the following tape, beginning in the initial position (the ﬁrst nonzero entry from the left): \@cdots 0 0 0 1 0 \@cdots ,0,,1,R , ,1,,0,R , ,1,,1,R , ,B,,0,R

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Question 46

Consider the Turing machine $T : \left( s _ { 0 } , 0 , s _ { 1 } , 1 , R \right) , \left( s _ { 0 } , 1 , s _ { 1 } , 1 , R \right) , \left( s _ { 1 } , 0 , s _ { 0 } , 1 , L \right) , \left( s _ { 1 } , 1 , s _ { 0 } , 0 , R \right) , \left( s _ { 0 } , B , s _ { 1 } , 1 , R \right)$ For the following tape, determine the final tape when T halts, assuming that T begins in state s₀ at the leftmost nonblank symbol. \@cdots 1 1 0 \@cdots

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Question 47

Let A={0,11} . Find A²

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Question 48

What language is generated by the phrase-structure grammar if the productions are S → S11, S → λ, where S is the start symbol?

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Question 49

Find all strings recognized by this deterministic ﬁnite-state automaton.

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Question 50

$S \rightarrow 0 B , B \rightarrow 1 A , B \rightarrow 0 , A \rightarrow 0 B$

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Question 51

Suppose V={S, A, a, b}, T={a, b} , and S is the start symbol. Find a set of productions that includes $S \rightarrow A a \text { and } A \rightarrow a$ and generates the language {a, b, ba, baa} .

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Question 52

What is the output produced by this ﬁnite-state machine when the input string is 11101?

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Question 53

Determine if 1101 belongs to the regular set $( 111 ) ^ { * } ( 01 ) ^ { * }$ .

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Question 54

In questions determine the output for - $10111 .$

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Question 55

Let G be the phrase-structure grammar with vocabulary V={A, B, a, b, S} , terminal element set T={a, b} start symbol S , and production set $P = \{ S \rightarrow A B a , S \rightarrow B a , A \rightarrow a B , A B \rightarrow b , B \rightarrow a b \}$ derivable from A ? (1) babaa, (2) aab , (3) bba .

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Question 56

Find a production of the form $“ A \rightarrow \underline{\quad\quad}"$ such that $S \rightarrow 0 A , A \rightarrow \underline{\quad\quad}$ produces {00} .

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Question 57

Consider the Turing machine $T : \left( s _ { 0 } , 0 , s _ { 1 } , 1 , R \right) , \left( s _ { 0 } , 1 , s _ { 1 } , 1 , R \right) , \left( s _ { 1 } , 0 , s _ { 0 } , 1 , L \right) , \left( s _ { 1 } , 1 , s _ { 0 } , 0 , R \right) , \left( s _ { 0 } , B , s _ { 1 } , 1 , R \right)$ For the following tape, determine the final tape when $T$ halts, assuming that $T$ begins in state $s _ { 0 }$ at the leftmost nonblank symbol. \@cdots 0 0 0 \@cdots

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Question 58

Let G be the phrase-structure grammar with vocabulary V={A, B, a, b, S} , terminal element set T={a, b} , start symbol S , and production set $P = \{ S \rightarrow A B a , S \rightarrow B a , A \rightarrow a B , A B \rightarrow b , B \rightarrow a b \}$ derivable from ABa? (1) ba , (2) abb , (3) aba , (4) b , (5) aababa.

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Question 59

$S \rightarrow B , A \rightarrow B , B \rightarrow A$

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Question 60

Let G be the phrase-structure grammar with vocabulary V={A, B, 0,1, S} , terminal elements T={0,1} , start symbol S , productions from S ? (1) 000 , (2) 11 , (3) 010 , (4) 0000 , (5) 0001 (6) 110 , (7) 0010 .

Determine if 1101 belongs to the regular set $11 ( 00 ) ^ { * } ( 10 ) ^ { * }$ .

$S \rightarrow A 10 , A B \rightarrow 0$

Find a deterministic ﬁnite-state automaton equivalent to the following nondeterministic ﬁnite-state machine.

For the following Turing machine T, ﬁnd the ﬁnal tape when T is run on the following tape, beginning in the initial position (the ﬁrst nonzero entry from the left): \@cdots 0 0 0 1 0 \@cdots ,0,,1,R , ,1,,0,R , ,1,,1,R , ,B,,0,R

Let A={0,11} . Find A²

What language is generated by the phrase-structure grammar if the productions are S → S11, S → λ, where S is the start symbol?

Find all strings recognized by this deterministic ﬁnite-state automaton.

$S \rightarrow 0 B , B \rightarrow 1 A , B \rightarrow 0 , A \rightarrow 0 B$

Suppose V={S, A, a, b}, T={a, b} , and S is the start symbol. Find a set of productions that includes $S \rightarrow A a \text { and } A \rightarrow a$ and generates the language {a, b, ba, baa} .

