Finite State Machine (Finite Automata)

Summary

In this lecture on the theory of computation, the focus is on finite state machines, also known as finite automata. These are divided into two categories: those with and without output. The lecture primarily discusses deterministic finite automata (DFA), emphasizing their structure and components, including states, transitions, inputs, and the distinction between initial and final states. The DFA is defined using five elements: Q (states), Sigma (inputs), Q0 (initial state), F (final states), and Delta (transition function). The lecture concludes by illustrating these concepts with a simple DFA example, preparing students for further examples in upcoming lectures.

Takeaways

• 📘 Finite State Machines (FSM) are the simplest model of computation with limited memory.
• 🔁 FSM can be divided into two main categories: with output (like Moore and Mealy machines) and without output.
• 🏁 Deterministic Finite Automata (DFA) is a type of finite automata without output that we focus on in this lecture.
• 🌐 DFA consists of states, transitions, an initial state, and a set of final states.
• 🔄 Transitions in DFA are determined by inputs and dictate how the machine moves from one state to another.
• 📍 States in DFA are represented by circles, with labeled edges (transitions) showing the flow between states based on inputs.
• 🔑 The initial state in DFA is indicated by an arrow with no source, pointing to the starting state.
• 🏁 The final state(s) in DFA is indicated by a double circle, signifying the terminating state(s) of the machine.
• 🔢 DFA is formally defined by a five-tuple: Q (states), Sigma (inputs), Q0 (initial state), F (final states), and Delta (transition function).
• 📊 The transition function Delta is represented as a table mapping each state-input pair to a resulting state in DFA.

Q & A

What are the two broad categories of finite automata?

The two broad categories of finite automata are finite automata with output and finite automata without output.

What are the two types of finite automata with output?

The two types of finite automata with output are Moore machines and Mealy machines.

What are the three categories of finite automata without output?

The three categories of finite automata without output are deterministic finite automata (DFA), non-deterministic finite automata (NFA), and Epsilon non-deterministic finite automata (Epsilon NFA).

What does DFA stand for?

DFA stands for deterministic finite automata.

What are the two important properties of finite state machines?

The two important properties of finite state machines are that they are the simplest model of computation and they have very limited memory.

What are the components of a DFA represented by circles in the diagram?

The components of a DFA represented by circles in the diagram are the states.

What do the edges in a DFA diagram represent?

The edges in a DFA diagram represent the transitions between states based on inputs.

What is the significance of a double circle around a state in a DFA diagram?

A double circle around a state in a DFA diagram signifies that it is the final state or the terminating state.

What is the initial state in a DFA diagram?

The initial state in a DFA diagram is represented by an arrow coming from nowhere pointing to a state.

What are the five components used to define a DFA?

The five components used to define a DFA are Q (set of states), Sigma (set of inputs), Q0 (initial state), F (set of final states), and Delta (transition function).

What is the transition function in a DFA?

The transition function in a DFA is a function that maps from the cross product of the set of states and the set of inputs to the set of states, representing the next state based on the current state and input.