000			02886nam a2200373 i 4500
001			CR9781108242066
003			UkCbUP
005			20240916201308.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			170102s2019||||enk o ||1 0|eng|d
020			_a9781108242066 (ebook)
020			_z9781108416849 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA9.54 _b.K72 2019
082	0	0	_a511.3/6 _223
100	1		_aKrajíček, Jan, _eauthor.
245	1	0	_aProof complexity / _cJan Krajíček.
264		1	_aCambridge : _bCambridge University Press, _c2019.
300			_a1 online resource (xiv, 516 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aEncyclopedia of mathematics and its applications ; _v170
500			_aTitle from publisher's bibliographic system (viewed on 22 Mar 2019).
505	0		_aConcepts 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.
520			_aProof 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.
650		0	_aProof theory.
650		0	_aComputational complexity.
776	0	8	_iPrint version: _z9781108416849
830		0	_aEncyclopedia of mathematics and its applications ; _v170.
856	4	0	_uhttps://doi.org/10.1017/9781108242066
942			_2ddc _cEB
999			_c9441 _d9441