1. Which of the following is a parse tree for the grammar S → abS, S → ab? SID S-D 13 13 а a کی о ་ ་ A 173 (a) a 5 113 a 173 S 15 b a (b) a (d) a 5 15 - 03 a 0-5 b 013 a S- 4-5 173 (c) 55 a (c) (f) Effective Discuss d) (e) b) 6 c) 3 d) 7 a) (d) 2. The length of the string cbccaba is: b) (f) (e) a) 8 3. Here is the transition table of a DFA: 01 →AED *BAC CGB DEA *E H FC GFE HBH c) G and H d) A and C Find the minimum-state DFA equivalent to the above. Then, identify in the list below the pair of equivalent states (states that get merged in the minimization process). ○ a) A and B b) B and E 4. Which automata define the same language? (a) (c) + 0 1 1 00 01 (b) 10 11 00 11 10 (d) 01 Note: (b) and (d) use transitions on strings. You may assume that there are nonaccepting intermediate states, not shown, that are in the middle of these transitions, or just accept the extension to the conventional finite automaton that allows strings on transitions and, like the conventional FA accepts strings that are the concatenation of labels along any path from the start state to an accepting state. a) a and d ○ b) c and d c) b and d d) b and c 5. h is a homomorphism from the alphabet {a,b,c} to {0,1}. If h(a) = 01, h(b) = 0, and h(c) = 10, which of the following strings is in h¨¹ (010010)? a) baba b) bcab c) cbbc d) baab 6. The Turing machine M has: • States q and p; q is the start state. • · Tape symbols 0, 1, and B; 0 and 1 are input symbols, and B is the blank. • The following next-move function: State Tape Move Symbol q 0 (q,0,R) q 1 (p,0,R) q B (q,B,R) p 0 (q,0,L) P 1 none (halt) P B (q,0,L) Your problem is to describe the property of an input string that makes M halt. Identify a string that makes M halt from the list below. a) 0110 b) 0010 1010 7. The homomorphism h is defined by h(a) = 01 and h(b) = 10. What is h(bbaa)? a) bbaa b) 10101010 8. Here is a context-free grammar G: S AB A → 0A1 | 2 B 1B | 3A Which of the following strings is in L(G)? a) 0021131100211 b) 00213021 c) 021300211 d) 0021113002111 c) 10100101 d) 001010 ○ d) 101001
1. Which of the following is a parse tree for the grammar S → abS, S → ab? SID S-D 13 13 а a کی о ་ ་ A 173 (a) a 5 113 a 173 S 15 b a (b) a (d) a 5 15 - 03 a 0-5 b 013 a S- 4-5 173 (c) 55 a (c) (f) Effective Discuss d) (e) b) 6 c) 3 d) 7 a) (d) 2. The length of the string cbccaba is: b) (f) (e) a) 8 3. Here is the transition table of a DFA: 01 →AED *BAC CGB DEA *E H FC GFE HBH c) G and H d) A and C Find the minimum-state DFA equivalent to the above. Then, identify in the list below the pair of equivalent states (states that get merged in the minimization process). ○ a) A and B b) B and E 4. Which automata define the same language? (a) (c) + 0 1 1 00 01 (b) 10 11 00 11 10 (d) 01 Note: (b) and (d) use transitions on strings. You may assume that there are nonaccepting intermediate states, not shown, that are in the middle of these transitions, or just accept the extension to the conventional finite automaton that allows strings on transitions and, like the conventional FA accepts strings that are the concatenation of labels along any path from the start state to an accepting state. a) a and d ○ b) c and d c) b and d d) b and c 5. h is a homomorphism from the alphabet {a,b,c} to {0,1}. If h(a) = 01, h(b) = 0, and h(c) = 10, which of the following strings is in h¨¹ (010010)? a) baba b) bcab c) cbbc d) baab 6. The Turing machine M has: • States q and p; q is the start state. • · Tape symbols 0, 1, and B; 0 and 1 are input symbols, and B is the blank. • The following next-move function: State Tape Move Symbol q 0 (q,0,R) q 1 (p,0,R) q B (q,B,R) p 0 (q,0,L) P 1 none (halt) P B (q,0,L) Your problem is to describe the property of an input string that makes M halt. Identify a string that makes M halt from the list below. a) 0110 b) 0010 1010 7. The homomorphism h is defined by h(a) = 01 and h(b) = 10. What is h(bbaa)? a) bbaa b) 10101010 8. Here is a context-free grammar G: S AB A → 0A1 | 2 B 1B | 3A Which of the following strings is in L(G)? a) 0021131100211 b) 00213021 c) 021300211 d) 0021113002111 c) 10100101 d) 001010 ○ d) 101001
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:1. Which of the following is a parse tree for the grammar S → abS, S → ab?
SID
S-D
13
13
а
a
کی
о
་ ་
A
173
(a)
a
5
113
a
173
S
15
b
a
(b)
a
(d)
a
5
15
- 03
a
0-5
b
013
a
S-
4-5
173
(c)
55
a
(c)
(f)
Effective Discuss
d) (e)
b) 6
c) 3
d) 7
a) (d)
2. The length of the string cbccaba is:
b) (f)
(e)
a) 8
3. Here is the transition table of a DFA:
01
→AED
*BAC
CGB
DEA
*E H
FC
GFE
HBH
c) G and H
d) A and C
Find the minimum-state DFA equivalent to the above. Then, identify in the list below the pair of
equivalent states (states that get merged in the minimization process).
○ a) A and B
b) B and E
Transcribed Image Text:4. Which automata define the same language?
(a)
(c)
+
0
1
1
00
01
(b)
10
11
00
11
10
(d)
01
Note: (b) and (d) use transitions on strings. You may assume that there are nonaccepting intermediate
states, not shown, that are in the middle of these transitions, or just accept the extension to the
conventional finite automaton that allows strings on transitions and, like the conventional FA accepts
strings that are the concatenation of labels along any path from the start state to an accepting state.
a) a and d
○ b) c and d
c) b and d
d) b and c
5. h is a homomorphism from the alphabet {a,b,c} to {0,1}. If h(a) = 01, h(b) = 0, and h(c) = 10, which of
the following strings is in h¨¹ (010010)?
a) baba
b) bcab
c) cbbc
d) baab
6. The Turing machine M has:
• States q and p; q is the start state.
•
· Tape symbols 0, 1, and B; 0 and 1 are input symbols, and B is the blank.
• The following next-move function:
State Tape Move
Symbol
q
0
(q,0,R)
q
1
(p,0,R)
q
B
(q,B,R)
p
0
(q,0,L)
P
1
none (halt)
P
B
(q,0,L)
Your problem is to describe the property of an input string that makes M halt. Identify a string that makes
M halt from the list below.
a) 0110
b) 0010
1010
7. The homomorphism h is defined by h(a) = 01 and h(b) = 10. What is h(bbaa)?
a) bbaa
b) 10101010
8. Here is a context-free grammar G:
S
AB
A → 0A1 | 2
B 1B | 3A
Which of the following strings is in L(G)?
a) 0021131100211
b) 00213021
c) 021300211
d) 0021113002111
c) 10100101
d) 001010
○ d) 101001
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
