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In this paper, we address the problem of the (reactive) realizability ofspecifications of theories richer than Booleans, including arithmetic theories.Our approach transforms theory specifications into purely Booleanspecifications by (1) substituting theory literals by Boolean variables, and(2) computing an additional Boolean requirement that captures the dependenciesbetween the new variables imposed by the literals. The resulting specificationcan be passed to existing Boolean off-the-shelf realizability tools, and isrealizable if and only if the original specification is realizable. The firstcontribution is a brute-force version of our method, which requires a number ofSMT queries that is doubly exponential in the number of input literals. Then,we present a faster method that exploits a nested encoding of the search forthe extra requirement and uses SAT solving for faster traversing the searchspace and uses SMT queries internally. Another contribution is a prototype inZ3-Python. Finally, we report an empirical evaluation using specificationsinspired in real industrial cases. To the best of our knowledge, this is thefirst method that succeeds in non-Boolean LTL realizability.

Boolean Abstractions for Realizability Modulo Theories (Extended version)