University of Birmingham > Talks@bham > Theoretical computer science seminar > Consistency of circuit lower bounds with bounded theories

## Consistency of circuit lower bounds with bounded theoriesAdd to your list(s) Download to your calendar using vCal - Igor Carboni Oliveira (Warwick University)
- Friday 14 February 2020, 11:00-12:00
- Computer Science, The Sloman Lounge (UG).
If you have a question about this talk, please contact Dr Anupam Das. Proving that there are problems in P Can we show that a large set of techniques cannot prove that NP is easy infinitely often? Motivated by this and related questions about the interaction between mathematical proofs and computations, we investigate circuit complexity from the perspective of logic. Among other results, we prove that for any parameter k > 1 it is consistent with theory T that computational class C ⊈ i.o. k">SIZE , where (T,C) is one of the pairs: T=T12 and C=P^NP, T=S12 and C=NP, T=PV and C=P. In other words, these theories cannot establish infinitely often circuit upper bounds for the corresponding problems. This is of interest because the weaker theory PV already formalizes sophisticated arguments, such as a proof of the PCP Theorem (Pich, 2015). These consistency statements are unconditional and improve on earlier theorems of Krajicek and Oliveira (2017) and Bydzovsky and Muller (2018) on the consistency of lower bounds with PV. Joint work with Jan Bydzovsky and Jan Krajicek. https://arxiv.org/abs/1905.12935 This talk is part of the Theoretical computer science seminar series. ## This talk is included in these lists:- Computer Science Departmental Series
- Computer Science Distinguished Seminars
- Computer Science, The Sloman Lounge (UG)
- Theoretical computer science seminar
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