Final answer:
A finite automaton, also known as a finite state machine, is an abstract mathematical model used to describe and analyze how systems behave. It is composed of a finite set of states, a set of inputs, a set of transitions, and an initial state. Finite automata are used in various technologies, such as lexical analysis, regular expression matching, compilers, network protocols, and circuit design. One example of a finite automaton is a vending machine.
Step-by-step explanation:
A Finite Automaton: Definition and Working:
An abstract mathematical model called a finite automaton, sometimes referred to as a finite state machine, is used to explain and examine the behavior of systems. It consists of an initial state, a set of transitions, a set of inputs, and a finite set of states. Depending on the inputs and its current state, the automaton moves between states. It operates by taking in inputs, changing states when needed, and then generating outputs.
Types of Finite Automata:
Finite automata come in various forms, such as nondeterministic finite automata (NFA) and deterministic finite automata (DFA). Every state in a DFA has a distinct next state for every input symbol. An input symbol in an NFA may have more than one next state in a given state.
Technologies that Use Finite Automata:
In computer science and other fields of technology, finite automata are extensively utilized. They are utilized in compilers, regular expression libraries, network protocols, circuit design, lexical analysis for pattern matching and tokenization. Finite automata, for instance, are useful in regular expression matching because they can identify patterns in textual data.
An Example of a Finite Automaton:
A vending machine is an illustration of a finite automaton. The vending machine can only be in a limited number of states, including empty, accepting payments, delivering goods, and giving change back. The customer's pressed buttons serve as the inputs, and the input and the current state determine the transitions. For example, the vending machine changes to the state of delivering a product when the customer presses the button for that product.