Read more
Offers a self-contained work presenting basic ideas, classical results, current state of the art and possible future directions in proof complexity.
List of contents
Introduction; Part I. Basic Concepts: 1. Concepts and problems; 2. Frege systems; 3. Sequent calculus; 4. Quantified propositional calculus; 5. Resolution; 6. Algebraic and geometric proof systems; 7. Further proof systems; Part II. Upper Bounds: 8. Basic example of the correspondence between theories and proof systems; 9. Two worlds of bounded arithmetic; 10. Up to EF via the <...> translation; 11. Examples of upper bounds and p-simulations; 12. Beyond EF via the || ... || translation; Part III. Lower Bounds: 13. R and R-like proof systems; 14. {LK}_{d + 1/2} and combinatorial restrictions; 15. F_d and logical restrictions; 16. Algebraic and geometric proof systems; 17. Feasible interpolation: a framework; 18. Feasible interpolation: applications; Part IV. Beyond Bounds: 19. Hard tautologies; 20. Model theory and lower bounds; 21. Optimality; 22. The nature of proof complexity; Bibliography; Special symbols; Index.
About the author
Jan Krajíček is Professor of Mathematical Logic in the Faculty of Mathematics and Physics at Charles University, Prague. He is a member of the Academia Europaea and of the Learned Society of the Czech Republic. He has been an invited speaker at the European Congress of Mathematicians and at the International Congresses of Logic, Methodology and Philosophy of Science.
Summary
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.
