Question 1

Suppose a phrase-structure grammar has productions $S \rightarrow S 0 , S \rightarrow A 1 , A \rightarrow 0$
Find a derivation of  010 .

Accepted Answer

The answer of Suppose a phrase-structure grammar has productions \(S...

Question 2

Suppose a phrase-structure grammar has productions $S \rightarrow S \rightarrow 1 , S \rightarrow 0 A , S \rightarrow A 1 , A \rightarrow 0$ Finf a derivation  of  01 .

Accepted Answer

The answer of Suppose a phrase-structure grammar has productions \(S...

Question 3

Suppose a phrase-structure grammar has productions $S \rightarrow 1 S 0 . S \rightarrow 0 A , A \rightarrow 0 .$ Find a derivation of 1000 .

Accepted Answer

The answer of Suppose a phrase-structure grammar has productions \(S...

Question 4

In questions determine the output for
-$$000 \text {. }$$

Accepted Answer

The answer of In questions determine the output for
-\[000 \text...

Question 5

For the following Turing machines 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): $\begin{array}{l|l|l|l|l|l|l|l|l|l|l|l}
\hline \cdots & \mathrm{B} & \mathrm{B} & 0 & 0 & 0 & 1 & \mathrm{~B} & 0 & \mathrm{~B} & \mathrm{~B} & \cdots \
\hline
\end{array}$
$$\left( s _ { 0 } , 0 , s _ { 0 } , 0 , R \right) , \left( s _ { 0 } , 1 , s _ { 1 } , 0 , R \right) , \left( s _ { 1 } , 0 , s _ { 1 } , 1 , R \right) , \left( s _ { 1 } , 1 , s _ { 2 } , 1 , L \right) , \left( s _ { 1 } , B , s _ { 1 } , 1 , L \right) .$$

Accepted Answer

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

Question 6

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): $$\begin{array} { l } 
\begin{array} { l | l | l | l | l | l | l | l | l | l | l | l } 
\hline \cdots & \mathrm { B } & \mathrm { B } & 0 & 0 & 0 & 1 & \mathrm {~B} & 0 & \mathrm {~B} & \mathrm {~B} & \cdots \
\hline
\end{array} \
\left( s _ { 0 } , 0 , s _ { 1 } , 1 , R \right) , \left( s _ { 0 } , 1 , s _ { 1 } , 1 , L \right) , \left( s _ { 1 } , 0 , s _ { 0 } , 1 , L \right) \
\end{array}$$

Accepted Answer

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

Question 7

Construct a ﬁnite-state machine that models a vending machine accepting only quarters that gives a container
of orange juice when 50 cents has been deposited, followed by a button being pushed. (The possible inputs
are quarters and the button, and the possible outputs are nothing, orange juice, and a quarter. The machine
returns any extra quarters.)

Accepted Answer

The answer of Construct a ﬁnite-state machine that models a...

Question 8

Suppose a phrase-structure grammar has productions $S \rightarrow S 11 , S \rightarrow 0 A , S \rightarrow A 1 , A \rightarrow 0$ Find a derivation of 0011 .

Accepted Answer

The answer of Suppose a phrase-structure grammar has productions \(S...

Question 9

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

Accepted Answer

All bit st

Question 10

In questions determine the output for
-$$11000 .$$

Accepted Answer

The answer of In questions determine the output for
-$$11000 .$$...

Question 11

$$S \rightarrow 1 A , A \rightarrow 1 , S \rightarrow \lambda$$

Accepted Answer

The answer of \[S \rightarrow 1 A , A \rightarrow...

Question 12

Determine if 1101 belongs to the regular set $( 0 \cup 1 ) ^ { * } \mathbf { 1 }$

Accepted Answer

The answer of Determine if 1101 belongs to the regular...

Question 13

Determine if 1101 belongs to the regular set  1*0*1 .

Accepted Answer

The answer of Determine if 1101 belongs to the regular...

