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NP search problems in low fragments of bounded arithmetic
NP search problems in low fragments of bounded arithmetic...
BA - Obecná matematika
- 2007 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
A note on conservativity relations among bounded arithmetic theories.
We give a new non-conservativity result for bounded arithmetic.
BA - Obecná matematika
- 2002 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Prague Bounded Arithmetic Workshop 2017
Bounded arithmetic is an area in logic that is closely related to computational complexity. It studies weak fragments of Peano Arithmetic associated with complexity classes. The aim is to capture the reasoning that only use...
Pure mathematics
- 2017 •
- W
Rok uplatnění
W - Uspořádání workshopu
Approximate counting by hashing in bounded arithmetic
We show how to formalize approximate counting via hash functions in subsystems of bounded arithmetic, using variants of the weak pigeonhole principle. We discuss several appications, including a proof of the tournament principle, an...
BA - Obecná matematika
- 2009 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
The strength of sharply bounded induction
We prove that the sharply bounded arithmetic T... in a language containing the function symbol [...] (often denoted by MSP) is equivalent to PV1....
BA - Obecná matematika
- 2006 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
LOGICAL STRENGTH OF COMPLEXITY THEORY AND A FORMALIZATION OF THE PCP THEOREM IN BOUNDED ARITHMETIC
We present several known formalizations of theorems from computational complexity in bounded arithmetic and formalize the PCP theorem in the theory PV1 (no formalization of this theorem was known). This includes a formalization of t...
BA - Obecná matematika
- 2015 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Approximate counting in bounded arithmetic
We develop approximate counting of sets definable by Boolean circuits in bounded arithmetic using the dual weak pigeonhole principle (dWPHP(PV)), as a generalization of results from [15]. We discuss applications to formalization of ...
BA - Obecná matematika
- 2007 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
On the weak pigeonhole principle.
We investigate the proof complexity, in (existensions of) resolution and in bounded arithmetic, of the weak pigeonhole principle and of Ramsey theorem of WPHP in fragments of bounded arithmetic and cryptographic as...
BA - Obecná matematika
- 2001 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
A sorting network in bounded arithmetic
We formalize the construction of Paterson?s variant of the Ajtai?Komlós?Szemerédi sorting network of logarithmic depth in the bounded arithmetical theory VNC1 (an extension of VNC1), under the assumption of the existence of suitable...
BA - Obecná matematika
- 2011 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
On theories of bounded arithmetic for NC1
We develop an arithmetical theory VNC1 and its variant VNC1, corresponding to "slightly nonuniform" NC1. Our theories sit between VNC1 and VL, and allow evaluation of log-depth bounded fan-in circuits under limited conditions. Propo...
BA - Obecná matematika
- 2011 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
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