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

TL;DR

This paper presents a method for synthesizing memory-efficient real-time controllers for safety objectives in timed automaton games, reducing memory requirements from exponential to linear in the number of clocks.

Contribution

It introduces a new approach to synthesize controllers that only need system clocks and linear memory, improving previous exponential bounds and addressing open questions about region strategies.

Findings

Memory of size (3*|C|+1 + log(|C|+1)) bits suffices for winning strategies.

Controllers can be designed without requiring internal infinitely precise clocks.

Region strategies for safety objectives do require memory, as shown by a counterexample.

Abstract

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.