Predictable and Performant Reactive Synthesis Modulo Theories via Functional Synthesis

TL;DR

This paper introduces the first full static synthesis method for LTLt, enabling predictable, efficient reactive controllers that operate over rich theories and optimize outputs, extending classical LTL synthesis techniques.

Contribution

It extends classical LTL reactive synthesis to full static synthesis for LTLt, combining Boolean abstraction with functional synthesis for rich theories.

Findings

First full static synthesis method for LTLt

Controllers can optimize outputs for safety and minimality

Method produces predictable, deterministic programs

Abstract

Reactive synthesis is the process of generating correct controllers from temporal logic specifications. Classical LTL reactive synthesis handles (propositional) LTL as a specification language. Boolean abstractions allow reducing LTLt specifications (i.e., LTL with propositions replaced by literals from a theory calT), into equi-realizable LTL specifications. In this paper we extend these results into a full static synthesis procedure. The synthesized system receives from the environment valuations of variables from a rich theory calT and outputs valuations of system variables from calT. We use the abstraction method to synthesize a reactive Boolean controller from the LTL specification, and we combine it with functional synthesis to obtain a static controller for the original LTLt specification. We also show that our method allows responses in the sense that the controller can optimize its outputs in order to e.g., always provide the smallest safe values. This is the first full static synthesis method for LTLt, which is a deterministic program (hence predictable and efficient).