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Proof Complexity
Offers a self-contained work presenting basic ideas, classical results, current state of the art and possible future directions in proof complexity.
Bounded Arithmetic, Propositional Logic and Complexity Theory
Discusses the deep connections between logic and complexity theory, and lists a number of intriguing open problems.
Forcing with Random Variables and Proof Complexity
This book introduces a new approach to building models of bounded arithmetic, with techniques drawn from recent results in computational complexity. Propositional proof systems and bounded arithmetics are closely related. In particular, proving lower bounds on the lengths of proofs in propositional proof systems is equivalent to constructing certain extensions of models of bounded arithmetic. This offers a clean and coherent framework for thinking about lower bounds for proof lengths, and it has proved quite successful in the past. This book outlines a brand new method for constructing models of bounded arithmetic, thus for proving independence results and establishing lower bounds for proof lengths. The models are built from random variables defined on a sample space which is a non-standard finite set and sampled by functions of some restricted computational complexity. It will appeal to anyone interested in logical approaches to fundamental problems in complexity theory.
Automata, Languages and Programming
This book constitutes the refereed proceedings of the 31st International Colloquium on Automata, Languages and Programming, ICALP 2004, held in Turku, Finland, in July 2004. The 97 revised full papers presented together with abstracts of 6 invited talks were carefully reviewed and selected from 379 submissions. The papers address all current issues in theoretical computer science including algorithms, automata, complexity, cryptography, database logics, program semantics, and programming theory.
Handbook of Satisfiability
Propositional logic has been recognized throughout the centuries as one of the cornerstones of reasoning in philosophy and mathematics. Over time, its formalization into Boolean algebra was accompanied by the recognition that a wide range of combinatorial problems can be expressed as propositional satisfiability (SAT) problems. Because of this dual role, SAT developed into a mature, multi-faceted scientific discipline, and from the earliest days of computing a search was underway to discover how to solve SAT problems in an automated fashion. This book, the Handbook of Satisfiability, is the second, updated and revised edition of the book first published in 2009 under the same name. The handb...
Computer Science Logic
This book constitutes the refereed proceedings of the 18th International Workshop on Computer Science Logic, CSL 2004, held as the 13th Annual Conference of the EACSL in Karpacz, Poland, in September 2004. The 33 revised full papers presented together with 5 invited contributions were carefully reviewed and selected from 88 papers submitted. All current aspects of logic in computer science are addressed ranging from mathematical logic and logical foundations to methodological issues and applications of logics in various computing contexts.
Logic for Programming, Artificial Intelligence, and Reasoning
This book constitutes the refereed proceedings of the 9th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR 2002, held in Tbilisi, Georgia in October 2002.The 30 revised full papers presented were carefully reviewed and selected from 68 submissions. Among the topics covered are constraint programming, formal software enginering, formal verification, resolution, unification, proof planning, agent splitting, binary decision diagrams, binding, linear logic, Isabelle theorem prover, guided reduction, etc.
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. The result is a uniform treatment of many systems in the literature.
Kurt Gödel: Collected Works: Volume IV
Kurt Gödel (1906 - 1978) was the most outstanding logician of the twentieth century, famous for his hallmark works on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, and the foundations of computability theory, as well as for the strong individuality of his writings on the philosophy of mathematics. He is less well known for his discovery of unusual cosmological models for Einstein's equations, in theory permitting time travel into the past. The Collected Works is a landmark resource that draws together a lifetime of creative thought...
Kurt Gödel: Collected Works: Volume V
Kurt Gödel (1906 - 1978) was the most outstanding logician of the twentieth century, famous for his hallmark works on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, and the foundations of computability theory, as well as for the strong individuality of his writings on the philosophy of mathematics. He is less well known for his discovery of unusual cosmological models for Einstein's equations, in theory permitting time travel into the past. The Collected Works is a landmark resource that draws together a lifetime of creative thought...
