Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider stochastic turn-based games where the winning objectives are given by formulae of the branching-time logic PCTL. These games are generally not determined and winning strategies may require memory and or randomization. Our main results concern history-dependent strategies. In particular,  show that the problem whether there exists a history-dependent winning strategy in 1frac12-player games is highly undecidable, even for objectives formulated in the Lscr(F =5/8  ,F =1 ,F >0 ,G =1 ) fragment of PCTL. On the other hand,  show that the problem becomes decidable (and in fact EXPTIME-complete) for the Lscr(F =1 ,F >0 ,G =1 ) fragment of PCTL, where winning strategies require only finite memory. This result is tight in the sense that winning strategies for Lscr(F =1 ,F >0 ,G =1 ,G >0  ) objectives may already require infinite memory
['Tomáš Brázdil', 'V. Bro!zek', 'Vojtch Forejt', 'Adam Kučera']
I am writing a research paper on a idea Stochastic Games with Branching-Time Winning Objectives
[{"from": "human", "value": "I am writing a research paper on a idea Stochastic Games with Branching-Time Winning Objectives"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider stochastic turn-based games where the winning objectives are given by formulae of the branching-time logic PCTL. These games are generally not determined and winning strategies may require memory and or randomization. Our main results concern history-dependent strategies. In particular,  show that the problem whether there exists a history-dependent winning strategy in 1frac12-player games is highly undecidable, even for objectives formulated in the Lscr(F =5/8  ,F =1 ,F >0 ,G =1 ) fragment of PCTL. On the other hand,  show that the problem becomes decidable (and in fact EXPTIME-complete) for the Lscr(F =1 ,F >0 ,G =1 ) fragment of PCTL, where winning strategies require only finite memory. This result is tight in the sense that winning strategies for Lscr(F =1 ,F >0 ,G =1 ,G >0  ) objectives may already require infinite memory"}]