Reachability games with relaxed energy constraints

We study games with reachability objectives under energy constraints. first prove that strict constraints (either only lower-bound constraint or interval constraint), those are LOGSPACE -equivalent to the same but without objective (i.e., for infinite runs). then consider two relaxations of upper-bound (while keeping strict): in one, called weak upper bound , is absorbing i.e., when reached, extra not stored; second we allow temporary violations bound, imposing limits on number amount violations. considering require memory, can still be solved polynomial-time one-player arenas; they co NP two-player setting. Allowing bounded makes problem PSPACE -complete arenas and EXPTIME players. address existence bounds a given arena. show objectives, simpler than game itself, conversely games, harder. • objectives. several notions as define new class soft violation this bound. compare their counterparts. decide whether an which winning exists.