Explain how these answers are calculated:

Problem 14 [ 18 points] Consider the Turing machine M=(Q,,,,q,F) such that: Q={q,t,s,x,v} LAST NAMP={a,b,c,g};T={B,a,b,c,g,A,P,K,G};F={x} and is defined by the following transition set: IRSI NAMP- [q,a,t,A,R][q,b,t,P,R][a,c,t,K,R](q,g,t,G,R][t,a,c,a,R][t,b,t,b,R][t,c,t,c,R][t,g,s,g,L][t,B,t,B,R][s,a,x,a,R][s,A,x,A,R][s,b,x,b,R][s,P,x,P,R] (d) Explain bow to construct an algorithm that solves the following problem. If such an algorithm does not exist, state that it does not exist and prove your claim. INPUT string te ; Quesmon: Is w LR ? B is the designated blank symbol. M sccepts ty finsl (the anower to part (e)) into a finite autotnaton, convert state.) Let LA be the set of strings which M acoepts. Let LR be the set of strings which M rejects. Let L be the set of strings on which M diverges. (a) Write a regular expression that defines LA. If such a regular expression does not exist, state that it does not exist and prove it. Advice for Answer: M rejects the empty string and otherwise diverges if it finde no g 's. Upon finding the first g, M accepts if it finds a or b to the left of this first g, and rejects otberwise, Answer: (abc)(ab)g(abcg) finite sutomaton on w, and decide ss it decides. (e) Explain how to construct an algorithm that solves the folloming peoblem. If such an algarithm does not exist, state that it does not exist and prove your claim. INPUT: A Turing Machine T; Qubstnos: Does T halt on at lesst obe element of L. (b) Write a regular expression that defices Lwa. If such (definod above)? a regular expression does not exist, state that it does not exist and prove it. exlstod, it would decide the set of Turing Machines wbose. langaages have the nontrivial ptoperty has a noo-ernpty intersectinn with (abc)(abc)n, which in tarn is imposeible by Rice's Theorem. The property thas a pob-empty intersoction whth (abc)(abc)n it (and both and are regular and thereby recursive (c) Write a regular expression that defines LR. If such a regular expression does not exist, state that it does not exist and prove it