Reactive Synthesis Modulo Theories Using Abstraction Refinement

TL;DR

This paper introduces a synthesis method for Temporal Stream Logic with theories, extending reactive synthesis to data domains, using abstraction refinement and counterexample analysis to handle complex specifications.

Contribution

It presents a novel synthesis procedure for TSL(T) that translates specifications to LTL and refines the process through counterexample analysis, addressing the challenge of undecidability.

Findings

Successfully synthesizes non-Boolean examples

Handles theory inconsistencies in counterstrategies

Proves unrealizability when applicable

Abstract

Reactive synthesis builds a system from a specification given as a temporal logic formula. Traditionally, reactive synthesis is defined for systems with Boolean input and output variables. Recently, new theories and techniques have been proposed to extend reactive synthesis to data domains, which are required for more sophisticated programs. In particular, Temporal stream logic(TSL) (Finkbeiner et al. 2019) extends LTL with state variables, updates, and uninterpreted functions and was created for use in synthesis. We present a synthesis procedure for TSL(T), an extension of TSL with theories. Synthesis is performed using a counter-example guided synthesis loop and an LTL synthesis procedure. Our method translates TSL(T) specifications to LTL and extracts a system if synthesis is successful. Otherwise, it analyzes the counterstrategy for inconsistencies with the theory. If the counterstrategy is theory-consistent, it proves that the specification is unrealizable. Otherwise, we add temporal assumptions and Boolean predicates to the TSL(T) specification and start the next iteration of the the loop. We show that the synthesis problem for TSL (T) is undecidable. Nevertheless our method can successfully synthesize or show unrealizability of several non-Boolean examples.