PPT-Input- shrinking functions

theory and application PhD candidate Francesco Davì Thesis committee Dr Stefan Dziembowski advisor Prof Luigi Vincenzo Mancini Prof Alessandro Mei Reviewers . M. . Siberstein. , A. Schuster, D. Geiger, A. . Patley. , J. Owens. Introduction. MPF characterized by. Complex data dependent . High data reuse . Low compute-to-memory access ration. Technique to solve MPF . State Key Lab of ASIC and System. Fudan University, Shanghai, China. Alan Mishchenko. Department of EECS. University of California, Berkeley. 1. Lazy Man’s Logic Synthesis. Outline. Introduction. Previous Work. Rajeev Alur. . . University of . Pennsylvania. Languages . vs. Functions. A language L is a subset of . S. *. A numerical function maps strings in . S. * to N (or integers Z). A string-to-string transformation maps . hrinking. SAT’10 Conference. Edinburgh, Scotland, UK . July 11, 2010 . A . signment. tack. Alexander Nadel, Intel,. Israel. Vadim Ryvchin, . Intel&Technion. , Israel. Agenda. Introduction. Evasive Functions. Boaz . Barak, . Nir. . Bitansky. , Ran Canetti,. Yael Tauman . Kalai, . Omer . Paneth, . Amit Sahai. Program Obfuscation . Obfuscated Program. Approved . Document . Signature . Obfuscation. A . New Logic . Synthesis Method . Based . on Pre-Computed Library. Wenlong. Yang . Lingli. Wang. State Key Lab of ASIC and System. Fudan. University, Shanghai, China. Alan Mishchenko. Department of EECS. Joanna Ganning, PhD. Executive Director, Metropolitan Research Center. Assistant Professor, Department of City & Metropolitan Planning. University of Utah. MISSION ACCOMPLISHED……Or not?. For fifteen years, scholars have written that the dawn of accessibility-based transportation planning has . A . New Logic . Synthesis Method . Based . on Pre-Computed Library. Wenlong. Yang . Lingli. Wang. State Key Lab of ASIC and System. Fudan. University, Shanghai, China. Alan Mishchenko. Department of EECS. 1. Discrete Mathematics: A Concept-based Approach. Introduction. Every relation involves sets and combination of the elements of the sets. One can map the elements of one set to the other. This mapping is also called function. All the functions are relations, but every relation is not a function. In general every program is viewed as a function. Input to the program is a set and output of the program as another set.. Paul . Beame. University of Washington. Outline. Branching program basics. Space (size) lower bounds. Multi-output functions. Time-Space tradeoff lower bounds for general BPs. Single-output functions. Boaz . Barak, . Nir. . Bitansky. , Ran Canetti,. Yael Tauman . Kalai, . Omer . Paneth, . Amit Sahai. Program Obfuscation . Obfuscated Program. Approved . Document . Signature . Obfuscation. Verify and sign. Quiz. What’s the transformation of y = . cf. (x) if c>1 from y = f(x)?. . . . A vertical shrinking. . B vertical stretching. . C horizontal shrinking. . D . horizontal stretching. Notation. Functions on binary / returning binary values. Finite automaton model. We haven’t completely left the world of counting. Sometimes we wish to know how many functions / how many inputs … . Introduction. Data Input: . Three methods. 1. Assign data to variables through an assignment statement . 2. Input data from Keyboard . 3. Read data from a file stored in computer memory. Data Input .