PPT-Ranjit Jhala Abstractions from Proofs

With T Henzinger R Majumdar K McMillan How to automatically prove assertion The Safety Verification Problem 0 x i y i 1 whilex 0 x y 2 . All Programmable Abstractions push beyond traditional RTL design methodologies to automate all aspects of system development and algorithm deployment into all programmable FPGAs SoC and 3D ICs Xilinx and its Alliance members are working together to Henzinger Ranjit Jhala Rupak Majumdar EECS Department University of California Berkeley CA 947201770 USA tahjhalarupak eecsberkeleyedu Kenneth L McMillan Cadence Berkeley Labs Berkeley CA USA mcmillancadencecom Abstract The suc Ranjit Jhala . Ken McMillan. Array Abstractions. From Proofs. The Problem: Reasoning about Data. for(i=0;i!=n;i++). M[i]=0;. for(j=0;j!=n;j. ++) . . . assert(M[j]==0);. All cells from . 0. to . Chapter 1, Part III: Proofs. Summary. Proof Methods. Proof Strategies. Introduction to Proofs. Section 1.7. Section Summary. Mathematical Proofs. Forms of Theorems. Direct Proofs. Indirect Proofs. Proof of the . Learner Objective: I will calculate midpoints of segments and complete proofs 
 requiring that more than one pair of triangles be shown congruent.. Advanced Geometry. Learner Objective: I will calculate midpoints of segments and complete proofs 
 requiring that more than one pair of triangles be shown congruent.. 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. 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. To prove an argument is valid or the conclusion follows . Chapter 1, Part III: Proofs. Summary. Proof Methods. Proof Strategies. Introduction to Proofs. Section 1.7. Section Summary. Mathematical Proofs. Forms of Theorems. Direct Proofs. Indirect Proofs. Proof of the . Dictionary ADT. : Arrays, Lists and . Trees. Kate Deibel. Summer 2012. June 27, 2012. CSE 332 Data Abstractions, Summer 2012. 1. Where We Are. Studying the absolutely essential ADTs of computer science and classic data structures for implementing them. Disjoint Set Union-Find . and . Minimum Spanning Trees. Kate Deibel. Summer 2012. August 13, 2012. CSE 332 Data Abstractions, Summer 2012. 1. Making Connections. You have a set of nodes (numbered 1-9) on a network. . CSE 332 Data Abstractions: A Heterozygous Forest of AVL, Splay, and B Trees Kate Deibel Summer 2012 July 2, 2012 CSE 332 Data Abstractions, Summer 2012 1 From last time… Binary search trees can give us great performance due to providing a structured binary search. Dictionary ADT. : Arrays, Lists and . Trees. Kate Deibel. Summer 2012. June 27, 2012. CSE 332 Data Abstractions, Summer 2012. 1. Where We Are. Studying the absolutely essential ADTs of computer science and classic data structures for implementing them.