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This two-volume set LNAI 12166 and 12167 constitutes the refereed proceedings of the 10th International Joint Conference on Automated Reasoning, IJCAR 2020, held in Paris, France, in July 2020. In 2020, IJCAR was a merger of the following leading events, namely CADE (International Conference on Automated Deduction), FroCoS (International Symposium on Frontiers of Combining Systems), ITP (International Conference on Interactive Theorem Proving), and TABLEAUX (International Conference on Analytic Tableaux and Related Methods). The 46 full research papers, 5 short papers, and 11 system descriptions presented together with two invited talks were carefully reviewed and selected from 150 submissions. The papers focus on the following topics: Part I: SAT; SMT and QBF; decision procedures and combination of theories; superposition; proof procedures; non classical logics Part II: interactive theorem proving/ HOL; formalizations; verification; reasoning systems and tools The conference was held virtually due to the COVID-19 pandemic. Chapter 'Constructive Hybrid Games' is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

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This two-volume set LNAI 12166 and 12167 constitutes the refereed proceedings of the 10th International Joint Conference on Automated Reasoning, IJCAR 2020, held in Paris, France, in July 2020. In 2020, IJCAR was a merger of the following leading events, namely CADE (International Conference on Automated Deduction), FroCoS (International Symposium on Frontiers of Combining Systems), ITP (International Conference on Interactive Theorem Proving), and TABLEAUX (International Conference on Analytic Tableaux and Related Methods). The 46 full research papers, 5 short papers, and 11 system descriptions presented together with two invited talks were carefully reviewed and selected from 150 submissions. The papers focus on the following topics: Part I: SAT; SMT and QBF; decision procedures and combination of theories; superposition; proof procedures; non classical logics Part II: interactive theorem proving/ HOL; formalizations; verification; reasoning systems and tools The conference was held virtually due to the COVID-19 pandemic. Chapter 'A Fast Verified Liveness Analysis in SSA Form' is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

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This book constitutes the refereed proceedings of the Third International Symposium on NASA Formal Methods, NFM 2011, held in Pasadena, CA, USA, in April 2011. The 26 revised full papers presented together with 12 tool papers, 3 invited talks, and 2 invited tutorials were carefully reviewed and selected from 141 submissions. The topics covered by NFM 2011 included but were not limited to: theorem proving, logic model checking, automated testing and simulation, model-based engineering, real-time and stochastic systems, SAT and SMT solvers, symbolic execution, abstraction and abstraction refinement, compositional verifcation techniques, static and dynamic analysis techniques, fault protection, cyber security, specification formalisms, requirements analysis, and applications of formal techniques.

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High Quality Content by WIKIPEDIA articles! The Valiant Vazirani theorem is an important result in computational complexity theory. It was proven by Leslie Valiant and Vijay Vazirani in their paper titled "NP is as easy as detecting unique solutions" published in 1986. The theorem states that if there is a polynomial time algorithm for UNIQUE-SAT, then NP=RP. The theorem implies that even if the number of satisfying assignments is very small, SAT (which is an NP-complete problem) still remains a hard problem. UNIQUE-SAT is a promise problem that decides whether a given Boolean formula is unsatisfiable or has exactly one satisfying assignment. In the first case a UNIQUE-SAT algorithm would reject, and in the second it would accept the formula. If the formula has more than one satisfying assignment then the behavior of the UNIQUE-SAT algorithm does not matter.

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High Quality Content by WIKIPEDIA articles! In computational complexity theory, a branch of computer science, Schaefer's theorem states necessary and sufficient conditions under which a finite set S of Boolean relations yields polynomial-time or NP-complete problems when the relations of S are used to constrain some of the propositional variables. More precisely, Schaefer defines a decision problem which he calls the Generalized Satisfiability problem for S (denoted SAT(S)). The problem is to determine whether the given formula is satisfiable, in other words if the variables can be assigned values such that they satisfy all the constraints. Special cases of SAT(S) include the variants of Boolean satisfiability problem and the problem can also be viewed as a constraint satisfaction problem over the Boolean domain.

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This bookconstitutes the refereed proceedings of the 12th International Conference on IntegratedFormal Methods, IFM 2016, held in Reykjavik, Iceland, in June 2016.The 33 paperspresented in this volume were carefully reviewed and selected from 99submissions. They were organized in topical sections named: invitedcontributions, program verification, probabilistic systems, concurrency, safetyand liveness, model learning, SAT and SMT solving, testing, theorem proving andconstraint satisfaction, case studies.

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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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This book constitutes the refereed proceedings of the 7th International Symposium on NASA Formal Methods, NFM 2015, held in Pasadena, CA, USA, in April 2015.The 24 revised regular papers presented together with 9 short papers were carefully reviewed and selected from 108 submissions. The topics include model checking, theorem proving, SAT and SMT solving, symbolic execution, static analysis, runtime verification, systematic testing, program refinement, compositional verification, security and intrusion detection, modeling and specification formalisms, model-based development, model-based testing, requirement engineering, formal approaches to fault tolerance, and applications of formal methods.

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