Proving Unrealizability for Syntax-Guided Synthesis [chapter]

Qinheping Hu, Jason Breck, John Cyphert, Loris D'Antoni, Thomas Reps
2019 Lecture Notes in Computer Science  
We consider the problem of automatically establishing that a given syntax-guided-synthesis (SyGuS) problem is unrealizable (i.e., has no solution). Existing techniques have quite limited ability to establish unrealizability for general SyGuS instances in which the grammar describing the search space contains infinitely many programs. By encoding the synthesis problem's grammar G as a nondeterministic program PG, we reduce the unrealizability problem to a reachability problem such that, if a
more » ... dard program-analysis tool can establish that a certain assertion in PG always holds, then the synthesis problem is unrealizable. Our method can be used to augment existing SyGuS tools so that they can establish that a successfully synthesized program q is optimal with respect to some syntactic cost-e.g., q has the fewest possible ifthen-else operators. Using known techniques, grammar G can be transformed to generate the set of all programs with lower costs than q-e.g., fewer conditional expressions. Our algorithm can then be applied to show that the resulting synthesis problem is unrealizable. We implemented the proposed technique in a tool called nope. nope can prove unrealizability for 59/132 variants of existing linear-integer-arithmetic SyGuS benchmarks, whereas all existing SyGuS solvers lack the ability to prove that these benchmarks are unrealizable, and time out on them.
doi:10.1007/978-3-030-25540-4_18 fatcat:h5owclerpvh27fhje5bi6rwq74