We convert the following Non-deterministic Finite Automaton (NFA) to an equivalent Dtererministic Finite Automaton (DFA) using the subset construction method. In the resulting DFA, if 6 is the transition function, then 6(A,0) is and 6 (A, 1) is 6.0.0 1 B 0,1 A C
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- Write Algorithm for Membership TestingA group G operating on the function f = 1, 2,..., n; a permutation of f = 1, 2,....., n; a base and strong energising set for G; and Schreier vectors v I 1 I k, for the stabilising chain; are the inputs.The function is in group(p: permutation; I 1..k+l): boolean; (* return true if the permutation p is in the group G I outputs a boolean value indicating if g G.make Membership Testing AlgorithmInput: a group G operating on f = 1,2,.....n; a permutation g of f = 1,2,.....n; a base and strong enerating set for G; Schreier vectors v I 1 I k, for the stabiliser chainOutput: a boolean result showing if g G is in the group; function is in group(p: permutation; I 1..k+l): boolean; (* return true if the permutation p is in the group G I *)Algorithm : Testing MembershipInput : a group G acting on f~ = { 1,2 ..... n };a permutation g of f~ = { 1,2 ..... n };a base and strong ~enerating set for G;Schreier vectors v (i) , 1 < i < k, for the stabiliser chain;Output: a boolean value answer, indicating whether g ~ G;
- Transform, using the subset construction, the following nondeterministic finite automaton into an equivalent deterministic finite automaton. a a Identify the result from the following options: Select one: O None of the other three options. {8, q} {p} a (s,p, q,r) {p,r} {s,q}, (s,p.q.r}) {s,p.q} a a a {p} {p,r} a {s} ({p,r} a a {p} a b a {s,q} {p,q} ) b. bLet A = ({40; 91, 42}, {0, 1}, 8, qo, {42}) be the NFA with transition table: 1 9o {40} | {9o, 41} 91 {42} 92 {1} The initial state is qo and the set of accepting states is F = {42}. Use the subset construction to construct a DFA A' that accepts the language L(A).Write Algorithm for Testing MembershipInput : a group G acting on f~ = { 1,2 ..... n };a permutation g on ~ = { 1,2 ..... n };a base and strong generating set for G;Schreier vectors v (i) ,1 < i < k, for the stabiliser chain;Similarly a non-re, cursiveOutput : a boolean value answer, indicating whether g ~ G;function is_in_group(p : permutation; i : 1..k+l ) : boolean;(* return true if the permutation p is in the group G (i) *)
- Algorithm for Testing MembershipInput : a group G acting on [2 = { 1,2 ..... n };a permutation g of ~2 = { 1,2 ..... n };a base and strong generating set forG;sets U (i) ,1 < i < k of coset representatives for stabiliser chain;Output : a boolean value answer, indicating whether g E G;adgis s o (6): = min { d(v) Ive V3 is the minimum degree of G. 0612 Z9Nto JJ V PO Go is called K-connected if IGI>K and GIX is connected for every set x CV with 1X1Let A = ({go, 41, 92}, {0, 1}, 8, qo, {2}) be the NFA with transition table: 9o {40} | {40; 41} 41 {42} 92 {qi} The initial state is qo and the set of accepting states is F = {q2}. Use the subset construction to construct a DFA A' that accepts the language L(A).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…9. Limitation Question. Using the idea of Pumping Lemma, please explain, why we can't build a Finite Automaton to generate all and only strings of the form 1³n0n where n>=0.implement Algorithm for Testing MembershipInput : a group G acting on f~ = { 1,2 ..... n };a permutation g of f~ = { 1,2 ..... n };a base and strong ~enerating set for G;Schreier vectors v (i) , 1 < i < k, for the stabiliser chain;Output: a boolean value answer, indicating whether g ~ G;function is_in_group(p : permutation; i : 1..k+l ) : boolean;(* return true if the permutation p is in the group G (i) *)SEE MORE QUESTIONS