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Concept
State diagram
Summary
A state diagram is a type of diagram used in computer science and related fields to describe the behavior of systems. State diagrams require that the system described is composed of a finite number of states; sometimes, this is indeed the case, while at other times this is a reasonable abstraction. Many forms of state diagrams exist, which differ slightly and have different semantics.
State diagrams are used to give an abstract description of the behavior of a system. This behavior is analyzed and represented by a series of events that can occur in one or more possible states. Hereby "each diagram usually represents objects of a single class and track the different states of its objects through the system".
State diagrams can be used to graphically represent finite-state machines (also called finite automata). This was introduced by Claude Shannon and Warren Weaver in their 1949 book The Mathematical Theory of Communication. Another source is Taylor Booth in his 1967 book Sequential Machines and Automata Theory. Another possible representation is the state-transition table.
A classic form of state diagram for a finite automaton (FA) is a directed graph with the following elements (Q, Σ, Z, δ, q0, F):
Vertices Q: a finite set of states, normally represented by circles and labeled 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 ordered pairs of input symbols and states onto output symbols, denoted mathematically as ω : Σ × Q→ Z.
Edges δ: represent transitions from one state to another 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 to the next state. This mapping describes the state transition that is to occur on input of a particular symbol.
Official source
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