The Complexity of LTL Rational Synthesis ORNA KUPFERMAN and NOAM SHENWALD present a study on the complexity of LTL rational synthesis, a method for automatically constructing reactive systems that meet their specifications in all rational environments. Rational synthesis assumes that environment components have their own objectives and act to achieve them. The authors analyze the complexity of this synthesis process, particularly when the environment's objectives are given by Linear Temporal Logic (LTL) formulas. The study contributes three main aspects: tightening known upper bounds for rational synthesis in various settings, providing a parametric complexity analysis that considers the game graph, system objectives, and environment objectives, and generalizing rational synthesis by incorporating hostile players and combining cooperative and non-cooperative approaches. The paper explores the complexity of rational synthesis (RS), distinguishing between cooperative rational synthesis (CRS) and non-cooperative rational synthesis (NRS). CRS assumes environment players are cooperative and can be suggested strategies, while NRS assumes they are non-cooperative and cannot be suggested strategies. The authors show that RS is not harder than traditional synthesis, and that the complexity of RS is closely related to the complexity of traditional synthesis. The paper also introduces a generalization of RS that allows for hostile players, who are rational players whose objectives complement the system's objective. The authors analyze the complexity of RS in both turn-based and concurrent settings, and show that the complexity of RS is doubly exponential in the size of the objectives, similar to traditional synthesis of the conjunction of objectives. The paper provides a detailed analysis of the complexity of CRS and NRS, showing that CRS is EXPTIME-hard and NRS is 2EXPTIME-hard. The authors also show that the complexity of RS is influenced by the number of players and the structure of the game graph. The study concludes that the complexity of RS is closely related to the complexity of traditional synthesis, and that the introduction of rationality into the game makes the problem more complex.The Complexity of LTL Rational Synthesis ORNA KUPFERMAN and NOAM SHENWALD present a study on the complexity of LTL rational synthesis, a method for automatically constructing reactive systems that meet their specifications in all rational environments. Rational synthesis assumes that environment components have their own objectives and act to achieve them. The authors analyze the complexity of this synthesis process, particularly when the environment's objectives are given by Linear Temporal Logic (LTL) formulas. The study contributes three main aspects: tightening known upper bounds for rational synthesis in various settings, providing a parametric complexity analysis that considers the game graph, system objectives, and environment objectives, and generalizing rational synthesis by incorporating hostile players and combining cooperative and non-cooperative approaches. The paper explores the complexity of rational synthesis (RS), distinguishing between cooperative rational synthesis (CRS) and non-cooperative rational synthesis (NRS). CRS assumes environment players are cooperative and can be suggested strategies, while NRS assumes they are non-cooperative and cannot be suggested strategies. The authors show that RS is not harder than traditional synthesis, and that the complexity of RS is closely related to the complexity of traditional synthesis. The paper also introduces a generalization of RS that allows for hostile players, who are rational players whose objectives complement the system's objective. The authors analyze the complexity of RS in both turn-based and concurrent settings, and show that the complexity of RS is doubly exponential in the size of the objectives, similar to traditional synthesis of the conjunction of objectives. The paper provides a detailed analysis of the complexity of CRS and NRS, showing that CRS is EXPTIME-hard and NRS is 2EXPTIME-hard. The authors also show that the complexity of RS is influenced by the number of players and the structure of the game graph. The study concludes that the complexity of RS is closely related to the complexity of traditional synthesis, and that the introduction of rationality into the game makes the problem more complex.