$1.$ Build a program that simulate the subset construction algorithm to convert a given NFA to DFA.

a$.$ The program takes as an input the mathematical representation of the NFA including the following:

i$.$ Set of states S

ii$.$ Start State S$0$

iii. Alphabet $$

iv$.$ Final State$($s$)$ F

v$.$ Transition T

b$.$ Then, it will display the converted equivalent DFA mathematical representation.

$2.$ Implement a top$-$down parser $($Predictive parser $-$ LL$1).$

a$.$ The program takes an input as following:

i$.$ The number of productions, and each production rules.

ii$.$ The first symbols of each rule.

iii. The number of terminals, and each terminal symbol.

iv$.$ The number of non$-$terminals, each non$-$terminal symbol, and the follow of each non$-$terminal.

b$.$ The program should construct and display the LL$1$ parse table.

c$.$ Test your constructed table by asking for a string as input. Then, show the parsing action and stack status step$-$by$-$step until the algorithm decide whether the input string is accepted or rejected.