Condition Synthesis Realizability via Constrained Horn Clauses

Condition synthesis takes a program in which some of the conditions in conditional branches are missing, and a specification, and automatically infers conditions to fill-in the holes such that the program meets the specification. In this paper, we propose CoSyn, an algorithm for determining the realizability of a condition synthesis problem, with an emphasis on proving unrealizability efficiently. We use the novel concept of a doomed initial state, which is an initial state that can reach an error state along every run of the program. For a doomed initial state σ, there is no way to make the program safe by forcing σ (via conditions) to follow one computation or another. CoSyn checks for the existence of a doomed initial state via a reduction to Constrained Horn Clauses (CHC). We implemented CoSyn in SeaHorn using Spacer as the CHC solver and evaluated it on multiple examples. Our evaluation shows that CoSyn outperforms the state-of-the-art syntax-guided tool Cvc5 in proving both realizability and unrealizability. We also show that joining forces of CoSyn and Cvc5 outperforms Cvc5 alone, allowing to solve more instances, faster.