Q1 Consider the following regular grammar with start symbol S. {SaS, SaB, SaA, A→bS, A→ bB, AA, BaS, B → bB, B → A} Q1.1 RG to RE conversion Covert the regular grammar into a regular expression. • Recommendation: eliminate variables in the order B then A then S. Q1.2 RG to DRG conversion Convert the regular grammar into a deterministic regular grammar.

first n Catalan numbers. 5. Write a Python generator for al

Instruction: Read Part 1: Chapter 1-4 of the book Automata, Computability and Complexity by Elaine Rich and answer the following Questions. 1 1. Let L₁ = {all string that ends in a} and L₂ = {all string that starts in b} for Σ = {a,b} Find the following language. a. L₂L1 b. ¬(L₂) (4₁) c. d. L₁ L₂ e. L₁ UL2 2. Let L {even numbers of a's and b's}. For each of the following strings, state whether it is an element of L. a. b. ababababaa aabbaabbaa aabbcc C. d. baabaabaabbb e. E 3. Let L = {up, down, right, left}. List the element of L² or LL in lexicographic order.

Can you explain the basic workings of a counting semaphore?