مورد إلكتروني
A proof complexity conjecture and the Incompleteness theorem
| العنوان: | A proof complexity conjecture and the Incompleteness theorem |
|---|---|
| بيانات النشر: | 2023-03-19 |
| تفاصيل مُضافة: | Krajicek, Jan |
| نوع الوثيقة: | Electronic Resource |
| مستخلص: | Given a sound first-order p-time theory $T$ capable of formalizing syntax of first-order logic we define a p-time function $g_T$ that stretches all inputs by one bit and we use its properties to show that $T$ must be incomplete. We leave it as an open problem whether for some $T$ the range of $g_T$ intersects all infinite NP sets (i.e. whether it is a proof complexity generator hard for all proof systems). A propositional version of the construction shows that at least one of the following three statements is true: - there is no p-optimal propositional proof system (this is equivalent to the non-existence of a time-optimal propositional proof search algorithm), - $E \not\subseteq P/poly$, - there exists function $h$ that stretches all inputs by one bit, is computable in sub-exponential time and its range $Rng(h)$ intersects all infinite NP sets. Comment: preliminary version March 2023 |
| مصطلحات الفهرس: | Computer Science - Logic in Computer Science, Mathematics - Logic, 03F20, 03F40, 68Q15, F.1.3, F.4.1, text |
| URL: | |
| الإتاحة: | Open access content. Open access content |
| أرقام أخرى: | COO oai:arXiv.org:2303.10637 1381610942 |
| المصدر المساهم: | CORNELL UNIV From OAIster®, provided by the OCLC Cooperative. |
| رقم الأكسشن: | edsoai.on1381610942 |
| قاعدة البيانات: | OAIster |
| الوصف غير متاح. |