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In the state-transition table, all possible inputs to the finite-state machine are enumerated across the columns of the table, while all possible states are enumerated across the rows. If the machine is in the state S 1 (the first row) and receives an input of 1 (second column), the machine will stay in the state S 1 .
The state-transition matrix is used to find the solution to a general state-space representation of a linear system in the following form ˙ = () + (), =, where () are the states of the system, () is the input signal, () and () are matrix functions, and is the initial condition at .
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.
A self transition is a transition where the initial and the final state are the same. A representative example is a do loop incrementing some counter until it overflows and becomes 0 again. Although the do loop executes the same increment command iteratively, its state space is not a cycle but a line.
Figure 7: State roles in a state transition. In UML, a state transition can directly connect any two states. These two states, which may be composite, are designated as the main source and the main target of a transition. Figure 7 shows a simple transition example and explains the state roles in that transition.
Stateflow uses a variant of the finite-state machine notation established by David Harel, enabling the representation of hierarchy, parallelism and history within a state chart. [ 2 ] [ 3 ] Stateflow also provides state transition tables and truth tables .
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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 ...