Reactive synthesis for specifications over bounded integer domains, such as fixed-width bitvectors, is typically handled by discretization via “bit-blasting”: each bit of the bounded integer is encoded as an independent Boolean signal, and the resulting specification is solved with plain LTL synthesis tools. While bit-blasting is simple and reuses existing solvers, it destroys the arithmetic structure of the domain, and the state space explored during synthesis grows exponentially with the bitwidth, making synthesis impractical for all but the smallest domains.

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LTL Modulo Theories (LTL^T) generalizes reactive synthesis to reason about theory atoms directly rather than plain Booleans, and has been shown to scale to infinite domains, such as integers and reals, using SMT-based reasoning. Bounded domains, such as bitvectors, pose a different challenge: because the domain is finite and equipped with a specific modular and bit-level structure,



decision procedures specialized for bounded integer arithmetic may enable synthesis algorithms that avoid the cost of bit-blasting while remaining decidable and efficient.
In this internship we will explore reactive synthesis modulo bounded integer theories, such as bitvectors, using theory reasoning over the bounded domain directly rather than blasting it into individual bits, aiming for synthesis algorithms whose cost scales much more gently with the bitwidth. We will then investigate which other “simple theories” admit decidable and practically efficient synthesis procedures, with the goal of building a family of fast, specialized synthesis tools for these theories.
Applications are invited to apply for an intern position at the IMDEA Software Institute, Madrid, Spain.
Selected candidates will work with César Sánchez and an international team of graduate students and researchers focusing on formal meth

📌 Internship in Fast Synthesis Modulo Simple Theories (Pozuelo de Alarcón)
🏢 IMDEA Software Institute
📍 Pozuelo de Alarcón