PPT-From Proofs

Ranjit Jhala Ken McMillan Array Abstractions From Proofs The Problem Reasoning about Data fori0ini Mi0 forj0jnj assertMj0 All cells from 0 to . J Hildebrand Evenodd proofs Practice problems Solutions The problems below illustrate the various proof techniques direct proof proof by contraposition proof by cases and proof by contradiction see the separate handout on proof techniques Logic and Proof. Fall . 2011. Sukumar Ghosh. Predicate Logic. Propositional logic has limitations. Consider this:. Is . x. . > 3. a proposition? No, it is a . predicate. . Call it . P(x. ). . Chapter 1, Part III: Proofs. With Question/Answer Animations. Summary. Valid Arguments and Rules of Inference. Proof Methods. Proof Strategies. Rules of Inference. Section 1.6. Section Summary. Valid Arguments. the refinement . algebra. Vlad. . Shcherbina. Ilya. . Maryassov. Alexander . Kogtenkov. Alexander . Myltsev. Pavel. . Shapkin. Sergey . Paramonov. Mentor: Sir Tony Hoare. Project motivation. Educational (get some experience with interactive theorem . Dominique Unruh. University of Tartu. Tartu, April 12, 2012. Why quantum ZK?. Zero-knowledge:. Central tool in crypto. Exhibits many issues “in the small case”. Post-quantum crypto:. Classical protocols. First points:. This is written for mathematical proofs. Unless you are doing math econ, formal game theory, or statistical/econometric development (not application) you may not do formal mathematical proofs.. Chapter 1, Part III: Proofs. With Question/Answer Animations. Summary. Valid Arguments and Rules of Inference. Proof Methods. Proof Strategies. Rules of Inference. Section 1.6. Section Summary. Valid Arguments. But, pictures are not proofs in themselves, but may offer . inspiration. and . direction. . . Mathematical proofs require rigor, but mathematical ideas benefit from insight. . Speaker: . Karl Ting, . rhetorics. , style and other mathematical elements. Jean . Paul Van . Bendegem. Vrije Universiteit Brussel. Centrum voor Logica en Wetenschapsfilosofie. Universiteit . Gent. Starting hypothesis. Mathematics is a heterogeneous activity. Hrube. š. . &. . Iddo. Tzameret. of Polynomial Identities. . Bounds on . Equational. Proofs . 1. High School . Problem. How to solve it by hand . ?. Use the . polynomial-ring axioms . !. Associativity. 1. NP-Completeness . Proofs. Presentation for use with the textbook, . Algorithm Design and Applications. , by M. T. Goodrich and R. Tamassia, Wiley, 2015. © 2015 Goodrich and Tamassia . NP-Completeness Proofs. . Iddo Tzameret. Royal Holloway, University of London . Joint work with Fu Li (Tsinghua) and Zhengyu Wang (Harvard). . Sketch. 2. Sketch. : a major open problem in . proof complexity . stems from seemingly weak results. 1.1 Propositional Logic. 1.2 Propositional Equivalences. 1.3 Predicates and Quantifiers. 1.4 Nested Quantifiers. 1.5 Rules of Inference. 1.6 Introduction to Proofs. 1.7 Proof Methods and Strategy. We wish to establish the truth of. Guy Katz. Schloss. . Dagstuhl. , October 2016. Acknowledgements . Based on joint work with Clark Barrett, Cesare . Tinelli. , Andrew Reynolds and Liana . Hadarean. (. FMCAD’16. ). 2. Stanford . University.