Description

Implement an FSA to RegExp Translator. Given an FSA description in the input.txt (see input file format) your program should output the output.txt containing an error description (see validation errors) or a regular expression that corresponds to the given FSA. The regular expression should be built according to a slightly modified version of the Kleene’s algorithm (see Kleene's algorithm).

Input file format

states=[s1,s2,...] // s1 , s2, ... ∈ latin letters, words and numbers
alpha=[a1,a2,...] // a1 , a2, ... ∈ latin letters, words, numbers and character _(underscore)
initial=[s] // s ∈ states
accepting=[s1,s2,...] // s1, s2 ∈ states
trans=[s1>a>s2,...] // s1,s2,...∈ states; a ∈ alpha

Validation result

Errors

E0: Input file is malformed
E1: A state 's' is not in the set of states
E2: Some states are disjoint
E3: A transition 'a' is not represented in the alphabet
E4: Initial state is not defined
E5: FSA is nondeterministic

Kleen's algorithm

Denote ∅ as {}
Denote Ɛ as eps
Define update rule with the additional parentheses:
R^k_ij = (R^k-1_ik)(R^k-1_kk)*(R^k-1_kj)|(R^k-1_ij)

Example 1

input.txt
states=[on,off]
alpha=[turn_on,turn_off]
initial=[off]
accepting=[]
trans=[off>turn_on>off,on>turn_off>on]

output.txt
Error:
E2: Some states are disjoint

Example 2

input.txt
states=[0,1]
alpha=[a,b]
initial=[0]
accepting=[1]
trans=[0>a>0,0>b>1,1>a>1,1>b>1]

output.txt
((a|eps)(a|eps)*(b)|(b))(({})(a|eps)*(b)|(a|b|eps))*(({})(a|eps)*(b)|(a|b|eps))|((a|eps)(a|eps)*(b)|(b))

Example 3

input.txt
states=[on,off]
alpha=[turn_on,turn_off]
initial=[off]
accepting=[]
trans=[off>turn_on>on,on>turn_off>off]

output.txt
{}