Let L be a language over the alphabet Σ = {a, b}. Prove that
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- Design a deterministic finite state automaton (DFA) that accepts exactly the strings over the alphabet {A, B, ...,Z} that contain at least two R, at most one T, and where every E comes after some S (there may be other letters in between). For instance, your DFA should accept the strings: • MYSTICWARRIORS • MARSMATRIX • SHOCKTROOPERS • CONTRAHARDCORPS STRIDER but not the strings • CRAZYTAXI (it does not contain at least two Rs) LASTRESORT (it contains more than one T) AFTERBURNER (there are Es without a S somewhere before them) • BATTLECIRCUIT (all of these at the same time) Clearly indicate the meaning of each state. One way to do this is to number the states and have a numbered list of their meanings, but any readable method you use to label and explain your states is fine. Hint: there are three separate conditions accepted strings must meet; states will need to encode whether or not each one is met (or perhaps partially met). You can label an edge with the word “else" to indicate it…Build a DFA and TG that accepts all those strings that have an ‘oddnumber of a’s’ but ‘any number of b’s’. DFA (deterministic Finite Automata) TG (Transition Graph) Theory of autometaConsider the following language: L {we (0,1}* |w ends with the substring 011) Which one of the following deterministic finite automata accepts L? 1 0. (a) Start 1 0. 0. (b) Start 0,1 0. 0. (C) Start 0. 0. 0. (d) Start
- Hello, Using the constructions described in the proof of Kleene’s theorem, find nondeterministic finite-state automata that recognize this set: (0 ∪ 11)* Please show each step to get the automaton. ALSO each step needs to have the finite state machine DRAWN BY HANDThis part is about finite-state automata (FSAs). Question 1) You are given the following automaton A over the alphabet Σ = {0, 1, 2}: (image attatched) Which of the following words are in the language accepted by the automaton A? (i answered this) Give, as transition graph, a deterministic FSA that accepts the same language as the FSA A ofQuestion 1.Justify your answer, for example by following the subset construction.10. a. Define clearly but completely: Language L is decidable. b. Let ALLDFA = {M: M is a DFA and L (M) = Σ*} — that is, this is the language of deterministic finite automata that accept all strings. Show that ALLDFA is decidable.
- Apply the Blue state method on each of the following FA’s and check whether the Finite Automata accepts a word or not1. Consider the following finite state automaton, A, over the alphabet {0, 1} of binary words:(i) What is the start state of the automaton A?(ii) What are the accepting states of the automaton A? (iii) Is the automaton A deterministic? Justify your answer.construct a deterministic finite automaton that describes R=ab*a*
- 1. Convert the regular expression (00)*(11)+01) into its equivalent NFA 2. Prove that the language L= {aP|p prime} is not regular using pumping lemma. 3. For the following Deterministic Finite Automata (DFA), write a Regular Expression that accepts the same language. a a 91 92 q3 aFinite AutomataC. {w| contains the substring "aba"D. {w| w has length at least 3 and its third symbol is an "a"}Using the constructions described in the proof of Kleene’s theorem, find nondeterministic finite-state automata that recognize this set: 0*1* Please show each step to get the automaton. ALSO each step needs to have the finite state machine drawn by hand.