expressing queries as finite state automata

In the locked state, pushing on the arm has no effect no matter how many times the input push is given, it stays in the locked state. There are two possible inputs that affect its state: putting a coin in the slot ( coin) and pushing the arm ( push). After the customer passes through, the arms are locked again until another coin is inserted.Ĭonsidered as a state machine, the turnstile has two possible states: Locked and Unlocked. Depositing a coin or token in a slot on the turnstile unlocks the arms, allowing a single customer to push through. Initially the arms are locked, blocking the entry, preventing patrons from passing through. A turnstile, used to control access to subways and amusement park rides is a gate with three rotating arms at waist height, one across the entryway. FSMs are studied in the more general field of automata theory.Īn example of a simple mechanism that can be modeled by a state machine is a turnstile. A finite-state machine has the same computational power as a Turing machine that is restricted such that its head may only perform 'read' operations, and always has to move from left to right. This is because an FSM's memory is limited by the number of states it has. The computational power distinction means there are computational tasks that a Turing machine can do but an FSM cannot. The finite-state machine has less computational power than some other models of computation such as the Turing machine.

Simple examples are vending machines, which dispense products when the proper 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 proper order. The behavior of state machines can be observed in many devices in modern society that perform a predetermined sequence of actions depending on a sequence of events with which they are presented. A deterministic finite-state machine can be constructed equivalent to any non-deterministic one.

Finite-state machines are of two types- deterministic finite-state machines and non-deterministic finite-state machines. An FSM is defined by a list of its states, its initial state, and the inputs that trigger each transition. The FSM can change from one state to another in response to some inputs the change from one state to another is called a transition. It is an abstract machine that can be in exactly one of a finite number of states at any given time. (Clicking on each layer gets an article on that subject)Ī finite-state machine ( FSM) or finite-state automaton ( FSA, plural: automata), finite automaton, or simply a state machine, is a mathematical model of computation.

Expressing queries as finite state automata