'Hasse diagram' diaporamas de présentation

Noam Rinetzky Lecture 9: Abstract Interpretation II

Program Analysis and Verification 0368- 4479 http://www.cs.tau.ac.il/~maon/teaching/2013-2014/paav/paav1314b.html. Noam Rinetzky Lecture 9: Abstract Interpretation II. Slides credit: Roman Manevich , Mooly Sagiv , Eran Yahav. From verification to analysis. Manual program verification

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Advanced Compiler Techniques

Advanced Compiler Techniques. Data Flow Analysis Extensions & Foundations. LIU Xianhua School of EECS, Peking University. REVIEW. Some Basic Ideas Reaching Definitions Available Expressions Live Variables. REVIEW. REVIEW. Dataflow Analysis Control flow graph

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?? : ???

Chapter 7. ?? : ???. Equivalence Classes. 7.1 Relations Revisited: Properties of Relations. Ex. 7.3 ????????? M =( S , I , O , v , w ). (a) ? s 1 , s 2 ? S , ?? s 1 R s 2 ? v ( s 1 , x )= s 2 ??? x ? I . ?? R ???????? (b) ? S ? ?????????????? ?? s 1 R s 2

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This report is very disappointing. What kind of software are you using?

This report is very disappointing. What kind of software are you using?. Data Space Age Stone Age Analysis Space Age + + Stone Age +. Space Age and Stone Age Syndrome. Data: Space Age/Stone Age Analysis: Space Age/Stone Age. Life and Death with Averages and Variability.

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Relations

Relations. Binary Relations. a relation between elements of two sets is a subset of their Cartesian product (of ordered pairs). Note the di ?erence between a relation and a function: in a relation, each a ? A can map to multiple elements in B. Thus, relations are generalizations of functions.

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Chap. 7 Relations: The Second Time Around

Chap. 7 Relations: The Second Time Around. Binary Relation. For sets A, B, any subset of A ? B is called a (binary) relation from A to B. Any subset of A ? A is called a (binary) relation on A. Reflexive Relation. e.g. Given a finite set A with |A|=n. Then,

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Relations

Relations. Chapter 9. Chapter Summary. Relations and Their Properties n - ary Relations and Their Applications ( not currently included in overheads ) Representing Relations Closures of Relations ( not currently included in overheads ) Equivalence Relations Partial Orderings.

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Q-operators and discrete Hirota dynamics for spin chains and sigma models

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Partial Orders

Partial Orders. Definitions. A relation R on set A is a partial order if it is: reflexive antisymmetric transitive. A is called a partially ordered set or poset . [A;R] means A is partially ordered by R. Example: [ P({1,2}); ? ] ( draw its digraph ). Definitions .

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CSNB 143 Discrete Mathematical Structures

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