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- Design a deterministic finite-state automaton over the alphabet {a, b, c}that accepts words where each character is immediately followed by atleast one identical character. For example, it accepts the words λ, aa, aaa,aabbbbaacc, but it rejects the words a, baba, cbbba. Write the transitionfunction of the automaton as a table and draw the automaton in the formof a transition diagram. Try to design the simplest possible automaton,i.e., an automaton with the smallest number of states.Let M= (Q, E, T, A, Ō, y) be a Finite State Machine(FSM) such that the Transition table of M is States a b a b A D 1 1 В C B 1 C A D 1 D A E В 1 a. Draw the Transition Diagram of M b. What is the output string produced for the following input string? i. abababbb ii. bbbaabbaHi, This part is about regular expressions (REs) and finite-state automata (FSAs). Notation: in the REs below, the Kleene star has higher precedence than sequencing; andsequencing has higher precedence than +. E.g. 10∗1 + 11∗1 = (1(0∗)1) + (1(1∗)1). Consider the regular expression r: (01 + 11)∗10 (1∗ + 0∗) 1.1) Which of the following words (ε is the empty word) belong to the language defined by r? Options: ε, 101, 001101, 111011, 111010 1.2) For each of your answers in Question 1.1, give a brief explanation. For example, you can explain how the regular expression will accept (i.e. match) the words that belong to its language, and how it will not accept those that do not belong in it. 1.3) Give, as a transition graph, an FSA (possibly with ε-transitions) recognising the same language as r.Note: You should not use transitions with composite labels, e.g. of the form q1 →42→ q2. Thanks for the help :)
- Think about the concept of extended transition functions δ* and ∆* of Deterministic Finite Automata and Nondeterministic Finite Automata respectively. Prove the following facts about those functions using mathematical induction. 1. Given a DFA M = (Q, Σ, δ, s0, F) and strings x, y ∈ Σ*, we have δ*(q, xy) = δ*(δ*(q, x), y). 2. Given a NFA N = (Q, Σ, ∆, S0, F), subsets A ⊆ Q, B ⊆ Q and a string x ∈ Σ∗, we have ∆* (A ∪ B, x) = ∆*(A, x) ∪ ∆*(B, x).DO NOT COPY FROM OTHER WEBSITES Q. Design a deterministic finite automaton for the given regular expression R. R = (0 + 1 (1 + 01) *00) *Choose the correct phrase * 1.1 • The Domain of f(x) = V1 – x is 1. [-1,0) 2. (-0, 1] 3. (-∞, 1) 4. [1, 0) 1 O 2 O 3 4 O
- 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…Design a deterministic finite-state automaton over the alphabet {a; b; c}that accepts words where each character is immediately followed by atleast one identical character. For example, it accepts the wordsY(gamma sigh), aa, aaa,aabbbbaacc, but it rejects the words a, baba, cbbba. Write the transition function of the automaton as a table and draw the automaton in the form of a transition diagram. Try to design the simplest possible automaton, i.e., an automaton with the smallest number of states.Create a membership testing algorithm.f = 1, 2,..... n, a group G operating on it, a permutation of it, a base and a strong energising set for G, are the inputs;Schreier vectors v I for the stabilising chain, 1 I k;a boolean value indicating if g > G as the output;
- Give English language translations of the following wffs if M(x): x is a man W(x): x is a woman i: Ivan p: Peter W(x, y): x works for y a. (Ax)(W(x) ^ (Vy)(M(y) → [W(x, y)1). b. (Vx)[M(x) → 3y)(W(y) ^ W(x, y))] c. (Vx)[M(x) → (Vy)(W(x, y) → W(y))] d. (Vx)(Vy)(M(x) A W(y, x) → W(y)) e. W(i, p) ^ (Vx)[W(p, x) → (W(x))') f. (Vx)[W(x, i) → (W(x))']Consider the following Nondeterministic Finite Automaton (NFA). b 1 a 2 b Page 3 b 3 a a a 4 (a) What are the possible states that this NFA could be in, after reading the input string bab? (b) Prove, by induction on n, that for all positive integers n, the string (bab)" is accepted by this NFA. (This string is obtained by n repetitions of bab.) Paragraph BIEEBayesian Networks Exercise 1 Given the following BN P(H) 0,1 H H P(S) T 0,3 F 0,9 S H S P(T) TT 0,9 т T F 0,5 F T 0,8 FF 0,2 T P(E) E T 0,6 F 0,1 1. Construct it using pgmpy Python library.