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lgli/Krajíček, Jan (2019), Proof Complexity (Encyclopedia of Mathematics and its Applications).pdf
Proof Complexity (Encyclopedia of Mathematics and its Applications, Series Number 170) 🔍
Jan Krajíček Cambridge University Press (Virtual Publishing), Encyclopedia of mathematics and its applications, 170, Cambridge, 2019
English [en] · PDF · 2.8MB · 2019 · 📘 Book (non-fiction) · 🚀/lgli/lgrs/zlib · Save
description
"Proof complexity is a rich subject drawing on methods from logic, combinatorics, algebra and computer science. This self-contained book presents the basic concepts, classical results, current state of the art and possible future directions in the field. It stresses a view of proof complexity as a whole entity rather than a collection of various topics held together loosely by a few notions, and it favors more generalizable statements. Lower bounds for lengths of proofs, often regarded as the key issue in proof complexity, are of course covered in detail. However, upper bounds are not neglected: this book also explores the relations between bounded arithmetic theories and proof systems and how they can be used to prove upper bounds on lengths of proofs and simulations among proof systems. It goes on to discuss topics that transcend specific proof systems, allowing for deeper understanding of the fundamental problems of the subject"-- Read more...
Alternative filename
lgrsnf/Krajíček, Jan (2019), Proof Complexity (Encyclopedia of Mathematics and its Applications).pdf
Alternative author
Krajíček, Jan
Alternative publisher
Cambridge Library Collection
Alternative edition
Encyclopedia of mathematics and its applications, Cambridge, United Kingdom, 2019
Alternative edition
Cambridge University Press, Cambridge, United Kingdom, 2019
Alternative edition
United Kingdom and Ireland, United Kingdom
Alternative edition
1, FR, 2019
metadata comments
0
metadata comments
lg2347952
Alternative description
"Proof complexity is a rich subject drawing on methods from logic, combinatorics, algebra and computer science. This self-contained book presents the basic concepts, classical results, current state of the art and possible future directions in the field. It stresses a view of proof complexity as a whole entity rather than a collection of various topics held together loosely by a few notions, and it favors more generalizable statements. Lower bounds for lengths of proofs, often regarded as the key issue in proof complexity, are of course covered in detail. However, upper bounds are not neglected: this book also explores the relations between bounded arithmetic theories and proof systems and how they can be used to prove upper bounds on lengths of proofs and simulations among proof systems. It goes on to discuss topics that transcend specific proof systems, allowing for deeper understanding of the fundamental problems of the subject"-- Provided by publisher
Alternative description
Concepts and problems --
Frege systems --
Sequent calculus --
Quantifed propositional calculus --
Resolution --
Algebraic and geometric proof systems --
Further proof systems --
Basic example of the correspondence --
Two worlds of bounded arithmetic --
Up to EF via the <
...>
translation --
Examples of upper bounds and p-simulations --
Beyond EF via the || ... || translation --
R and R-like proof systems --
LKD+1/2 and combinatorial restrictions --
Fd and logical restrictions --
Algebraic and geometric proof systems --
Feasible interpolation: a framework --
Feasible interpolation: applications --
Hard tautologies --
Model theory and lower bounds --
Optimality --
The nature of proof complexity.
Alternative description
Proof complexity is a rich subject drawing on methods from logic, combinatorics, algebra and computer science. This self-contained book presents the basic concepts, classical results, current state of the art and possible future directions in the field. Suitable for doctoral students and researchers in mathematics and theoretical computer science.
date open sourced
2019-04-06
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