Suppose alphabet Σ = {a} and consider the following regular language A, A = {w |...
Suppose alphabet Σ = {a} and consider the following regular language A,
A = {w | |w| ≥ 4},
i.e., strings whose length is at least 4 (equivalently, unary numbers x ≥ 4).
a) Construct a DFA that recognizes A with as few states as possible (draw a state diagram).
b) Construct a PDA that recognizes A with as few states as possible (draw a state diagram). Note that the stack alphabet may include additional symbols.
Homework Answers
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Suppose alphabet Σ = {a} and consider the following regular
language A,
A = {w |...
1(a)Draw the state diagram for a DFA for accepting the following language over alphabet {0,1}: {w...
1(a)Draw the state diagram for a DFA for accepting the following language over alphabet {0,1}: {w | the length of w is at least 2 and has the same symbol in its 2nd and last positions} (b)Draw the state diagram for an NFA for accepting the following language over alphabet {0,1} (Use as few states as possible): {w | w is of the form 1*(01 ∪ 10*)*} (c)If A is a language with alphabet Σ, the complement of A is...
1. Construct a Finite Automata over Σ={0,1} that recognizes the language {w | w ∈ {0,1}*...
1. Construct a Finite Automata over Σ={0,1} that recognizes the language {w | w ∈ {0,1}* contains a number of 0s divisible by four and exactly three 1s} 2. Construct a Finite Automata that recognizes telephone numbers from strings in the alphabet Σ={1,2,3,4,5,6,7,8,9, ,-,(,),*,#,}. Allow the 1 and area code prefixing a phone number to be optional. Allow for the segments of a number to be separated by spaces (denote with a _ character), no separation, or – symbols.
Construct a regular expression that recognizes the following language of strings over the alphabet {0 1}:...
Construct a regular expression that recognizes the following language of strings over the alphabet {0 1}: The language consisting of the set of all bit strings that contain two or three symbols.
Give a DFA for the following language over the alphabet Σ = {0, 1}: L={ w...
Give a DFA for the following language over the alphabet Σ = {0, 1}: L={ w | w starts with 0 and has odd length, or starts with 1 and has even length }. E.g., strings 0010100, 111010 are in L, while 0100 and 11110 are not in L.
Part B - Automata Construction Draw a DFA which accepts the following language over the alphabet...
Part B - Automata Construction Draw a DFA which accepts the following language over the alphabet of {0,1}: the set of all strings such that the number of 0s is divisible by 2 and the number of 1s is divisible by 5. Your DFA must handle all intput strings in {0,1}*. Here is a methodical way to do this: Figure out all the final states and label each with the shortest string it accepts, work backwards from these states to...
4(10 points] Let A be the language over the alphabet -(a, b) defined by regular expression...
4(10 points] Let A be the language over the alphabet -(a, b) defined by regular expression (ab Ub)aUb. Give an NFA that recognizes A. Draw an NFA for A here 5.10 points] Convert the following NFA to equivalent DFA a, b
4(10 points] Let A be the language over the alphabet -(a, b) defined by regular expression (ab Ub)aUb. Give an NFA that recognizes A. Draw an NFA for A here 5.10 points] Convert the following NFA to equivalent DFA...
Construct an DFA automaton that recognizes the following language of strings over the alphabet {a,b}: the...
Construct an DFA automaton that recognizes the following language of strings over the alphabet {a,b}: the set of all strings over alphabet {a,b} that contain aa, but do not contain aba.
Draw a DFA which accepts the following language over the alphabet of {0,1}: the set of...
Draw a DFA which accepts the following language over the alphabet of {0,1}: the set of all strings such that there are no consecutive 0s, and the number of 1s is divisible by 5. Your DFA must handle all intput strings in {0,1}*. Here is a way to approach the problem: First focus only building the DFA which accepts the language: As you build your DFA, label your states with an explanation of what the state actually represents in terms...
Find a regular expression for the following language over the alphabet Σ = {a,b}. L = {strings th...
Find a regular expression for the following language over the alphabet Σ = {a,b}. L = {strings that begin and end with a and contain bb}.
Construct a regular expression that recognizes the following language of strings over the alphabet {0 1}:...
Construct a regular expression that recognizes the following language of strings over the alphabet {0 1}: The language consisting of the set of all bit strings that start with 00 or end with 101 (or both). Syntax The union is expressed as R|R, star as R*, plus as R+, concatenation as RR. Epsilon is not supported but you can write R? for the regex (R|epsilon).
4(10 points] Let A be the language over the alphabet -(a, b) defined by regular expression (ab Ub)aUb. Give an NFA that recognizes A. Draw an NFA for A here 5.10 points] Convert the following NFA to equivalent DFA a, b
4(10 points] Let A be the language over the alphabet -(a, b) defined by regular expression (ab Ub)aUb. Give an NFA that recognizes A. Draw an NFA for A here 5.10 points] Convert the following NFA to equivalent DFA...
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