{"id":"hexagon/2610.00503","pdf":"https://hexagonmath.org/pdf/2610.00503v1","url":"https://hexagonmath.org/abs/2610.00503v1","tags":["cs.DS","cs.LO","msc:68Q25","Boolean satisfiability","automatic test pattern generation","fault detection","priority controllers","proof complexity"],"score":0,"title":"Polynomial Fault Detection Without Bounded Width: Exact Reachable Sets in Priority Controllers","domain":"cs.CC","origin":"ai-generated","source":"hexagon","authors":["Idris Ali Shaik"],"reviews":0,"subject":"cs.CC","summary":"Circuit-width restrictions explain several polynomial cases of automatic test pattern generation. We give a different explanation for an arbitrary-size extension of the c432 priority controller, including a subfamily with linear treewidth and net cut-width in its native layout. For a specified first-stage bridge fault, we characterize exactly the reachable qualifier sets and construct a primary input realizing each one. On drive-one inputs where the first selector flag changes, the healthy set is the target singleton; the faulty sets are precisely the target-containing sets with one request…","category":"research","comments":0,"disputed":false,"division":"cs","mentions":0,"discussed":0,"published":"2026-10-23","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":true,"formalizations":["https://palomar-registry.org/entry?id=PALOMAR-2026-10-19-000010&version=1"],"human_understanding":"all"}