Homework Answers
6.[15 points] Recall the pumping lemma for regular languages: Theorem: For every regular language L, there...
6.[15 points] Recall the pumping lemma for regular languages: Theorem: For every regular language L, there exists a pumping length p such that, if s€Lwith s 2 p, then we can write s xyz with (i) xy'z E L for each i 2 0, (ii) ly > 0, and (iii) kyl Sp. Prove that A ={a3"b"c?" | n 2 0 } is not a regular language. S=
6.[15 points] Recall the pumping lemma for regular languages: Theorem: For every regular...
2. If L is a regular language, prove that the language 11 = { uv/ u...
2. If L is a regular language, prove that the language 11 = { uv/ u E 1 , |v|-2) is also regular. (Hint: Can you build an NFA of L1 using an NFA of a language L? Use N, the NFA of the language L)
2. Prove that {a"6"c" |m,n0}is not a regular language. Answer: 3. Let L = { M...
2. Prove that {a"6"c" |m,n0}is not a regular language. Answer: 3. Let L = { M M is a Turing machine and L(M) is empty), where L(M) is the language accepted by M. Prove L is undecidable by finding a reduction from Aty to it, where Arm {<M.w>M is a Turing machine and M accepts Answer: 4. a) Define the concept of NP-completeness b) If A is NP-complete, and A has a polynomial time algorithm, then a polynomial time algorithm...
Suppose that L is a regular language. Prove that the language p r e f i...
Suppose that L is a regular language. Prove that the language p
r e f i x (L )={w |
x, wx
L } is regular. (For example, if L = {abc, def}, prefix(L) = {?,
a, ab, abc, d, de, def}.)
Finite state machines & Regular Expressions Please select the best option 1. For the following questions...
Finite state machines & Regular Expressions
Please select the best option
1.
For the following questions Let r, s, t be regular expressions
for the same alphabet "á" (left column). Get the property on the
right side that produces equality for each regular expression.
2.
From the diagram of the solution M = (Σ, Q, s,, F) is
respectively:
e would be NONE.
3.
The following graph corresponds to a diagram of:
A. Transition machine and states
b. Transition...
Show that L = {anbm : m ≥ n +3} is deterministic. This is for formal languages and automata... Ca...
Show that L = {anbm : m ≥ n +3} is
deterministic.
This is for formal languages and automata...
Can you please try to explain what you are doing and why (if
necessary, if not ill try my best to figure it out.)
The definitions i'm working based off of are posted as a image
below.
Thanks!
DEFINITION 7.3 A pushdown automaton M-О. Е, Г, 0, qo, z, Fİs said to be deterministic ifit is an automaton as defined in...
Determining whether languages are finite, regular, context free, or recursive 1. (Each part is worth 2 points) Fill in the blanks with one of the following (some choices might not be used): a) finit...
Determining whether languages are finite, regular, context free,
or recursive
1. (Each part is worth 2 points) Fill in the blanks with one of the following (some choices might not be used): a) finite b) regular but not finite d) context-free but not deterministic context-free e) recursive (that is, decidable) but not context-free f) recursively enumerable (that is, partially decidable) but not recursive g) not recursively enumerable Recall that if M is a Turing machine then "M" (also written as...
(1) Write a regular expression for the language. (2) Define a finite state machine (FSM) that...
(1) Write a regular expression for the language. (2) Define a finite state machine (FSM) that recognizes words in the language (input alphabet, states, start state, state transition table, and accept states). Include a state digraph for the FSM. A: For alphabet {p,q,r}, all strings that contain the substring rqr or end with pp.
I need to construct a deterministic finite automata, DFA M, such that language of M, L(M),...
I need to construct a deterministic finite automata, DFA M, such that language of M, L(M), is the set of all strings over the alphabet {a,b} in which every substring of length four has at least one b. Note: every substring with length less than four is in this language. For example, aba is in L(M) because there are no substrings of at least 4 so every substring of at least 4 contains at least one b. abaaab is in...
3. (8) Let L be the language accepted by the following finite state machine: q0 q1...
3. (8) Let L be the language accepted by the following finite state machine: q0 q1 q2 q3 Answer Yes or No: Does each of the following regular expressions correctly describe L? (1) (a uba)bb'a (2) (EU b)a(bb%)* (3) ba u ab*a (4) (a ba)(bb*a)*
6.[15 points] Recall the pumping lemma for regular languages: Theorem: For every regular language L, there exists a pumping length p such that, if s€Lwith s 2 p, then we can write s xyz with (i) xy'z E L for each i 2 0, (ii) ly > 0, and (iii) kyl Sp. Prove that A ={a3"b"c?" | n 2 0 } is not a regular language. S=
6.[15 points] Recall the pumping lemma for regular languages: Theorem: For every regular...
2. If L is a regular language, prove that the language 11 = { uv/ u E 1 , |v|-2) is also regular. (Hint: Can you build an NFA of L1 using an NFA of a language L? Use N, the NFA of the language L)
2. Prove that {a"6"c" |m,n0}is not a regular language. Answer: 3. Let L = { M M is a Turing machine and L(M) is empty), where L(M) is the language accepted by M. Prove L is undecidable by finding a reduction from Aty to it, where Arm {<M.w>M is a Turing machine and M accepts Answer: 4. a) Define the concept of NP-completeness b) If A is NP-complete, and A has a polynomial time algorithm, then a polynomial time algorithm...
Suppose that L is a regular language. Prove that the language p
r e f i x (L )={w |
x, wx
L } is regular. (For example, if L = {abc, def}, prefix(L) = {?,
a, ab, abc, d, de, def}.)
Finite state machines & Regular Expressions
Please select the best option
1.
For the following questions Let r, s, t be regular expressions
for the same alphabet "á" (left column). Get the property on the
right side that produces equality for each regular expression.
2.
From the diagram of the solution M = (Σ, Q, s,, F) is
respectively:
e would be NONE.
3.
The following graph corresponds to a diagram of:
A. Transition machine and states
b. Transition...
Show that L = {anbm : m ≥ n +3} is
deterministic.
This is for formal languages and automata...
Can you please try to explain what you are doing and why (if
necessary, if not ill try my best to figure it out.)
The definitions i'm working based off of are posted as a image
below.
Thanks!
DEFINITION 7.3 A pushdown automaton M-О. Е, Г, 0, qo, z, Fİs said to be deterministic ifit is an automaton as defined in...
Determining whether languages are finite, regular, context free,
or recursive
1. (Each part is worth 2 points) Fill in the blanks with one of the following (some choices might not be used): a) finite b) regular but not finite d) context-free but not deterministic context-free e) recursive (that is, decidable) but not context-free f) recursively enumerable (that is, partially decidable) but not recursive g) not recursively enumerable Recall that if M is a Turing machine then "M" (also written as...
3. (8) Let L be the language accepted by the following finite state machine: q0 q1 q2 q3 Answer Yes or No: Does each of the following regular expressions correctly describe L? (1) (a uba)bb'a (2) (EU b)a(bb%)* (3) ba u ab*a (4) (a ba)(bb*a)*
Most questions answered within 3 hours.
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