Alternating-time temporal logic

Two alternating-time temporal logic, ATL and ATL*, were developed which depended on the arbitrary nesting of selective path quantifiers and temporal operators. Alternating-time logics are natural specification languages for open systems. Both the alternating-time temporal logic offered selective quantification over the possible outcome paths of the games. It was observed that the model checking complexity of ATL was linear in size of the game structure and length of the formula, while that of ATL* is closely related to the synthesis problem for linear-time formulas.