Efficient Reactive Synthesis

TL;DR

This paper introduces a polynomial-time algorithm for deciding realizability of the GXU fragment of linear temporal logic, enabling efficient synthesis of reactive control programs for embedded systems.

Contribution

It presents the first polynomial-time decision procedure for GXU realizability, linking it to 2QBF satisfiability and proposing methods to infer environment assumptions.

Findings

Realizability for GXU is equivalent to solving certain 2QBF problems.

The algorithm operates in cubic time relative to specification size.

Stronger environment assumptions can be extracted for unrealizable specifications.

Abstract

Our main result is a polynomial time algorithm for deciding realizability for the GXU sublogic of linear temporal logic. This logic is particularly suitable for the specification of embedded control systems, and it is more expressive than GR(1). Reactive control programs for GXU specifications are represented as Mealy machines, which are extended by the monitoring of input events. Now, realizability for GXU specifications is shown to be equivalent to solving a certain subclass of 2QBF satisfiability problems. These logical problems can be solved in cubic time in the size of GXU specifications. For unrealizable GXU specifications, stronger environment assumptions are mined from failed consistency checks based on Padoa's characterization of definability and Craig interpolation.