Question 14

Which strings are recognized by the following finite-state automaton?

Accepted Answer

Strings co

Question 15

Suppose a phrase-structure grammar has productions $S \rightarrow S 0 , S \rightarrow A 1 , A \rightarrow 0$ Find a derivation of 0100 .

Accepted Answer

The answer of Suppose a phrase-structure grammar has productions \(S...

Question 16

$$\text { Find the set recognized by this deterministic finite-state machine. }$$

Accepted Answer

The set re

Question 17

Suppose that  A={1,11,01}  and  B={0,10} . Find  BA .

Accepted Answer

BA={01, 0

Question 18

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): $\begin{array}{l|l|l|l|l|l|l|l|l|l|l|l}
\hline \cdots & \mathrm{B} & \mathrm{B} & 0 & 0 & 0 & 1 & \mathrm{~B} & 0 & \mathrm{~B} & \mathrm{~B} & \cdots \
\hline
\end{array}$
$$\left( s _ { 0 } , 0 , s _ { 2 } , 0 , R \right) , \left( s _ { 0 } , B , s _ { 0 } , 1 , R \right) , \left( s _ { 1 } , 0 , s _ { 2 } , 1 , R \right) , \left( s _ { 2 } , 0 , s _ { 1 } , 1 , L \right) , \left( s _ { 2 } , 1 , s _ { 0 } , 1 , R \right) .$$

Accepted Answer

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

Question 19

In questions determine the output for
-$$1111 .$$ each input string, using this state table.

Accepted Answer

The answer of In questions determine the output for
-$$1111 .$$...

Question 20

Suppose a phrase-structure grammar has productions $S \rightarrow 1 S 0 , S \rightarrow 0 A , A \rightarrow 0 .$
Find a derivation of 110000 .

Accepted Answer

The answer of Suppose a phrase-structure grammar has productions \(S...

Suppose a phrase-structure grammar has productions $S \rightarrow S 0 , S \rightarrow A 1 , A \rightarrow 0$ Find a derivation of 010 .

Suppose a phrase-structure grammar has productions $S \rightarrow S \rightarrow 1 , S \rightarrow 0 A , S \rightarrow A 1 , A \rightarrow 0$ Finf a derivation of 01 .

Suppose a phrase-structure grammar has productions $S \rightarrow 1 S 0 . S \rightarrow 0 A , A \rightarrow 0 .$ Find a derivation of 1000 .

In questions determine the output for - $000 \text {. }$

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,,1,L , ,0,,1,L

Suppose a phrase-structure grammar has productions $S \rightarrow S 11 , S \rightarrow 0 A , S \rightarrow A 1 , A \rightarrow 0$ Find a derivation of 0011 .

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

In questions determine the output for - $11000 .$

$S \rightarrow 1 A , A \rightarrow 1 , S \rightarrow \lambda$

Determine if 1101 belongs to the regular set $( 0 \cup 1 ) ^ { * } \mathbf { 1 }$

Determine if 1101 belongs to the regular set 101 .

Which strings are recognized by the following finite-state automaton?

Suppose a phrase-structure grammar has productions $S \rightarrow S 0 , S \rightarrow A 1 , A \rightarrow 0$ Find a derivation of 0100 .

$\text { Find the set recognized by this deterministic finite-state machine. }$ $\text { Find the set recognized by this deterministic finite-state machine. }$

Suppose that A={1,11,01} and B={0,10} . Find BA .

In questions determine the output for - $1111 .$ each input string, using this state table.

Suppose a phrase-structure grammar has productions $S \rightarrow 1 S 0 , S \rightarrow 0 A , A \rightarrow 0 .$ Find a derivation of 110000 .

The Foundations: Logic and Proofs

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Exam 13: Modeling Computation

Suppose a phrase-structure grammar has productions S→S0,S→A1,A→0S \rightarrow S 0 , S \rightarrow A 1 , A \rightarrow 0S→S0,S→A1,A→0 Find a derivation of 010 .

