# Constructing a DFA from a Regular Expression: How to Handle * and () Operators?

• l flipboi l
In summary, the conversation is about constructing a DFA based on a given regular expression, which includes the use of a, ab, and c. The suggestion is made to construct a NFA first and then convert it to a DFA. It is also noted that there may be a typo in the regular expression, as it should likely be a* instead of *a.
l flipboi l

## Homework Statement

Construct a DFA based on the regular express.

Regular expr = *a(ab)*c*

## Homework Equations

How do you construct a DFA out of this regular expr?

## The Attempt at a Solution

Here's what I think it says...

it can accept 0 or more a,c, and ordered pair of ab.

the construction of the DFA is where I am stuck.

doh! yeah it's a*(ab)*c*

## 1. What is an automaton?

An automaton, also known as a finite state machine, is a mathematical model used to describe and analyze the functioning of a system. It consists of a set of states, a set of possible inputs, a set of transitions between states, and a set of final or accepting states.

## 2. What is a regular expression?

A regular expression, or regex, is a sequence of characters that define a search pattern. It is used for pattern matching and text manipulation, and is commonly used in programming languages and text editors.

## 3. How does a regular expression relate to an automaton?

A regular expression can be converted into an equivalent automaton, where the states represent the possible matches of the regular expression and the transitions represent the possible ways to reach those matches. This allows for efficient pattern matching and text processing.

## 4. What is a DFA?

A DFA, or deterministic finite automaton, is an automaton that has a unique transition for each possible input in each state. This means that for a given state and input, the next state is always determined. DFAs are commonly used in compiler design and string searching algorithms.

## 5. How is a regular expression converted to a DFA?

The process of converting a regular expression to a DFA involves creating a transition table that maps the states and inputs of the automaton. This table is then used to construct the DFA by following the transitions for each input. There are various algorithms and tools available to automate this conversion process.

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