A finite-state machine (FSM), sometimes known as a finite-state automaton (FSA), or simply a state machine, is a mathematical model of computing. It's a machine that can only be in one of a finite set of states at any one moment. In response to some inputs, the FSM can transition from one state to another; this is referred to as a transition.

The states, beginning state, and inputs that cause each transition describe an FSM. There are two kinds of finite-state machines: deterministic and non-deterministic. Any non-deterministic finite-state machine may be made deterministic.

Many technologies in modern civilization behave like state machines, performing a programmed set of actions in response to a set of circumstances. Vending machines, which dispense products when the correct combination of coins is deposited, elevators, whose sequence of stops is determined by the floors requested by riders, traffic lights, which change sequence when cars are waiting, and combination locks, which require the input of a sequence of numbers in the correct order, are all simple examples.

In this “Finite State Automata - Mathematical Foundation of Computer Science” you will learn about the following topics:

- Alphabets and Language
- The notion of a State
- State Machine (FSM and DFA)
- Regular Expression
- Equivalence Relation

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This article Finite State Automata - Mathematical Foundation of Computer Science is contributed by Namrata Chaudhary, a student of Lumbini Engineering College (LEC).

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