# Reactive Synthesis Modulo Theories Using Abstraction Refinement

arXiv: https://arxiv.org/abs/2108.00090 · HTML: https://mlsanity.com/paper/2108.00090/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jul 2021.

## Built on by (most cited first, 3 of 3)

- [Shield Synthesis for LTL Modulo Theories](https://mlsanity.com/paper/2406.04184/) (2024)
- [Predictable and Performant Reactive Synthesis Modulo Theories via Functional Synthesis](https://mlsanity.com/paper/2407.09348/) (2024)
- [Research Vision: Multi-Agent Path Planning for Cops And Robbers Via Reactive Synthesis](https://mlsanity.com/paper/2503.11475/) (2025)

## Abstract (arXiv)

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.