Suppose a phrase-structure grammar has productions S→S→1,S→0A,S→A1,A→0S \rightarrow S \rightarrow 1 , S \rightarrow 0 A , S \rightarrow A 1 , A \rightarrow 0S→S→1,S→0A,S→A1,A→0 Finf a derivation of 01 .

Suppose a phrase-structure grammar has productions S→1S0.S→0A,A→0.S \rightarrow 1 S 0 . S \rightarrow 0 A , A \rightarrow 0 .S→1S0.S→0A,A→0. Find a derivation of 1000 .

In questions determine the output for - 000. 000 \text {. }000.

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,,1,L , ,0,,1,L

Suppose a phrase-structure grammar has productions S→S11,S→0A,S→A1,A→0S \rightarrow S 11 , S \rightarrow 0 A , S \rightarrow A 1 , A \rightarrow 0S→S11,S→0A,S→A1,A→0 Find a derivation of 0011 .

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

In questions determine the output for - 11000.11000 .11000.

S→1A,A→1,S→λS \rightarrow 1 A , A \rightarrow 1 , S \rightarrow \lambdaS→1A,A→1,S→λ

Determine if 1101 belongs to the regular set (0∪1)∗1( 0 \cup 1 ) ^ { * } \mathbf { 1 }(0∪1)∗1

Determine if 1101 belongs to the regular set 1*0*1 .

Which strings are recognized by the following finite-state automaton?

Suppose a phrase-structure grammar has productions S→S0,S→A1,A→0S \rightarrow S 0 , S \rightarrow A 1 , A \rightarrow 0S→S0,S→A1,A→0 Find a derivation of 0100 .

Find the set recognized by this deterministic finite-state machine. \text { Find the set recognized by this deterministic finite-state machine. } Find the set recognized by this deterministic finite-state machine.

Suppose that A={1,11,01} and B={0,10} . Find BA .

In questions determine the output for - 1111.1111 .1111. each input string, using this state table.

Suppose a phrase-structure grammar has productions S→1S0,S→0A,A→0.S \rightarrow 1 S 0 , S \rightarrow 0 A , A \rightarrow 0 .S→1S0,S→0A,A→0. Find a derivation of 110000 .

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

Suppose a phrase-structure grammar has productions $S \rightarrow S 0 , S \rightarrow A 1 , A \rightarrow 0$ Find a derivation of 010 .

Suppose a phrase-structure grammar has productions $S \rightarrow S \rightarrow 1 , S \rightarrow 0 A , S \rightarrow A 1 , A \rightarrow 0$ Finf a derivation of 01 .

Suppose a phrase-structure grammar has productions $S \rightarrow 1 S 0 . S \rightarrow 0 A , A \rightarrow 0 .$ Find a derivation of 1000 .

In questions determine the output for - $000 \text {. }$

Suppose a phrase-structure grammar has productions $S \rightarrow S 11 , S \rightarrow 0 A , S \rightarrow A 1 , A \rightarrow 0$ Find a derivation of 0011 .

In questions determine the output for - $11000 .$

$S \rightarrow 1 A , A \rightarrow 1 , S \rightarrow \lambda$

Determine if 1101 belongs to the regular set $( 0 \cup 1 ) ^ { * } \mathbf { 1 }$

Determine if 1101 belongs to the regular set 101 .

Suppose a phrase-structure grammar has productions $S \rightarrow S 0 , S \rightarrow A 1 , A \rightarrow 0$ Find a derivation of 0100 .

$\text { Find the set recognized by this deterministic finite-state machine. }$ $\text { Find the set recognized by this deterministic finite-state machine. }$

In questions determine the output for - $1111 .$ each input string, using this state table.

Suppose a phrase-structure grammar has productions $S \rightarrow 1 S 0 , S \rightarrow 0 A , A \rightarrow 0 .$ Find a derivation of 110000 .