How to Analyze Graph-Based Models - Www-st.inf.tu-dresden.de ...

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Cost of Transitive Closure ► Transitive closure (TC) has many implementations ► Naive: multiplication of boolean matrices O(n 3 ) ► Multiplication of boolean matrices with Russian Method is O(n 2.4 ) ► Nested-loop joins from relational algebra: O(n 3 ) ■ Gets better with semi-naive evaluation, hashed joins, semi-joins, and indices ► Munro/Purdue algorithm is almost linear, but costs space Prof. Uwe Aßmann, Softwaretechnologie II 66
Exercise: Railway Routes ► Base (Facts): ■ directlyLinked(Berlin, Potsdam). ■ directlyLinked(Potsdam,Braunschweig). ■ directlyLinked(Braunschweig, Hannover). ► Define the predicates ■ linked(A,B) ■ alsoLinked(A,B) ■ unreachable(A,B) ► Answer the queries ■ linked(Berlin,X) ■ unreachable(Berlin, Hannover) Prof. Uwe Aßmann, Softwaretechnologie II 67
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How to</st
Page 3 and 4:
Obligatory Reading
Page 5 and 6:
Goals ► Understand that software
Page 7 and 8:
The Problem: How <
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Partially Collapsed Prof. Uwe Aßma
Page 11 and 12:
Requirements for Modelling in Requi
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Example: Rename Refacto</st
Page 15 and 16: Refactoring on Def
Page 17 and 18: Data-Flow Graphs
Page 19 and 20: Precise Call Graph
Page 21 and 22: Types of Graphs in
Page 23 and 24: Definitions ► Fan-in ■ In-degre
Page 25 and 26: Trees ► One source (root) ► Man
Page 27 and 28: Directed Graphs (D
Page 29 and 30: Reducible Graphs (
Page 31 and 32: Strength of Assertions in M
Page 33 and 34: Structuring Improves Worst Case Lis
Page 35 and 36: Methods and Tools for Analysis of <
Page 37 and 38: Graphs and Fact Da
Page 39 and 40: Queries on Graphs
Page 41 and 42: Layering of Systems ► To be compr
Page 43 and 44: Pattern and Rules ► Parenthood ca
Page 45 and 46: Same Generation ► Beyond sisters
Page 47 and 48: Same Generation Introduces Layers
Page 49 and 50: Searching Graphs -
Page 51 and 52: Same Generation Datalog Program isP
Page 53 and 54: Description Logic (DL) ► Is a spe
Page 55 and 56: Application Areas of Datalog, DL, O
Page 57 and 58: Answer Alternative category text Ex
Page 59 and 60: Example: Web Queries with Logic ►
Page 61 and 62: Who is Descendant of Whom? ► Some
Page 63 and 64: Impact of Basic Rule GustavAdolf Ad
Page 65: [S|M][S|M]PP Path Problems: Variant
Page 69 and 70: Central Theorem of Datalog/DL/EARS
Page 71 and 72: Applications of Graph</stro
Page 73 and 74: Generic Datalog Queries ► Transit
Page 75 and 76: Example 1: Consistency Checking for
Page 77 and 78: Second Idea ► Analyze</st
Page 79 and 80: Example 2: Consistency Checking of
Page 81 and 82: Second Idea ► Write queries that
Page 83 and 84: Example 3: UML Specifications in So
Page 85 and 86: Answer Alternative category text Ex
Page 87 and 88: Third Idea: Use Onto</stron
Page 89: The End Softwaretechnologie II, ©
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How to Analyze Graph-Based Models - Www-st.inf.tu-dresden.de ...

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