Unprovability of circuit upper bounds in Cook's theory PV
We establish unconditionally that for every integer $k \geq 1$ there is a language $L \in \mbox{P}$ such that it is consistent with Cook's theory PV that $L \notin Size(n^k)$. Our argument is non-constructive and does not provide an explicit description of this language.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Logical Methods in Computer Science e.V.
2017-02-01
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| Series: | Logical Methods in Computer Science |
| Subjects: | |
| Online Access: | https://lmcs.episciences.org/3119/pdf |
| Summary: | We establish unconditionally that for every integer $k \geq 1$ there is a
language $L \in \mbox{P}$ such that it is consistent with Cook's theory PV that
$L \notin Size(n^k)$. Our argument is non-constructive and does not provide an
explicit description of this language. |
|---|---|
| ISSN: | 1860-5974 |