# Determinization of finite automaton

### S = {A, B, C}

### Σ = {a, b}

### Transitions:

(A, a, A)

(A, a, B)

(A, b, C)

(B, a, A)

(B, b, B)

(C, b, A)

(C, b, B)

### Initial State(s) = {A}

### Final State(s) = {C}

### After Determinization (Subset Construction)

### S = {A, A-B, C, B-C, T}

### Σ = {a, b}

### Transitions:

(A, a, A-B)

(A, b, C)

(A-B, a, A-B)

(A-B, b, B-C)

(C, a, T)

(C, b, A-B)

(B-C, a, A)

(B-C, b, A-B)

(T, a, T)

(T, b, T)

### Initial State(s) = {A}

### Final State(s) = {B-C, C}

Groups: 2

States in group: 3

States in group: 2

[[{"0":"A","1":"A-B","4":"T"},["B-C","C"]],[["A","A-B","T"],["B-C","C"]]]

["A","A-B","C","B-C","T"]

["B-C","C"]