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State diagram for a turnstile A turnstile. An example of a simple mechanism that can be modeled by a state machine is a turnstile. [4] [5] 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.
An oracle machine or o-machine is a Turing a-machine that pauses its computation at state "o" while, to complete its calculation, it "awaits the decision" of "the oracle"—an entity unspecified by Turing "apart from saying that it cannot be a machine" (Turing (1939), The Undecidable, p. 166–168).
The butterfly diagram show a data-flow diagram connecting the inputs x (left) to the outputs y that depend on them (right) for a "butterfly" step of a radix-2 Cooley–Tukey FFT algorithm. This diagram resembles a butterfly as in the Morpho butterfly shown for comparison, hence the name. A commutative diagram depicting the five lemma
The state diagram for a Mealy machine associates an output value with each transition edge, in contrast to the state diagram for a Moore machine, which associates an output value with each state. When the input and output alphabet are both Σ , one can also associate to a Mealy automata a Helix directed graph [ clarification needed ] ( S × Σ ...
A zoomed-out space-time diagram of the 5-state busy beaver machine (for S(n), then Σ(n)). The machine runs for 47,176,870 steps, peaking with 12288 zeroes, and leaving behind 4098 zeroes upon halt. The diagram is compressed so only steps which change the tape are shown.
UML state machine, [1] formerly known as UML statechart, is an extension of the mathematical concept of a finite automaton in computer science applications as expressed in the Unified Modeling Language (UML) notation.
The mathematical category of deterministic automata, sequential machines or sequential automata, and Turing machines with automata homomorphisms defining the arrows between automata is a Cartesian closed category, [18] it has both categorical limits and colimits.
A state diagram for a door that can only be opened and closed. A state diagram is used in computer science and related fields to describe the behavior of systems. State diagrams require that the system is composed of a finite number of states. Sometimes, this is indeed the case, while at other times this is a reasonable abstraction.