Unless otherwise noted, the alphabet for all questions below is assumed to be Σ (ab). Also...
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...
1. (a) Give state diagrams of DFA’s recognizing the following languages. That alphabet is Σ = {a,b} L1 = {w | w any string that does not contain the substring aab} L2 = {w | w ∈ A where A = Σ*− {a, aa, b}} 2. (a) Give state diagrams of DFA’s recognizing the following languages. The alphabet is {0, 1}. L3 = {w | w begins with 0 ends with 1} (b) Write the formal definition of the DFA...
Construct DFA's that recognize the following languages over the alphabet {a,b}: 1. {w|w is any string except abba or aba}. Prove that your DFA recognizes exactly the specified language. 2. {w|w contains a substring either ababb or bbb}. Write the formal description for this DFA too.
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...
Answer all questions. Unless otherwise stated, all the DFAs and NFAs in this homework use 2- 10,1j as the alphabet. 1. (50 point) For i-1,2 and 3, design NFAs Ni, such that L(N) - B5, where: (a) Bi-{w|w has an even number of O's, or, contains exactly two 1's) (b) ) B2- w every odd position of w is 1 (c) B3 - [w| all strings except the empty string and the string 11) (d) B4- [0j with two states....
Question 9 10 pts Select all the statements below which are true: Every dfa is also an nfa. A maximum of 1 final state is allowed for a dfa. Alanguage that is accepted by a dfa is a regular language. Each dfa must have a trap state 0 Let M be an nfa, and let w be an input string. If Mends in a non-final state after reading w, then wis rejected. Let = {a,b,c,d}and M be an nfa with...
1) 2) Give formal descriptions (5-tuples) for the DFAs shown in figure below: 3) Give the state diagrams of DFAs recognizing the following languages over ? = {0, 1}: a) LÆ b) L? c) {e, 1001} d) {e, 101, 1001} e) {w : w has prefix 10} f) {w : w does not contain the substring 011} 4) Give the state diagrams of DFAs recognizing the following languages over ? = {0, 1}: a) {w: |w| ? 5} b) {w...
Question 1. Let Σ = {a, b}, and consider the language L = {w ∈ Σ ∗ : w contains at least one b and an even number of a’s}. Draw a graph representing a DFA (not NFA) that accepts this language. Question 2. Let L be the language given below. L = {a n b 2n : n ≥ 0} = {λ, abb, aabbbb, aaabbbbbb, . . .} Find production rules for a grammar that generates L.
Please Answer Question#02 Solution of Question 1 is attached. Solution of Questions #01 Please do Questions #01 As soon as possible. = {a, b} will be used for all of the following exercises. The alphabet 1. Give regular expressions which exactly define the following languages. [7 marks] (a) L1 which has exactly one b but any number of as. (b) L2 which has an even number of as and an even number of bs. [7 marks] (c) L3 which contains...
Question 1: Every language is regular T/F Question 2: There exists a DFA that has only one final state T/F Question 3: Let M be a DFA, and define flip(M) as the DFA which is identical to M except you flip that final state. Then for every M, the language L(M)^c (complement) = L( flip (M)). T/F Question 4: Let G be a right linear grammar, and reverse(G)=reverse of G, i.e. if G has a rule A -> w B...