Convert NFA with only accepting states to regular expression?

Question

Suppose you wanted to find a Regular Expression that defines the language accepted by the folowing Finite State Automaton. Where S1 and S2 are both accepting states.

How would I go on doing this?

Answer 1

An NFA with only accepting states will accept the input, no matter what the input is. Every string over its input alphabet is accepted. Do you know how to write a regular expression for any string over an alphabet?

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Your comment “There are two final states which intervene with each-other”. I am not sure what you mean by "intervene". An NFA may have several accepting states. When it has finished reading the input, if it could have finished in an accepting state, it accepts the input. There might be different computations which finish in different accepting states; that doesn't matter; it accepts the input if there is even one possible computation that finishes in an accepting state.

Answer 2

Your automaton accepts any string of 0's and 1's.

Therefore the regular expression is {0, 1}*.

Or posix style: [01]*.