Languages to NFA / ε-NFA
A) Make an ε-NFA (An Epsilon NFA) for the language L3 = L1L2. Where:
L1 = all strings over Σ= {0,1} that end in…001 and L2 = all strings over Σ= {0,1} that contain 010 anywhere in the string...(beginning, middle or end)
B) Convert the ε-NFA (Epsilon NFA) from Part A into a regular NFA.
C) Convert the NFA From Part B into a DFA.
Languages to NFA / ε-NFA A) Make an ε-NFA (An Epsilon NFA) for the language L3...
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...
Design an NFA with at most 5 states for the language (without epsilon transitions) L2= {w ∈ {0, 1}∗ | w contains the substring 0101} Provide the formal 5 tuples(Q,Σ, δ, q0, F) for the NFA Draw/provide a state diagram for your NFA Provide at least three test casesthat prove your NFA accepts/rejects the strings from the language
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...
Regular expressions, DFA, NFA, grammars, languages Regular Languages 4 4 1. Write English descriptions for the languages generated by the following regular expressions: (a) (01... 9|A|B|C|D|E|F)+(2X) (b) (ab)*(a|ble) 2. Write regular expressions for each of the following. (a) All strings of lowercase letters that begin and end in a. (b) All strings of digits that contain no leading zeros. (c) All strings of digits that represent even numbers. (d) Strings over the alphabet {a,b,c} with an even number of a's....
2. a. Draw a NFA that accepts all strings over Σ = {?, ?} that either end in ?? or contain the substring ??. b. Then convert the NFA in the previous exercise to a DFA
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. (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...
1. Write regular expressions to capture the following regular languages: (a) The set of binary strings which have a 1 in every even position. (Note: odd positions may be either 0 or 1.) (b) The set of binary strings that do not contain 011 as a substring. (c) Comments in Pascal. These are delimited by (* and *) or by { and }, and can contain anything in between; they are NOT allowed to nest, however. 2. Write a DFA...
For each of the following statements. state whether it is True or False. Prove your answer: a. ∀L1 , L2(L1= L2)iff L1*·=L2*). b. (ØuØ*)n(¬Ø- (ØØ*)) = Ø (where ¬Ø is the complement of Ø). c. Every infinite language is the complement of a finite language. d. ∀L ((LR)R = L). e. ∀L1, L2((L1L2)*= L1*L2*). f. ∀L1, L2(( ((L1*L2*L1*)*= (L2UL1)*). g . ∀L1, L2(( ( ( L 1 U L 2 ) * = L 1 * U L 2 *...
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...