'Loop invariant' presentation slideshows

Jeff Edmonds York University

Models of Computability. History & Overview Church's Thesis Goto vs Loop Models Turing Machines Loop Invariant Example Adding Example (single tape) Adding Example (multi tape) Table Lookup Example Single vs Multi Tape TMs Java to TM Constant vs Finite vs Infinite Universal TM

2.3k views • 222 slides

Course project presentations

Course project presentations. Midterm project presentation Originally scheduled for Tuesday Nov 4 th Can move to Th Nov 6 th or Th Nov 13 th. From last time: Loop-invariant code motion. Two steps: analysis and transformations Step1: find invariant computations in loop

932 views • 74 slides

Semantics

Semantics. Describing the meanings of Programs:. Programmers need to know precisely what the statements of a language do. English explanations in language manuals are often imprecise and incomplete. Semantics formalisms are needed by programmers and compiler writers. Operational Semantics.

866 views • 65 slides

Program Representations

Program Representations. Representing programs. Goals. Representing programs. Primary goals analysis is easy and effective just a few cases to handle directly link related things transformations are easy to perform general, across input languages and target machines Additional goals

820 views • 64 slides

2IL50 Data Structures

2IL50 Data Structures. Spring 2014 Lecture 1: Introduction. Algorithms. Algorithm a well-defined computational procedure that takes some value, or a set of values, as input and produces some value, or a set of values, as output.

606 views • 46 slides

2IL65 Algorithms

2IL65 Algorithms. Fall 2013 Lecture 1: Introduction. Algorithms. Algorithm a well-defined computational procedure that takes some value, or a set of values, as input and produces some value, or a set of values, as output.

561 views • 45 slides

Predicate Abstraction for Software Verification

Predicate Abstraction for Software Verification. Shaz Qadeer Compaq Systems Research Center (joint work with Cormac Flanagan). Systems software. OS components file system, buffer cache manager Abstract from low-level to high-level operations tedious low-level programming detail

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Example in SSA

423 views • 34 slides

Chapter 24.

Chapter 24. Single-Source Shortest Paths. Shortest Paths. How to find the shortest route between two points on a map. Input: Directed graph G = (V, E) Weight function w : E ? R Weight of path p = ( v 0 , v 1 , . . . , v k ) = = sum of edge weights on path p .

500 views • 33 slides

Loop variant & invariant

Loop variant & invariant. Some kinds of errors are typical for loops The loop does not terminate The loop body is execute once too often or too less Special cases like zero iterations are not handled. Loop invariant. The loop invariant specifies a condition that must be satisfied at

600 views • 29 slides

Lecture 3: Quantifiers and Proof Techniques

Lecture 3: Quantifiers and Proof Techniques Discrete Mathematical Structures: Theory and Applications Quantifiers and First Order Logic Predicate or Propositional Function Let x be a variable and D be a set; P ( x ) is a sentence

741 views • 28 slides

Loop variant and invariant Part II

Loop variant and invariant Part II. Recitation on OOSC Ohad Barzilay IDC, June 2004. Merge problem. Proving Loop Correctness. The following routine merges two sorted arrays into a new sorted array that contains all their elements

394 views • 28 slides

Code Improving Transformations Chapter 13,14

Code Improving Transformations Chapter 13,14. Mooly Sagiv. Outline. Chapter 12- Redundency Elimination Global common sub-expression elimination/Forward Substitution Loop-Invariant Code Motion Partial Redundency Elimination Code Hoisting Chapter 13 - Loop Optimization (Friday)

450 views • 25 slides

Abstract Reasoning of Programs Part 2

Abstract Reasoning of Programs Part 2. Francis Tang March 21, 2003. References. [CLRS] Cormen, Leiserson, Rivest and Stein, Introduction to Algorithms 2 nd Ed , MIT Press, 2001.

311 views • 23 slides

CS 201 Compiler Construction

CS 201 Compiler Construction. Code Optimizations: Partial Redundancy Elimination. Redundancy Elimination. The goal of redundancy elimination is to eliminate unnecessary reevaluations of the same computation. Global Common Sub-expression Elimination Loop Invariant Code Motion

346 views • 19 slides

CS 201 Compiler Construction

CS 201 Compiler Construction. Lecture 7 Code Optimizations: Partial Redundancy Elimination. Redundancy Elimination. The goal of redundancy elimination is to eliminate unnecessary reevaluations of the same computation. Global Common Sub-expression Elimination Loop Invariant Code Motion

280 views • 18 slides

352 views • 17 slides

Using Loop Invariants to Detect Transient Faults in the Data Caches

359 views • 17 slides

Hardware-Software Interface

Hardware-Software Interface. Program. Machine. Available resources. Required resources. statically fixed. dynamically varying. Designed to support. Designed to run well on. X. wide variety of programs. a variety of machines. Interested in running. Interested in having.

289 views • 16 slides

Insertion Sort and Its Analysis

915 views • 13 slides