Logical Foundations of Proof Complexity

Logical Foundations Of Proof Complexity


This 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.



  • Condition: New
    HPB condition ratings
    • New: Item is brand new, unused and unmarked, in flawless condition.
    • Fine/Like New (F): No defects, little usage. May show remainder marks. Older books may show minor flaws.
    • Very Good (VG): Shows some signs of wear and is no longer fresh. Attractive. Used textbooks do not come with supplemental materials.
    • Good (G): Average used book with all pages present. Possible loose bindings, highlighting, cocked spine or torn dust jackets. Used textbooks do not come with supplemental materials.
    • Fair (FR): Obviously well-worn, but no text pages missing. May be without endpapers or title page. Markings do not interfere with readability. Used textbooks do not come with supplemental materials.
    • Poor (P): All text is legible but may be soiled and have binding defects. Reading copies and binding copies fall into this category. Used textbooks do not come with supplemental materials.
    Conditions Guide
  • Format: Hardcover
  • Sold by: HPB.com
  • Seller rating:
  • Language: English
  • Publisher: Cambridge Univ Pr
  • ISBN-13: 9780521517294
  • ISBN: 052151729X
  • Publication Year: 2010
  • Edition: 1


Loading...
Loading marketplace...
HPB condition ratings
  • New: Item is brand new, unused and unmarked, in flawless condition.
  • Fine/Like New (F): No defects, little usage. May show remainder marks. Older books may show minor flaws.
  • Very Good (VG): Shows some signs of wear and is no longer fresh. Attractive. Used textbooks do not come with supplemental materials.
  • Good (G): Average used book with all pages present. Possible loose bindings, highlighting, cocked spine or torn dust jackets. Used textbooks do not come with supplemental materials.
  • Fair (FR): Obviously well-worn, but no text pages missing. May be without endpapers or title page. Markings do not interfere with readability. Used textbooks do not come with supplemental materials.
  • Poor (P): All text is legible but may be soiled and have binding defects. Reading copies and binding copies fall into this category. Used textbooks do not come with supplemental materials.
Conditions Guide
HPB condition ratings
  • New: Mint condition or still sealed (SS). Absolutely perfect in every way. New.
  • Fine/Like New (EX): No defects, little sign of use, well cared for. Plays perfectly. Close to new. Not necessarily sealed or unused, but close. Could be an unopened promotional or cut item. Sometimes called: mint-minus.
  • Very Good (VG): Will show some signs that it was played and otherwise handled by a previous owner who took good care of it.
  • Good (G): Attractive and well cared for, but no longer fresh. Minor signs of wear, scuffing or scratching, but will play almost perfectly. For vinyl: barely detectable crackles or pops.
  • Fair (FR): This item is in okay condition. For vinyl: good is not so good and the record may have low level crackles or pops when playing. CD: one or more tracks may skip.
  • Poor (P): Obviously well-worn and handled. Most vinyl collectors will not buy good or below, but some tracks on CD or vinyl will play.
Conditions Guide
HPB condition ratings
  • New: This movie is unopened and brand new.
  • Fine/Like New (EX): Near new. No defects, little sign of use. Plays perfectly. Not necessarily sealed or unused, but close. No skipping; no fuzzy or snowy frames in VHS.
  • Very Good (VG): Attractive and well cared for but no longer fresh. Minor signs of wear, but will play almost perfectly. For VHS: barely detectable distortion or very few fuzzy or snowy frames.
  • Good (G): This item is in okay condition and basically works well. There may be some minor distortion on VHS tape; slight scratching or wear on DVD.
  • Fair (FR): Basically plays, but may be obviously well-worn with some scratching or tape distortion.
  • Poor (P): Disc or tape is intact, but may be scratched or stretched. There may be skips or distortion or product defects.
Conditions Guide
×