README

		-Regex Engine-


The archive contains:
- the main.py file;
- ReGex.g4 grammar used by ANTLR to generate the files needed for parsing;
- the files generated by ANTLR - are included in the archive because I overwrote ReGexListener
with methods of generating RegEx for each type of input;

** ANTLR files should not be regenerated **

Main.py contains the following functions:

- converRegToEr (expression): composes ER equivalent of "expression", where expression
is a RegEx type object that is furthermore used by the following functions
(for SYMBOL_ANY, SYMBOL_SET, SYMBOL_RANGE):
- alphabet (): compose ER for regex "." : the union of all the characters in the alphabet
(SYMBOL_ANY)
- setAlph (range): the union of the characters in the set, or between the character limits
of existing tuples (SYMBOL_SET)
- rangeAlphabet (): ER equivalent to "{}" for all three cases (eg exact interval
{4,4}, min range {4,}, max range {, 4}, normal range {2,4}) (SYMBOL_RANGE)

- rename_states (target, reference): receives an NFA and restores renamed states using
the reference automata("reference")

- new_states (* nfas): receives an NFA and creates a new set of states

- reToNfa (expression): receives an ER and builds the appropriate NFA: we approach the basic cases
(empty language, empty string, ER consisting of a single character) and then compose the cases
for concatenation, reunion and Kleene Star.

- getEpsilonClosuresState (s, nfa): receives an "s" state and returns all the states of the machine
that can be reached in 0 or more steps only with transitions on "ε" (empty string); traversals of
states are made according to the dfs model

- getEpsilonClosuresStates (setStates, nfa): receives a set of states and returns the union of 
"ε" closures of all states in the set ("setStates")

- move (delta, T, char): returns the tuple formed by all the states of the machine than can be 
reached through transitions on the "c" character of the "T" state

- nfaToDfa (nfa):

	- we start from the state eS (tuple formed by the "concatenation" of all the states in which
	it can be reached from the initial state of the NFA automata, in 0 or more steps, on transitions
	of "ε"), which will become the initial state for the DFA;

	- add this state to the stack and continue by checking all the tansitions on
	any character (if any), for all the states on the stack according to the dfs model
	for a state, which belongs to the state space of the NFA we will create a state s'
	which we will add in the space of the states of the DFA:

		s' = tuple consisting of "ε" -Closures of each state where that can be reached in the NFA 
		from the s' state, through transitions on any character in the alphabet (if any)
		*s' will be added if it has not been previously discovered

	- we check which of the states of the DFA built contains at least one final state for the NFA
	-> those will become final states for the newly built DFA

- check (word, dfa): receives a DFA and a word, and simulates the machine's transitions for
the sequence of characters (the word); if the machine finds no transition on the current character
-> halts -> does not accept word, otherwise, check if it has finished input and reached a final state n which it stops transitioning
(if so -> True, otherwise -> False)