Transition system

This article is about transition systems as used in operational semantics. For an automata-theoretic view, see semiautomaton.

In theoretical computer science, a transition system is a concept used in the study of computation . 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.

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