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
✿ ❉ ❉ ❉ ❉ ❉ ❉ ❉ ❉ ❉ ❉ ❉ ❉ ❉ ❉ ❉ ❉ ❉ ❉ ❊ ❊ ❊ ❊ ❊ ❉ ❉ ❊ ❈ ❈ ❈ ❈ ❈ ❈ ❈ ❈ ❈ ❈ ❈ ❈ ❉ ❈ ❈ ❈ ❈ ❈ ❈ ❈ ❈ ❉ ❉ ❉ ❊ ❊ ❈ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ◗ ❊ ❋ ❊ ❊ ❊ ❊ ❊ ❊ ❊ ❋ ❋ ❋ ❋ ◗ ❋ ❋ ❋ ❋ ❋ ❋ ❋ ❋ ❋ ❋ ❋ ❈ ❈ ■ ✿ ✿ ✿ ✿ ✿ ✿ ✿ ◗ ✿ ✿ ✿ ✿ ✿ ✿ ✿ ✿ ✿ ❀ ❀ ❀ ❀ ❀ ❀ ✿ ✿ ❀ ✾ ✽ ✽ ✽ ✾ ✾ ✾ ✾ ✾ ✾ ✾ ✾ ✿ ✾ ✾ ✾ ✾ ✾ ✾ ✾ ✾ ✾ ✾ ✾ ❀ ❀ ❈ ❁ ❁ ❁ ❁ ❁ ❁ ❁ ❁ ❁ ❁ ❁ ❁ ❁ ❁ ❁ ❁ ❁ ❁ ◗ ◗ ◗ ◗ ◗ ◗ ❁ ❁ ❀ ❀ ❀ ❀ ❀ ❀ ❀ ❀ ❀ ❀ ❀ ❀ ❀ ❁ ❀ ❀ ❀ ❀ ❀ ❁ ❁ ❁ ❁ ❁ ❁ ■ ■ ✽ ◆ ▼ ▼ ▼ ▼ ▼ ▼ ◆ ◆ ◆ ◆ ◆ ▼ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ▼ ▼ ❖ ▲ ❑ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▼ ▲ ▲ ▲ ▲ ▲ ▼ ▼ ▼ ▼ ▼ ▼ ❖ ❖ ❑ ◗ P ◗ ◗ ◗ ◗ ◗ ◗ ◗ ◗ ◗ ◗ P ◗ ◗ ◗ ◗ ◗ ◗ ◗ ◗ ◗ ◗ P P ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ ❖ P P P P P P P P P P P P ❑ ❑ ■ ❏ ■ ■ ■ ■ ■ ❏ ❏ ❏ ❏ ❏ ❏ ■ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ■ ■ ❏ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ❏ ❏ ❑ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❑ ❑ ❑ ❑ ❑ ❑ ❑ ❑ ❑ ❑ ❑ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ✽ ✽ ◗ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ✺ ◗ ❘ ❘ ❘ ❘ ❘ ❘ ❘ ❘ ❘ ◗ ◗ ❘ ◗ ✸ ✸ ✸ ✸ ✸ ✸ ✸ ✸ ✸ ❘ ❘ ✸ ❘ ❘ ❘ ❘ ❘ ❘ ❘ ❘ ❘ ❘ ❘ ❘ ❘ ❘ ❘ ❘ ❘ ❘ ❘ ❘ ❘ ❘ ❘ ❘ ✸ ✸ ✺ ✹ ✹ ✹ ✹ ✹ ✹ ✹ ✹ ✹ ✹ ✹ ✹ ✹ ✹ ✹ ✹ ✹ ✹ ✹ ✹ ✹ ✺ ✺ ✹ ✹ ✸ ✸ ✸ ✸ ✸ ✸ ✸ ✸ ✸ ✸ ✸ ✸ ✸ ✹ ✸ ✸ ✸ ✸ ✸ ✹ ✹ ✹ ✹ ✹ ✹ ✺ ✻ ✽ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✻ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✼ ✻ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✼ ✽ ✼ ✼ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✽ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ✻ ◗ Hans Vangheluwe Induced Acyclic Graph (blob/orth comp alternation) g ✩✠✩ ★✠★ ✧✠✧ ✦✠✦ ✤✠✤ ✥✠✥ i ☛✠☛ ☞✠☞ h hv@cs.mcgill.ca ❆✠❆✠❆✠❆✠❆✠❆✠❆✠❆ ❇✠❇✠❇✠❇✠❇✠❇✠❇✠❇ ❂✠❂✠❂✠❂✠❂✠❂✠❂✠❂ ❃✠❃✠❃✠❃✠❃✠❃✠❃✠❃ ✓✠✓ ✔✠✔ ✫✠✫ ✪✠✪ ✌✠✌ ✍✠✍ d ✗✠✗ ✘✠✘ b ✮✠✮ ✯✠✯ ●✠●✠●✠●✠●✠●✠●✠● ❍✠❍✠❍✠❍✠❍✠❍✠❍✠❍ ❄✠❄✠❄✠❄✠❄✠❄✠❄✠❄ ❅✠❅✠❅✠❅✠❅✠❅✠❅✠❅ e a ✬✠✬ ✭✠✭ ✏✠✏ ✎✠✎ ✡✠✡ ✖✠✖ ✕✠✕ ✟✠✟ ✢✠✢ ✣✠✣ f c ✙✠✙ ✚✠✚ ✷✠✷ ✶✠✶ k ✴✠✴ ✵✠✵ ✒✠✒ ✑✠✑ ✰✠✰ ✱✠✱ l ✜✠✜ ✛✠✛ j ✲✠✲ ✳✠✳ Modelling and Simulation: Higraphs/Statecharts m AND level (orthogonal component level) OR level (blob level) OR level AND level OR level 11/30
� � � 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
Recommend
More recommend
