állapotgépeket

Állapotgépek, often translated as state machines or finite automata, are mathematical models of computation. They consist of a finite number of states, transitions between these states, and an input alphabet. An állapítgép operates by reading an input symbol and changing its state based on the current state and the input symbol. This transition is defined by a transition function.

There are two main types of állapotgépek: deterministic finite automata (DFA) and non-deterministic finite automata (NFA). In a DFA, for each state and input symbol, there is exactly one next state. In an NFA, there can be zero, one, or multiple next states for a given state and input symbol. NFAs can also have transitions on an empty input, known as epsilon transitions. Despite their differences, DFAs and NFAs are equivalent in terms of the languages they can recognize; any language recognizable by an NFA can also be recognized by a DFA, and vice versa.

Állapotgépek are used to model a wide range of phenomena and computational problems. They are fundamental in areas such as compiler design, where they are used for lexical analysis to recognize tokens in source code. They are also applied in text processing, pattern matching (like in regular expressions), digital circuit design, and artificial intelligence for simple decision-making processes. The behavior of an állapítgép can be visualized using a state diagram, which is a directed graph where nodes represent states and edges represent transitions labeled with input symbols.