1,009 research outputs found
Overfitting in Synthesis: Theory and Practice (Extended Version)
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 mean speedup.Comment: 24 pages (5 pages of appendices), 7 figures, includes proofs of
theorem
Real Hypercomputation and Continuity
By the sometimes so-called 'Main Theorem' of Recursive Analysis, every
computable real function is necessarily continuous. We wonder whether and which
kinds of HYPERcomputation allow for the effective evaluation of also
discontinuous f:R->R. More precisely the present work considers the following
three super-Turing notions of real function computability:
* relativized computation; specifically given oracle access to the Halting
Problem 0' or its jump 0'';
* encoding real input x and/or output y=f(x) in weaker ways also related to
the Arithmetic Hierarchy;
* non-deterministic computation.
It turns out that any f:R->R computable in the first or second sense is still
necessarily continuous whereas the third type of hypercomputation does provide
the required power to evaluate for instance the discontinuous sign function.Comment: previous version (extended abstract) has appeared in pp.562-571 of
"Proc. 1st Conference on Computability in Europe" (CiE'05), Springer LNCS
vol.352
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