Automated Incremental Synthesis of Timed Automata

In this paper, we concentrate on incremental synthesis of timed automata for automatic addition of different types of bounded response properties. Bounded response – that something good will happen soon, in a certain amount of time – captures a wide range of requirements for specifying real-time and embedded systems. We show that the problem of automatic addition of a bounded response property to a given timed automaton while maintaining maximal nondeterminism is NP-hard in the size of locations of the input automaton. Furthermore, we show that by relaxing the maximality requirement, we can devise a sound and complete algorithm that adds a bounded response property to a given timed automaton, while preserving its existing universally quantified properties (e.g., MTL). This synthesis method is useful in adding properties that are later discovered as a crucial part of a system. Moreover, we show that addition of interval-bounded response, where the good thing should not happen sooner than a certain amount of time, is also NP-hard in the size of locations even without maximal nondeterminism. Finally, we show that the problems of adding bounded and unbounded response properties are both PSPACE-complete in the size of the input timed automaton.