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Hardcover ISBN:  9780821805770 
Product Code:  DIMACS/39 
List Price:  $84.00 
MAA Member Price:  $75.60 
AMS Member Price:  $67.20 
eBook ISBN:  9781470439972 
Product Code:  DIMACS/39.E 
List Price:  $79.00 
MAA Member Price:  $71.10 
AMS Member Price:  $63.20 
Hardcover ISBN:  9780821805770 
eBook ISBN:  9781470439972 
Product Code:  DIMACS/39.B 
List Price:  $163.00 $123.50 
MAA Member Price:  $146.70 $111.15 
AMS Member Price:  $130.40 $98.80 

Book DetailsDIMACS  Series in Discrete Mathematics and Theoretical Computer ScienceVolume: 39; 1998; 320 ppMSC: Primary 03; 68;
Questions of mathematical proof and logical inference have been a significant thread in modern mathematics and have played a formative role in the development of computer science and artificial intelligence. Research in proof complexity and feasible theories of arithmetic aims at understanding not only whether logical inferences can be made, but also what resources are required to carry them out. Understanding the resources required for logical inferences has major implications for some of the most important problems in computational complexity, particularly the problem of whether NP is equal to coNP. In addition, these have important implications for the efficiency of automated reasoning systems.
The last dozen years have seen several breakthroughs in the study of these resource requirements. Papers in this volume represent the proceedings of the DIMACS workshop on “Feasible Arithmetics and Proof Complexity” held in April 1996 at Rutgers University in New Jersey as part of the DIMACS Institute's Special Year on Logic and Algorithms.
This book brings together some of the most recent work of leading researchers in proof complexity and feasible arithmetic reflecting many of these advances. It covers a number of aspects of the field, including lower bounds in proof complexity, witnessing theorems and proof systems for feasible arithmetic, algebraic and combinatorial proof systems, interpolation theorems, and the relationship between proof complexity and Boolean circuit complexity.
Copublished with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1–7 were copublished with the Association for Computer Machinery (ACM).
ReadershipGraduate students and research mathematicians interested in mathematical logic and foundations.

Table of Contents

Chapters

Plausibly hard combinatorial tautologies

More on the relative strength of counting principles

Ranking arithmetic proofs by implicit ramification

Lower bounds on Nullstellensatz proofs via designs

Relating the provable collapse of $\mathbf P$ to ${\mathbf NC}^1$ and the power of logical theories

On $PHP$, $st$connectivity, and odd charged graphs

Descriptive complexity and the $W$ hierarchy

Lower bounds on sizes of cutting plane proofs for modular coloring principles

Equational calculi and constant depth propositional proofs

Exponential lower bounds for semantic resolution

Bounded arithmetic: Comparison of Buss’ witnessing method and Sieg’s Herbrand analysis

Towards lower bounds for boundeddepth Frege proofs with modular connectives

A quantifierfree theory based on a string algebra for $NC^1$

A propositional proof system for $R^i_2$

Algebraic models of computation and interpolation for algebraic proof systems

Selfreflection principles and NPhardness


Reviews

The volume adequately reflects current interests and trends in the area of feasible proofs, and many papers in it simply define the current state of the art there. Its importance for everybody interested in this beautiful theory, be it the experienced researcher, a beginner, or just a curious outsider, can hardly be overstated.
Journal of Symbolic Logic


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Questions of mathematical proof and logical inference have been a significant thread in modern mathematics and have played a formative role in the development of computer science and artificial intelligence. Research in proof complexity and feasible theories of arithmetic aims at understanding not only whether logical inferences can be made, but also what resources are required to carry them out. Understanding the resources required for logical inferences has major implications for some of the most important problems in computational complexity, particularly the problem of whether NP is equal to coNP. In addition, these have important implications for the efficiency of automated reasoning systems.
The last dozen years have seen several breakthroughs in the study of these resource requirements. Papers in this volume represent the proceedings of the DIMACS workshop on “Feasible Arithmetics and Proof Complexity” held in April 1996 at Rutgers University in New Jersey as part of the DIMACS Institute's Special Year on Logic and Algorithms.
This book brings together some of the most recent work of leading researchers in proof complexity and feasible arithmetic reflecting many of these advances. It covers a number of aspects of the field, including lower bounds in proof complexity, witnessing theorems and proof systems for feasible arithmetic, algebraic and combinatorial proof systems, interpolation theorems, and the relationship between proof complexity and Boolean circuit complexity.
Copublished with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1–7 were copublished with the Association for Computer Machinery (ACM).
Graduate students and research mathematicians interested in mathematical logic and foundations.

Chapters

Plausibly hard combinatorial tautologies

More on the relative strength of counting principles

Ranking arithmetic proofs by implicit ramification

Lower bounds on Nullstellensatz proofs via designs

Relating the provable collapse of $\mathbf P$ to ${\mathbf NC}^1$ and the power of logical theories

On $PHP$, $st$connectivity, and odd charged graphs

Descriptive complexity and the $W$ hierarchy

Lower bounds on sizes of cutting plane proofs for modular coloring principles

Equational calculi and constant depth propositional proofs

Exponential lower bounds for semantic resolution

Bounded arithmetic: Comparison of Buss’ witnessing method and Sieg’s Herbrand analysis

Towards lower bounds for boundeddepth Frege proofs with modular connectives

A quantifierfree theory based on a string algebra for $NC^1$

A propositional proof system for $R^i_2$

Algebraic models of computation and interpolation for algebraic proof systems

Selfreflection principles and NPhardness

The volume adequately reflects current interests and trends in the area of feasible proofs, and many papers in it simply define the current state of the art there. Its importance for everybody interested in this beautiful theory, be it the experienced researcher, a beginner, or just a curious outsider, can hardly be overstated.
Journal of Symbolic Logic