Completeness of Synthesis under Realizability Assumptions using Superposition
Abstract
Program synthesis is the task of automatically deriving a program that has been specified by a user in advance. Combining automated theorem proving with program synthesis enables the automated construction of proven-to-be-correct programs, thereby ensuring software reliability. In this paper, we consider the superposition-based calculus extended to support synthesis of recursion-free programs allowing reasoning with uncomputable symbols. We present cases where the calculus fails and refine it to solve them. We prove that the refined calculus is sound. Finally, we also prove completeness in the following sense: if at least one computable program satisfying the given specification exists, we show that the modified calculus finds one.
Cite
@article{arxiv.2605.19683,
title = {Completeness of Synthesis under Realizability Assumptions using Superposition},
author = {Márton Hajdu and Petra Hozzová and Laura Kovács and Eva Maria Wagner},
journal= {arXiv preprint arXiv:2605.19683},
year = {2026}
}
Comments
to be published in IJCAR 2026