Transition system¶
In theoretical computer science, a transition system is a state machine that may have infinite states.
Core Idea¶
Transition system is treated here as the recurring computerscienceandinformation identity summarized by this source-grounded definition: In theoretical computer science, a transition system is a state machine that may have infinite states. In theoretical computer science, a transition system is a state machine that may have infinite states. It is used to describe the potential behavior of discrete systems. It consists of states and transitions between states, which may be labeled with labels chosen from a set; the same label may appear on more than one transition.
Scope of Application¶
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Coalgebra formulation. Labelled state transition systems on S with labels from \Lambda correspond one-to-one with functions S \to \mathcal{P}(\Lambda \times S) , where \mathcal{P} is the (covariant) powerset functor.
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Extensions. In model checking, a transition system is sometimes defined to include an additional labeling function for the states as well, resulting in a notion that encompasses that of Kripke structure.
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Extensions. Action languages are extensions of transition systems, adding a set of fluents F, a set of values V, and a function that maps F × S to V.
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Documented setting. It is used to describe the potential behavior of discrete systems.
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Formal definition. Formally, a transition system is a pair (S, T) where S is a set of states and T , the transition relation, is a subset of S \times S .
Clarity¶
A clear use of Transition system names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In theoretical computer science, a transition system is a state machine that may have infinite states. The strongest recognition evidence in the frozen account is: It consists of states and transitions between states, which may be labeled with labels chosen from a.
Manages Complexity¶
Transition system compresses multiple computerscienceandinformation details into a stable diagnostic relation. The source shows both the central mechanism—some are simple, such as observing that a labelled transition system where the set of labels consists of only one element is equivalent to an unlabelled transition system.—and the practical consequence—we say that there is a transition from state p to state q if (p, q) \in T , and denote.
Abstract Reasoning¶
- Type the carrier. Identify the computerscienceandinformation entities to which the claim applies.
- State the relation. Use the source-grounded identity: In theoretical computer science, a transition system is a state machine that may have infinite states.
- Check operation and conditions. In a transition system one is interested in interpreting the labels as actions, whereas in an abstract rewriting system the focus is on how objects may be transformed (rewritten) into others.
- Demand recognition evidence.
Knowledge Transfer¶
Within the home domain. Knowledge about Transition system transfers literally when a new case preserves the same carrier type, relation, and recognition test. Labelled state transition systems on S with labels from \Lambda correspond one-to-one with functions S \to \mathcal{P}(\Lambda \times S) , where \mathcal{P} is the (covariant) powerset functor. In model checking, a transition system is sometimes defined to include an additional labeling function for the states as well, resulting in a notion that encompasses that of Kripke structure. Beyond the home domain. No.
Relationships to Other Abstractions¶
Current abstraction Transition system Domain-specific
Parents (1) — more general patterns this builds on
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Transition system is a kind of Formal Model Domain-specific
It is a canonical formal state-transition model.
Hierarchy path (1) — routes to 1 parentless root
- Transition system → Formal Model → Representation → Abstraction
Neighborhood in Abstraction Space¶
Transition system sits in a sparse region of the domain-specific corpus (64th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Unclustered & Miscellaneous (2551 abstractions)
Nearest neighbors
- Discrete system — 0.85
- Data element — 0.84
- Typing Environment — 0.84
- Single Vegetative Obstruction Model — 0.84
- Worker–machine activity chart — 0.84
Computed from structural-signature embeddings · 2026-10-08