 Transition system

A model consisting of a set $S$ of states, a transition relation $\to \subseteq S\times S$, initial states $I\subseteq S$, a set $AP$ of atomic propositions, and a label function $L:S\to 2^{AP}$ identifying which atomic propositions hold at each state. A path in a transition system follows permitted transitions. Some definitions omit labels or initial conditions; specify the convention used in each application.

A **transition system** is a mathematical model used to describe the behavior of a system in terms of states and transitions. It is particularly useful in fields such as computer science, particularly in the study of formal verification, automata theory, and modeling dynamic systems. A transition system is formally defined as a tuple \( T = (S, S_0, \Sigma, \rightarrow) \), where: - \( S \): A set of states.