Structural Synthesis for GXW Specifications

TL;DR

This paper introduces GXW, a fragment of linear temporal logic for synthesizing control software in safety-critical systems, offering a scalable, structured approach that ensures traceability and handles industrial-sized problems efficiently.

Contribution

The paper presents a novel structural synthesis method for GXW specifications, enabling efficient, traceable control code generation for safety-critical applications.

Findings

GXW synthesis scales well to industrial-sized problems

The approach ensures traceability between requirements and code

Synthesis operates in PSPACE, more efficient than full LTL synthesis

Abstract

We define the GXW fragment of linear temporal logic (LTL) as the basis for synthesizing embedded control software for safety-critical applications. Since GXW includes the use of a weak-until operator we are able to specify a number of diverse programmable logic control (PLC) problems, which we have compiled from industrial training sets. For GXW controller specifications, we develop a novel approach for synthesizing a set of synchronously communicating actor-based controllers. This synthesis algorithm proceeds by means of recursing over the structure of GXW specifications, and generates a set of dedicated and synchronously communicating sub-controllers according to the formula structure. In a subsequent step, 2QBF constraint solving identifies and tries to resolve potential conflicts between individual GXW specifications. This structural approach to GXW synthesis supports traceability between requirements and the generated control code as mandated by certification regimes for safety-critical software. Synthesis for GXW specifications is in PSPACE compared to 2EXPTIME-completeness of full-fledged LTL synthesis. Indeed our experimental results suggest that GXW synthesis scales well to industrial-sized control synthesis problems with 20 input and output ports and beyond.