AutoTW-ASP: Automatic Low-Treewidth Encoding Synthesis and Backend Routing for Neurosymbolic ASP

Neurosymbolic answer set programming (ASP) systems often achieve exact semantics only after manual encoding redesign, which makes runtime gains difficult to scale beyond expert-curated benchmarks. We present AutoTW-ASP, a hybrid exact-inference method that automates two coupled decisions: (i) whether a candidate rewrite of a grounded ASP program should be accepted under explicit semantic guards, and (ii) whether each instance should be executed with stable-model enumeration or compilation-based counting. The method combines structure-aware proxies, a guarded rewrite objective, and uncertainty-gated routing. On six benchmark families and nineteen seeds, AutoTW-ASP preserves semantic equivalence for guarded rewrites and reduces median runtime relative to fixed exact baselines, while exposing where calibration and counterexample detection remain brittle. The strongest empirical signal is exactness preservation with runtime improvement against naive exact baselines; the weakest signal is universal closure of strict threshold targets for router-envelope violations and cache counterexample recall. These bounded findings support the central claim that exact neurosymbolic optimization can be automated without relaxing stable-model correctness, while making clear which components still limit generalization.