Transition system
abstract machine used in the study of computation
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. If the label set is a singleton, the system is essentially unlabeled, and a simpler definition that omits the labels is possible.
Transition systems coincide mathematically with abstract rewriting systems (as explained further in this article) and directed graphs. They differ from finite-state automata in several ways:
The set of states is not necessarily finite, or even countable.
The set of transitions is not necessarily finite, or even countable.
No "start" state or "final" states are given.
Transition systems can be represented as directed graphs.
Formal definition
Formally, a transition system is a pair
(
S
,
T
)
{\displaystyle (S,T)}
where
S
{\displaystyle S}
is a set of states and
T
{\displaystyle T}
, the transition relation, is a subset of
S
×
S
{\displaystyle S\times S}
.
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