What is the output produced by this ﬁnite-state machine when the input string is 11101?

Determine if 1101 belongs to the regular set $( 111 ) ^ { * } ( 01 ) ^ { * }$ .

In questions determine the output for - $10111 .$

Find a production of the form $“ A \rightarrow \underline{\quad\quad}"$ such that $S \rightarrow 0 A , A \rightarrow \underline{\quad\quad}$ produces {00} .

$S \rightarrow B , A \rightarrow B , B \rightarrow A$

The Foundations: Logic and Proofs

Basic Structures: Sets, Functions, Sequences, Sums, Matrices

Algorithms

Number Theory and Cryptography

Induction and Recursion

Counting

Discrete Probability

Advanced Counting Techniques

Relations

Graphs

Trees

Boolean Algebra

Filters

Exam 13: Modeling Computation

Let G be the phrase-structure grammar with vocabulary V={A, B, 0,1, S} , terminal elements T={0,1} , start symbol S , productions from S ? (1) 000 , (2) 11 , (3) 010 , (4) 0000 , (5) 0001 (6) 110 , (7) 0010 .

Determine if 1101 belongs to the regular set 11(00)∗(10)∗11 ( 00 ) ^ { * } ( 10 ) ^ { * }11(00)∗(10)∗ .

Suppose V={S, A, a, b}, T={a, b} , and S is the start symbol. Find a set of productions that includes and A→aA \rightarrow aA→a and generates the language {a, aa} .

S→A10,AB→0S \rightarrow A 10 , A B \rightarrow 0S→A10,AB→0

Find a deterministic ﬁnite-state automaton equivalent to the following nondeterministic ﬁnite-state machine.

For the following Turing machine T, ﬁnd the ﬁnal tape when T is run on the following tape, beginning in the initial position (the ﬁrst nonzero entry from the left): \@cdots 0 0 0 1 0 \@cdots ,0,,1,R , ,1,,0,R , ,1,,1,R , ,B,,0,R

Let A={0,11} . Find A2

What language is generated by the phrase-structure grammar if the productions are S → S11, S → λ, where S is the start symbol?

Find all strings recognized by this deterministic ﬁnite-state automaton.

S→0B,B→1A,B→0,A→0BS \rightarrow 0 B , B \rightarrow 1 A , B \rightarrow 0 , A \rightarrow 0 BS→0B,B→1A,B→0,A→0B

Suppose V={S, A, a, b}, T={a, b} , and S is the start symbol. Find a set of productions that includes S→Aa and A→aS \rightarrow A a \text { and } A \rightarrow aS→Aa and A→a and generates the language {a, b, ba, baa} .

What is the output produced by this ﬁnite-state machine when the input string is 11101?

Determine if 1101 belongs to the regular set (111)∗(01)∗( 111 ) ^ { * } ( 01 ) ^ { * }(111)∗(01)∗ .

In questions determine the output for - 10111.10111 .10111.

Find a production of the form “A→‾"“ A \rightarrow \underline{\quad\quad}"“A→​" such that S→0A,A→‾S \rightarrow 0 A , A \rightarrow \underline{\quad\quad}S→0A,A→​ produces {00} .

S→B,A→B,B→AS \rightarrow B , A \rightarrow B , B \rightarrow AS→B,A→B,B→A

The Foundations: Logic and Proofs

Basic Structures: Sets, Functions, Sequences, Sums, Matrices

Algorithms

Number Theory and Cryptography

Induction and Recursion

Counting

Discrete Probability

Advanced Counting Techniques

Relations

Graphs

Trees

Boolean Algebra

Filters

Determine if 1101 belongs to the regular set $11 ( 00 ) ^ { * } ( 10 ) ^ { * }$ .

$S \rightarrow A 10 , A B \rightarrow 0$

Let A={0,11} . Find A²

$S \rightarrow 0 B , B \rightarrow 1 A , B \rightarrow 0 , A \rightarrow 0 B$

Suppose V={S, A, a, b}, T={a, b} , and S is the start symbol. Find a set of productions that includes $S \rightarrow A a \text { and } A \rightarrow a$ and generates the language {a, b, ba, baa} .

Determine if 1101 belongs to the regular set $( 111 ) ^ { * } ( 01 ) ^ { * }$ .

In questions determine the output for - $10111 .$

Find a production of the form $“ A \rightarrow \underline{\quad\quad}"$ such that $S \rightarrow 0 A , A \rightarrow \underline{\quad\quad}$ produces {00} .

$S \rightarrow B , A \rightarrow B , B \rightarrow A$