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.
Give a DFA for the following language over the alphabet Σ = {0, 1}: L={ 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...
Automata Question. Over the alphabet Σ = {0, 1}: 1) Give a DFA, M1, that accepts a Language L1 = {all strings that contain 00} 2) Give a DFA, M2, that accepts a Language L2 = {all strings that end with 01} 3) Give acceptor for L1 intersection L2 4) Give acceptor for L1 - L2
1. Give a DFA for each of the following languages defined over the alphabet Σ (0, i): a) (3 points) L={ w | w contains the substring 101 } b) (3 points) L-wl w ends in 001)
Automata Theory Give a context-free grammar producing the following language over Σ = {0, 1}: {w : every odd position of w is 1 and w = wR} (HINT: All strings in the language will be of odd length).
Give regular expressions generating the languages of 1. {w over the alphabet of {0, 1} | w is any string except 11 and 111} 2. {w over the alphabet of {0, 1} | w contains at least two 0’s and at most one 1} 3. {w over the alphabet of {0, 1} | the length of w is at most 9} 4. {w over the alphabet of {0, 1} | w contains at least three 1 s} 5. {w over...
John Doe claims that the language L, of all strings over the alphabet Σ = { a, b } that contain an even number of occurrences of the letter ‘a’, is not a regular language. He offers the following “pumping lemma proof”. Explain what is wrong with the “proof” given below. “Pumping Lemma Proof” We assume that L is regular. Then, according to the pumping lemma, every long string in L (of length m or more) must be “pumpable”. We...
Give the state diagram for a deterministic finite automaton (DFA) recognizing the following language over Σ = {0,1}: L1 = {w : w contains an even number of 0’s AND w ends in 1}
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.
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 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...