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State diagrams is a diagram used in the field of computer science, representing the behavior of a system, which is composed of a finite number of states. There are many forms of state diagrams, which differ slightly and have different semantics.

State diagram can be used to graphically represent finite state machines. This was introduced by Taylor Booth in his 1967 book "Sequential Machines and Automata Theory". Another possible representation is the State transition table.

A classic form of a state diagram for a finite state machine is a directed graph with the following elements:

- States Q: a finite set of vertices normally represented by circles and labelled with unique designator symbols or words written inside them;
- Input symbols Σ: a finite collection of input symbols or designators;
- Output symbols Z: a finite collection of output symbols or designators;

The output function ω represents the mapping of input symbols into output symbols, denoted mathematically as ω : Σ × Q→ Z.

- Edges δ: represent the "transitions" between two states as caused by the input (identified by their symbols drawn on the "edges"). An 'edge' is usually drawn as an arrow directed from the present-state toward the next-state. This mapping describes the state transitions that is to occur on input of a particular symbol. This is written mathematically as δ : Σ × Q → Z
- Start state q
_{0}: (not shown in the examples below). The start state q_{0}∈ Q is usually represented by an arrow with no origin pointing to the state. In older texts, the start state is not shown and must be inferred from the text. - Accepting state(s) F: If used, for example for accepting automata, F ∈ Q is the accepting state. It is usually drawn as a double circle. Sometimes the accept state(s) function as "Final" (halt, trapped) states.

For a deterministic finite state machine (DFA), nondeterministic finite state machine (NFA), generalized nondeterministic finite state machine (GNFA), or Moore machine, the input is denoted on each edge. For a Mealy machine, input and output are signified on each edge, separated with a slash "/": "1/0" denotes the state change upon encountering the symbol "1" causing the symbol "0" to be output. For a Moore machine the state's output is usually written inside the state's circle, also separated from the state's designator with a slash "/". There are also variants that combine these two notations.

For example, if a state has a number of outputs (e.g. "a= motor counter-clockwise=1, b= caution light inactive=0") the diagram should reflect this : e.g. "q5/1,0" designates state q5 with outputs a=1, b=0. This designator will be written inside the state's circle.

Classic state diagrams are "or" (disjunctive) diagrams, because the machine can only be in one of all the possible states. With Harel statecharts it is possible to model "and" machines, where a machine can be in two or more states concurrently. This is due in part to the modelling of superstates and in part to the modelling of concurrent machines.

The Unified Modeling Language (UML) state diagram is essentially a Harel statechart with standardized notation, which can describe many systems, from computer programs to business processes. The following are the basic notational elements that can be used to make up a diagram:

- Filled circle, pointing to the initial state
- Hollow circle containing a smaller filled circle, indicating the final state (if any)
- Rounded rectangle, denoting a state. Top of the rectangle contains a name of the state. Can contain a horizontal line in the middle, below which the activities that are done in that state are indicated
- Arrow, denoting transition. The name of the event (if any) causing this transition labels the arrow body. A guard expression may be added before a "/" and enclosed in square-brackets (eventName[guardExpression] ), denoting that this expression must be true for the transition to take place. If an action is performed during this transition, it is added to the label following a "/" (eventName[guardExpression]/action ).
- Thick horizontal line with either x>1 lines entering and 1 line leaving or 1 line entering and x>1 lines leaving. These denote join/fork, respectively.

According to Pilone, the only predefined guard condition is ELSE. No other examples are provided within that publication.

Another extension allows the integration of flowcharts within Harel statecharts. This extension supports the development of software that is both event driven and workflow driven.

- SCXML an XML language that provides a generic state-machine based execution environment based on Harel statecharts.
- David Harel

- Introduction to UML 2 State Machine Diagrams by Scott W. Ambler
- UML 2 State Machine Diagram Guidelines by Scott W. Ambler
- Practical Statecharts in C/C++ by Miro Samek
- Practical UML Statecharts in C/C++, 2nd Edition by Miro Samek
- Round-trip Engineering State Charts
- sinelaboreRT - generates human readable c-code from state-charts especially targeting embedded real-time systems
- Advanced State Management - video introduction to state charts and thinking in hierarchical states.

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Last updated on Wednesday October 01, 2008 at 20:08:15 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Wednesday October 01, 2008 at 20:08:15 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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