Állapotgépek

Állapotgépek, often translated as "state machines" or "finite automata," 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 machine transitions from one state to another in response to external inputs. This transition is determined by a set of rules, often represented as a state transition table or diagram.

The concept of an állapítgép is fundamental in computer science and theoretical computer science. They are used to design and analyze digital circuits, parse text, model sequential logic, and understand the capabilities of different computational models. A key characteristic is their finite memory, meaning they only "remember" their current state.

There are several types of állapotgépek, including deterministic finite automata (DFA) and non-deterministic finite automata (NFA). In a DFA, for each state and input, there is exactly one transition to a next state. In contrast, an NFA can have multiple possible transitions for a given state and input, or no transition at all. Despite this difference, DFAs and NFAs are equivalent in their computational power; any language that can be recognized by an NFA can also be recognized by a DFA.

Állapotgépek are widely applied in areas such as compiler design, where they are used to recognize tokens in programming languages, and in the development of control systems, where they model the behavior of devices and processes. Their simplicity and clear definition make them a powerful tool for understanding and solving complex computational problems.