állapotsgépek

Állapotsgépek, a Hungarian term translating to "state machines," are a fundamental concept in computer science and mathematics. They are abstract computational models that can be in exactly one of a finite number of states at any given time. The machine can transition from one state to another in response to external inputs; the set of all states, the set of all possible input symbols, and the transition function that determines the next state given the current state and input are all finite.

The behavior of an állapotsgép is determined by its current state and the input it receives. When an input symbol is processed, the machine moves to a new state according to its predefined transition rules. Some states may be designated as "accepting" or "final" states, indicating a successful completion of a particular process or recognition of a specific pattern.

Állapotsgépek are widely used for modeling various systems, including digital circuits, software protocols, lexical analyzers in compilers, and even simple game AI. They are particularly useful for tasks involving pattern recognition, sequence processing, and control logic. The two primary types are deterministic finite automata (DFA), where for each state and input, there is exactly one next state, and non-deterministic finite automata (NFA), where multiple transitions might be possible for a given state and input. While NFAs can be more intuitive for describing certain problems, any NFA can be converted into an equivalent DFA.