Given the following language, L = {10 10m | m > n} and = {0, 1]. (a) (10 Points) Build a context-free grammar (CFG) that generates strings in L. (b) (5 Points) Use the derivation rules () to show the CFG in (a) recognizes the string 1001000. (c) (10 Points) Write down the pushdown automaton (PDA) pseudo code algorithm in English that recognizes L. (d) (10 Points) Build a PDA that recognizes L. (e) (10 Points) Show a sequence of single moves of PDA in (d) that the string 100100 is NOT in L. (f) (10 Points) Write down the Turing Machine (TM) pseudo code algorithm in English that recognizes L. (g) (10 Points) Build a TM, M that recognizes L. (h) (10 Points) Specify the configuration at each single moves of TM in (g)ivate by step that the string 10100 is in L. Go to Setti