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This book constitutes the refereed proceedings of the 23rd International Conference on Automated Deduction, CADE-23, held in Wroclaw, Poland, in July/August 2011.The 28 revised full papers and 7 system descriptions presented were carefully reviewed and selected from 80 submissions. Furthermore, four invited lectures by distinguished experts in the area were included. Among the topics addressed are systems and tools for automated reasoning, rewriting logics, security protocol verification, unification, theorem proving, clause elimination, SAT, satifiability, interactive theorem proving, theory reasoning, static analysis, decision procedures, etc.

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There are many complex problems in computer science that occur in knowledge-representation, artificial learning, Very Large Scale Integration (VLSI) design, security protocols and other areas. These complex problems may be deduced into satisfiability problems where the Boolean Satisfiability Problem (SAT) may be applied. This deduction is made in order to simplify complex problems into a specific propositional logic problem. The SAT problem is the most well-known nondeterministic polynomial time (NP) complete problem in computer science. In this book, we solve the SAT problem using a clustering technique - Multilevel - combined first with the Tabu Search algorithm and combined thereafter with finite Learning Automata. Tabu Search and finite Learning Automata are two very efficient approaches that have been used to solve SAT.

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The development of new and improved proof systems, proof formats and proof search methods is one of the most essential goals of Logic. But what is a proof? What makes a proof better than another? How can a proof be found efficiently? How can a proof be used? Logicians from different communities usually provide radically different answers to such questions. Their principles may be folklore within their own communities but are often unknown to outsiders. This book provides a snapshot of the current state of the art in proof search and proof production as implemented in contemporary automated reasoning tools such as SAT-solvers, SMT-solvers, first-order and higher-order automated theorem provers and proof assistants. Furthermore, various trends in proof theory, such as the calculus of inductive constructions, deduction modulo, deep inference, foundational proof certificates and cut-elimination, are surveyed; and applications of formal proofs are illustrated in the areas of cryptography, verification and mathematical proof mining. Experts in these topics were invited to present tutorials about proofs during the Vienna Summer of Logic and the chapters in this book reflect their tutorials. Therefore, each chapter is intended to be accessible not only to experts but also to novice researchers from all fields of Logic.

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This book is devoted to recent progress made in solving propositional satisfiability and related problems. Propositional satisfiability is a powerful and general formalism used to solve a wide range of important problems including hardware and software verification. The core of many reasoning problems in automated deduction are propositional. Research into methods to automate such reasoning has therefore a long history in artificial intelligence. In 1957, Allen Newell and Herb Simon introduced the Logic Theory Machine to prove propositional theorems from Whitehead and Russel's 'Principia mathematica'. In 1960, Martin Davis and Hillary Putnam introduced their eponymous decision procedure for satisfiability reasoning (though, for space reasons, it was quickly superseded by the modified procedure proposed by Martin Davis, George Logemann and Donald Loveland two years later). In 1971, Stephen Cook's proof that propositional satisfiability is NP-Complete placed satisfiability as the cornerstone of complexity theory. TOC:Preface.- 1. Heuristic-Based Backtracking Relaxation for Propositional Satisfiability.- 2. Symbolic Techniques in Satisfiability Solving.- 3. Exponential lower bounds for the running time of DPLL algorithms on satisfiable formulas.- 4. Backdoor Sets for DLL Subsolvers.- 5. The Complexity of Pure Literal Elimination.- 6. Clause Weighting Local Search for SAT.- 7. Solving Non-Boolean Satisfiability Problems with Stochastic Local Search: A Comparison of Encodings.- 8. Regular random k-SAT: properties of balanced formulas.- 9. Applying SAT Solving for Classification in Finite Algebra.- 10. The SAT-Based Approch to Separation Logic.- 11. MathSAT: Tight Integration of SAT and Mathematical Decision Procedures.

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