1. In the Roman number system, numbers are represented by strings on the alphabet {M, D, C, L, X, V, 1}. Design an accepter that accepts such strings only if they are properly formed Roman numbers. For simplicity, replace the "subtraction" convention in which the number nine is represented by IX with an addition equivalent that uses VIII instead. 2. Prove that: (L1L2R = LLI for all languages L1 and L2