Lõppautomaatide

Lõppautomaatide, commonly translated as finite automata or finite state machines, are mathematical models of computation. They are abstract machines that can be in exactly one of a finite number of states at any given time. The automaton can transition from one state to another in response to some external inputs. The set of states and the transition rules are finite.

A finite automaton consists of a finite set of states, a set of input symbols called an alphabet, a transition function, a start state, and a set of accept states. The transition function dictates how the automaton moves from one state to another based on the current state and the input symbol. When the automaton finishes reading an input string, if it is in one of the accept states, the string is considered accepted; otherwise, it is rejected.

Finite automata are widely used in computer science for tasks such as text processing, lexical analysis in compilers, and designing digital circuits. They are also fundamental to the theory of computation, serving as a basic model for understanding what can and cannot be computed. While simple, finite automata are powerful enough to recognize a class of languages known as regular languages. There are two main types: deterministic finite automata (DFA), where for each state and input symbol there is exactly one transition, and non-deterministic finite automata (NFA), where there can be multiple transitions for a single state and input symbol, or even transitions on the empty string. Despite their differences, DFAs and NFAs are equivalent in their computational power.