REGULAR EXPRESSION TO NFA COP 4620 Programming Language

REGULAR EXPRESSION TO NFA COP 4620 – Programming Language Translators Dr. Manuel E. Bermudez

RE TO NFA So far, RGR RGL Minimum DFA RE NFA Done Soon DFA Now

RE TO NFA • Algorithm 1 (bottom-up): Recursively build the FSA, • Mimicking structure of the RE. • Each FSA built has one start state, and one final state. Conversions: 1 2 1 1 a 2 if ø, if ℇ, and if a.

RE TO NFA ε P ε 1 2 ε P 1 if P + Q, ε ε Q ε or Q ε P ε ε ε 1 2 P ε Q ε 2 if PQ, and if P*.

RE TO NFA EXAMPLE: 1 a 3 5 7 10 3 a b 4 b a a ε (b (aba + ε) a)* 2 (b (aba + ε) a)* 4 (b (aba + ε) a)* 6 (b (aba + ε) a)* 8 (b (aba + ε) a)* 9 (b (aba + ε) a)* 11 (b (aba + ε) a)* 5 b 8 a 6 ε 7 (b (aba + ε) a)*

RE TO NFA 3 a ε 9 ε 12 ε 4 4 ε 13 ε b 2 b 5 6 ε 8 a 5 b 8 a (b (aba + ε) a)* 7 6 (b (aba + ε) a)* ε 7 1 ε ε 12 ε 3 a 9 ε 4 ε 13 ε 5 b 8 a 6 ε 7 (b (aba + ε) a)*

RE TO NFA b 2 2 (b (aba + ε) a)* 1 12 ε 11 3 9 a a ε 10 4 ε 3 a ε 9 ε 12 ε 13 b 5 8 ε 6 ε 4 ε 13 ε 5 8 b 6 ε a 7 (b (aba + ε) a)* 7 a 1 ε ε ε b ε 14 ε ε ε 15 1 b ε 11 ε 9 a 10 2 ε ε 13 ε 12 ε 3 a ε ε 8 4 5 a 7 ε 6 (b (aba + ε) a)*

RE TO NFA • Algorithm 2 (top-down): 4 Rules • Start: • Apply Rules: E a a* ε ε ab a b a+b a b

RE TO NFA EXAMPLE (a + b)* (aa + bb) (a + b)* aa + bb ε aa ε bb a+b ε ε a b a a b b

RE TO NFA (ANOTHER EXAMPLE) ba(a + b)* ab a ε ε b a b

SUMMARY Algorithm 1: • Builds FSA bottom up • Good for machines • Bad for humans Algorithm 2: • Builds FSA top down • Bad for machines • Good for humans

RE TO NFA So far, RGR RGL Minimum DFA RE NFA Done Soon DFA Two algorithms