Problem 3. Consider the following scheme to describe chess positions. We use the letters P, B, N, R, Q, and K to denote, respectively, white pawns, bishops, knights, rooks, queens and kings; their black counterparts are denoted by the corresponding lower-case letter; empty board cells are denoted by the underscore character (-); and a chess position is denoted by the string of characters that is obtained by traversing the board in row-major order. For instance, the position depicted below is denoted by the string --_r_---_b_----_R_---------pkn_--------_BP-_-q_K___P_--- AJ . 8 pilte _ a b c d e f g h Consider some standard rule set of chess and the language of all strings over the alphabet {P,B, N, R, Q, K, p, b,n,r, q, k, - } that, under our established scheme, represent a legal chess position from which, if White were to start the game and play perfectly, White would be assured victory. Is this language regular? Prove that your answer is correct