000 02292nam a22003858i 4500
001 CR9780511676277
003 UkCbUP
005 20200124160238.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 100212s2010||||enk o ||1 0|eng|d
020 _a9780511676277 (ebook)
020 _z9780521517294 (hardback)
020 _z9781107694118 (paperback)
040 _aUkCbUP
_beng
_erda
_cUkCbUP
050 0 0 _aQA267.7
_b.C695 2010
082 0 0 _a511.3/6
_222
100 1 _aCook, Stephen,
_d1948-
_eauthor.
245 1 0 _aLogical foundations of proof complexity /
_cStephen Cook, Phuong Nguyen.
264 1 _aCambridge :
_bCambridge University Press,
_c2010.
300 _a1 online resource (xv, 479 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aPerspectives in logic
500 _aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
520 _aThis book treats bounded arithmetic and propositional proof complexity from the point of view of computational complexity. The first seven chapters include the necessary logical background for the material and are suitable for a graduate course. Associated with each of many complexity classes are both a two-sorted predicate calculus theory, with induction restricted to concepts in the class, and a propositional proof system. The complexity classes range from AC0 for the weakest theory up to the polynomial hierarchy. Each bounded theorem in a theory translates into a family of (quantified) propositional tautologies with polynomial size proofs in the corresponding proof system. The theory proves the soundness of the associated proof system. The result is a uniform treatment of many systems in the literature, including Buss's theories for the polynomial hierarchy and many disparate systems for complexity classes such as AC0, AC0(m), TC0, NC1, L, NL, NC, and P.
650 0 _aComputational complexity.
650 0 _aProof theory.
650 0 _aLogic, Symbolic and mathematical.
700 1 _aNguyen, Phuong,
_d1977-
_eauthor.
776 0 8 _iPrint version:
_z9780521517294
830 0 _aPerspectives in logic.
856 4 0 _uhttps://doi.org/10.1017/CBO9780511676277
999 _c518266
_d518264