  In syntax-guided synthesis (SyGuS), a synthesizer's goal is to automatically
generate a program belonging to a grammar of possible implementations that
meets a logical specification. We investigate a common limitation across
state-of-the-art SyGuS tools that perform counterexample-guided inductive
synthesis (CEGIS). We empirically observe that as the expressiveness of the
provided grammar increases, the performance of these tools degrades
significantly.
  We claim that this degradation is not only due to a larger search space, but
also due to overfitting. We formally define this phenomenon and prove
no-free-lunch theorems for SyGuS, which reveal a fundamental tradeoff between
synthesizer performance and grammar expressiveness.
  A standard approach to mitigate overfitting in machine learning is to run
multiple learners with varying expressiveness in parallel. We demonstrate that
this insight can immediately benefit existing SyGuS tools. We also propose a
novel single-threaded technique called hybrid enumeration that interleaves
different grammars and outperforms the winner of the 2018 SyGuS competition
(Inv track), solving more problems and achieving a $5\times$ mean speedup.
