# Temporal CSP

A temporal constraint satisfaction problem (TCSP) is a constraint satisfaction problem that involves a set of variables $LaTeX: \{x_1,\dots , x_n\}$ having continuous or discrete domains; each variable represents a time point. Each constraint is represented by a set of intervals $LaTeX: \{I_1, \dots , I_k\}=\{[a_1,b_1], \dots , [a_k,b_k]\}$.
A unary constraint $LaTeX: T_i$ restricts the domain of variable $LaTeX: x_i$ to the given set of intervals; that is, it represents the disjunction $LaTeX: (a_1\leq x_i\leq b_1) \vee \dots \vee >(a_k\leq x_i\leq b_k)$.
A binary constraint $LaTeX: T_{ij}$ restricts the permissible values for the distance $LaTeX: x_j-x_i$; it represents the disjunction $LaTeX: (a_1\leq x_j-x_i\leq b_1) \vee \dots \vee >(a_k\leq x_j-x_i\leq b_k)$.