Statecharts aka Harel Charts Visual Modelling 1. Higraph formalism - PowerPoint PPT Presentation

Statecharts aka Harel Charts Visual Modelling 1. Higraph formalism 2. Statechart formalism (combines Higraphs and State Automata) Diverse applications. In particular: concurrent systems behaviour Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: Higraphs/Statecharts 1/30

� � � � Higraphs: Visualising Information complex non-quantitative, structural topological, not geometrical Euler – Venn diagrams (Jordan curve: inside/outside): enclosure, intersection – graphs (nodes, edges: binary relation ); hypergraphs Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: Higraphs/Statecharts 2/30

� � Venn diagrams, Euler circles P&Q Q P B P&Q&R P&R Q&R A R topological notions (syntax): enclosure, exclusion, intersection Used to represent (denote) mathematical set operations: union, difference, intersection Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: Higraphs/Statecharts 3/30

� � ✂ ✁ ✁ ✂ ✁ � Hypergraphs a c b d e f g h i a hypergraph a graph topological notion (syntax): connectedness Used to represent (denote) relations between sets. Hyperedges: non longer binary relation ( X X ): 2 X (undirected), 2 X (directed). 2 X Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: Higraphs/Statecharts 4/30

� � Higraphs : combining graphs and Venn diagrams sets + cartesian product hypergraphs Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: Higraphs/Statecharts 5/30

Blobs: set inclusion, not membership A D E Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: Higraphs/Statecharts 6/30

☎ ☎ ☎ � ☎ ✄ ✄ ✆ � � Unique Blobs (atomic sets, no intersection) A C D W B X P K Q R N U L O V F M S P T E atomic blobs are identifiable sets other blobs are union of enclosed sets ( e.g., K L M N O P ) empty space meaningless, identify intersection ( e.g., N K W ) Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: Higraphs/Statecharts 7/30

☎ ✞ ✂ ✝ ✄ ✝ ✂ ☎ ✄ ☎ ✂ ✞ ✄ Unordered Cartesian Product: Orthogonal Components A C D W B X Y P K Q R N U L O V F M S P T G H E K G H H G L M N O P Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: Higraphs/Statecharts 8/30

Meaningless syntactic constructs C A D B Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: Higraphs/Statecharts 9/30

Simple Higraph blobs orthogonal components A B J D C E K L M F G H I Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: Higraphs/Statecharts 10/30

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� � � Adding (hyper) edges A C D W B X Y P K Q R N U L O V F M S P T E hyper edges attach to contour of any blob inter-level possible ( e.g., denote global variables binding) Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: Higraphs/Statecharts 12/30

Clique Example B C A E D Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: Higraphs/Statecharts 13/30

Clique: fully connected semantics A B C D E Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: Higraphs/Statecharts 14/30

Entity Relationship Diagram ( is-a ) DATES EMPLOYEES PAID ON WORKS FOR IS IS A A SALARIES SECRETARIES CAN FLY AIRCRAFT PILOTS Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: Higraphs/Statecharts 15/30

Higraph version of E-R diagram dates works for months ... paid employees on years secretaries ... salaries others arrived in pilots equipment nuts aircraft can fly bolts Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: Higraphs/Statecharts 16/30

Extending the E-R diagram works for paid employees on men women secretaries others pilots can fly married Hans Vangheluwe hv@cs.mcgill.ca Modelling and Simulation: Higraphs/Statecharts 17/30