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

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Modelling <strong>Graph</strong>s on Two Abstraction Levels ► We deal here mostly with directed graphs (digraphs) ■ lists, trees, dags, (di-)graphs ► There are two different abstraction levels; we are interested in the logical level: ► Logical level (abstract, often declarative, problem oriented) ■ Data type List, Tree, Dag, <strong>Graph</strong> ■ Methods <strong>to</strong> handle graphs: ♦ Relational algebra ♦ Datalog ♦ Description logic ♦ <strong>Graph</strong> rewriting ♦ <strong>Graph</strong> grammars ♦ Recursion schemas ► Physical level (concrete, often imperative, machine oriented) ■ Data type adjacency list, boolean (bit)matrix, ■ Imperative algorithms ■ Pointer based algorithms Prof. Uwe Aßmann, Softwaretechnologie II 22
Definitions ► Fan-in ■ In-degree of node under a certain relation ■ Fan-in(n = 0): n is root node (source) ■ Fan-in(n) > 0: n is reachable from other nodes ► Fan-out ► Path ■ Out-degree of node under a certain relation ■ Fan-out(n) = 0: n is leaf node (sink) ■ An inner node is neither a root nor a leaf ■ A path p = (n 1, n 2,…,n k) is a sequence of nodes of length k Prof. Uwe Aßmann, Softwaretechnologie II 23
Page 1 and 2: How to</st
Page 3 and 4: Obligatory Reading
Page 5 and 6: Goals ► Understand that software
Page 7 and 8: The Problem: How <
Page 9 and 10: Partially Collapsed Prof. Uwe Aßma
Page 11 and 12: Requirements for Modelling in Requi
Page 13 and 14: 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: Types of Graphs in
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 and 66: [S|M][S|M]PP Path Problems: Variant
Page 67 and 68: Exercise: Railway Routes ► Base (
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
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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
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Third Idea: Use Onto</stron
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The End Softwaretechnologie II, ©
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