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.