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 Introduction Softwarede64257ned networking SDN has received a lot of attention in recent years as a means of addressing some of the longstanding challenges in networking SDN starts from two simple ideas i generalize network hardware so it provide 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 . Madhu Sudan. . MIT CSAIL. 09/23/2009. 1. Probabilistic Checking of Proofs. TexPoint fonts used in EMF. . Read the TexPoint manual before you delete this box.: . A. A. A. A. Can Proofs Be Checked Efficiently?. 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.. Watercolor Paint - Abstractions. Watercolor Paint – Non-Representational. Pastel Abstractions. 6/16/2010. Parallel Programming Abstractions. 1. Tasks . vs. Threads. Similar but not the same.. 6/16/2010. Parallel Programming Abstractions. 2. h/w processors. Operating System. T. hreads. Task Scheduler. 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. 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. . Chapter 1 — Computer Abstractions and Technology — . 2. Classes of Computers. Personal computers. General purpose, variety of software. Subject to cost/performance tradeoff. Server computers. Network based. 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. Lecture 19: Analysis of Fork-Join Parallel Programs. Dan Grossman. Spring 2010. Where are we. Done:. How to use . fork. , and . join. to write a parallel algorithm. Why using divide-and-conquer with lots of small tasks is best. Lecture 6: Dictionaries; Binary Search Trees. Dan Grossman. Spring 2010. Where we are. Studying the absolutely essential ADTs of computer science and classic data structures for implementing them. ADTs so far:. Lecture 9: B Trees. Dan Grossman. Spring 2010. Our goal. Problem: A dictionary with so much data most of it is on disk. Desire: A balanced tree (logarithmic height) that is even shallower than AVL trees so that we can minimize disk accesses and exploit disk-block size.