onvert the following regular expression into Non-Deterministic Finite Automata (NFAs), show all the steps.(a) (0 + 1)*000(0 + 1)*(b) (((00)*(11))+ 01)*
Question
onvert the following regular expression into Non-Deterministic Finite Automata (NFAs), show all the steps.(a) (0 + 1)000(0 + 1)(b) (((00)(11))+ 01)
Solution
Sure, let's break down the process of converting the regular expressions into Non-Deterministic Finite Automata (NFAs).
(a) (0 + 1)000(0 + 1)
Step 1: Draw a start state.
Step 2: Draw an arrow from the start state to a new state. Label this arrow with "0 + 1" to represent the (0 + 1)* part of the regular expression. This means that from the start state, we can transition to this new state with either a 0 or a 1.
Step 3: From this new state, draw three arrows, each labeled with "0", leading to three new states. This represents the "000" part of the regular expression.
Step 4: From the last of these three new states, draw an arrow back to itself, labeled with "0 + 1". This represents the final (0 + 1)* part of the regular expression.
Step 5: Mark the last state as an accept state.
(b) (((00)(11))+ 01)
Step 1: Draw a start state.
Step 2: Draw an arrow from the start state to a new state. Label this arrow with "00" and draw an arrow from this state back to itself, also labeled with "00". This represents the (00)* part of the regular expression.
Step 3: From this state, draw an arrow to a new state, labeled with "11". Draw an arrow from this state back to itself, also labeled with "11". This represents the (11) part of the regular expression.
Step 4: From the start state, draw an arrow to a new state, labeled with "01". This represents the "01" part of the regular expression.
Step 5: Draw an arrow from both the state with the "11" loop and the state with the "01" transition back to the start state. This represents the "+" and the "*" in the regular expression, meaning that we can either repeat the process or move on to the "01" part.
Step 6: Mark the start state as an accept state, as the "*" in the regular expression means that we can also accept the empty string.
Please note that this is a textual representation of the process. The actual NFAs would be diagrams with states and transitions.
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