Synthesis of Memory-Efficient Real-Time Controllers for Safety Objectives (Full Version)

We study synthesis of controllers for real-time systems, where the objective is to stay in a given safe set. The problem is solved by obtaining winning strategies in concurrent two-player \emph{timed automaton games} with safety objectives. To prevent a player from winning by blocking time, we restrict each player to strategies that ensure that the player cannot be responsible for causing a zeno run. We construct winning strategies for the controller which require access only to (1) the system clocks (thus, controllers which require their own internal infinitely precise clocks are not necessary), and (2) a linear (in the number of clocks) number of memory bits. Precisely, we show that a memory of size $\big(3\cdot|C|+1 + \lg(|C|+1)\big)$ bits suffices for winning controller strategies for safety objectives, where $C$ is the set of clocks of the timed automaton game, significantly improving the previous known exponential bound. We also settle the open question of whether \emph{region} strategies for controllers require memory for safety objectives by showing with an example that region strategies do require memory for safety objectives.