st s rs trs - PowerPoint PPT Presentation

Pr❡❧✐♠✐♥❛r✐❡s ❙✐♠♣❧✐❢✐❝❛t✐♦♥ ✭❇✐✮s✐♠✉❧❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥ ❇✐s✐♠✉❧❛t✐♦♥ ♠❛♣s ✐♥ ♣r❡s❤❡❛❢ ❝❛t❡❣♦r✐❡s ❍❛rs❤ ❇❡♦❤❛r ✶ ❛♥❞ ❙❡❜❛st✐❛♥ ❑ü♣♣❡r ✷ 1 ❯♥✐✈❡rs✐t② ♦❢ ❉✉✐s❜✉r❣✲❊ss❡♥ ❤❛rs❤✳❜❡♦❤❛r❅✉♥✐✲❞✉❡✳❞❡ 2 ❋❡r♥❯♥✐✈❡rs✐tät ✐♥ ❍❛❣❡♥ s❡❜❛st✐❛♥✳❦✉❡♣♣❡r❅❢❡r♥✉♥✐✲❤❛❣❡♥✳❞❡ ✶ ✴ ✸✽

❖❜❥❡❝t✐✈❡s ❋✐♥❞ ❛♥ ✏❛❜str❛❝t✑ s❡♠❛♥t✐❝ ✉♥✐✈❡rs❡ t♦ st✉❞② ❜❡❤❛✈✐♦✉r ♦❢ ❞②♥❛♠✐❝❛❧ s②st❡♠s✳ ❲❤❛t ✐s r❡✜♥❡♠❡♥t ♦❢ ❜❡❤❛✈✐♦✉r❄ ❈❛♥ ✇❡ st✉❞② ❜✐s✐♠✉❧❛t✐♦♥s ✐♥ ❛♥ ❛❜str❛❝t ✇❛②❄ Pr❡❧✐♠✐♥❛r✐❡s ❙✐♠♣❧✐❢✐❝❛t✐♦♥ ✭❇✐✮s✐♠✉❧❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥ ▼♦t✐✈❛t✐♦♥ Syntax analysis Process Axioms Syntactical Calculation Description terms on Bisimulation using Rules solution axiomatisation Semantics Transition Bisimulation Systems Equivalence analysis Semantical Theoretical Description using Notions ❋✐❣✉r❡✿ ▼❛t❤❡♠❛t✐❝❛❧ ▼♦❞❡❧❧✐♥❣ ✭❈✉✐❥♣❡rs ✷✵✵✹✮✳ ✷ ✴ ✸✽

❖❜❥❡❝t✐✈❡s ❋✐♥❞ ❛♥ ✏❛❜str❛❝t✑ s❡♠❛♥t✐❝ ✉♥✐✈❡rs❡ t♦ st✉❞② ❜❡❤❛✈✐♦✉r ♦❢ ❞②♥❛♠✐❝❛❧ s②st❡♠s✳ ❲❤❛t ✐s r❡✜♥❡♠❡♥t ♦❢ ❜❡❤❛✈✐♦✉r❄ ❈❛♥ ✇❡ st✉❞② ❜✐s✐♠✉❧❛t✐♦♥s ✐♥ ❛♥ ❛❜str❛❝t ✇❛②❄ Pr❡❧✐♠✐♥❛r✐❡s ❙✐♠♣❧✐❢✐❝❛t✐♦♥ ✭❇✐✮s✐♠✉❧❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥ ▼♦t✐✈❛t✐♦♥ Syntax analysis Process Axioms Syntactical Calculation Description terms on Bisimulation using Rules solution axiomatisation Semantics Transition Bisimulation Systems Equivalence analysis Semantical Theoretical Description using Notions ❋✐❣✉r❡✿ ▼❛t❤❡♠❛t✐❝❛❧ ▼♦❞❡❧❧✐♥❣ ✭❈✉✐❥♣❡rs ✷✵✵✹✮✳ ✸ ✴ ✸✽

Pr❡❧✐♠✐♥❛r✐❡s ❙✐♠♣❧✐❢✐❝❛t✐♦♥ ✭❇✐✮s✐♠✉❧❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥ ▼♦t✐✈❛t✐♦♥ Process Axioms terms on Bisimulation Semantics analysis Semantical Theoretical Description using Notions Transition Bisimulation Systems Equivalence ❋✐❣✉r❡✿ ▼❛t❤❡♠❛t✐❝❛❧ ▼♦❞❡❧❧✐♥❣ ✭❈✉✐❥♣❡rs ✷✵✵✹✮✳ ❖❜❥❡❝t✐✈❡s ❋✐♥❞ ❛♥ ✏❛❜str❛❝t✑ s❡♠❛♥t✐❝ ✉♥✐✈❡rs❡ t♦ st✉❞② ❜❡❤❛✈✐♦✉r ♦❢ ❞②♥❛♠✐❝❛❧ s②st❡♠s✳ ❲❤❛t ✐s r❡✜♥❡♠❡♥t ♦❢ ❜❡❤❛✈✐♦✉r❄ ❈❛♥ ✇❡ st✉❞② ❜✐s✐♠✉❧❛t✐♦♥s ✐♥ ❛♥ ❛❜str❛❝t ✇❛②❄ ✹ ✴ ✸✽

❇❡❤❛✈✐♦✉r ✐s ❣✐✈❡♥ ❜② ❝♦❧❧❡❝t✐♦♥ ♦❢ ❡①❡❝✉t✐♦♥s✳ ❆ ♣r❡s❤❡❛❢ r❡❝♦r❞s ❡①❡❝✉t✐♦♥s ♦❢ ❛ s②st❡♠✳ ❘❡✜♥❡♠❡♥t ♦❢ ❜❡❤❛✈✐♦✉r ✭s✐♠✉❧❛t✐♦♥✮ ❛s ♣r❡s❤❡❛❢ ♠♦r♣❤✐s♠✳ ❇✐s✐♠✉❧❛t✐♦♥ ♠❛♣s ❛r❡ s♣❡❝✐❛❧ ♣r❡s❤❡❛❢ ♠♦r♣❤✐s♠s✳ str♦♥❣ ❜✐s✐♠✉❧❛t✐♦♥ ✲❢❛✐r ❜✐s✐♠✉❧❛t✐♦♥ ❜r❛♥❝❤✐♥❣ ❜✐s✐♠✉❧❛t✐♦♥ ❘❡❝❛❧❧ t❤❛t ✐s t❤❡ ♣♦s❡t ♦❢ ✜♥✐t❡ ✇♦r❞s✳ ✐s t❤❡ ♣♦s❡t ♦❢ ✐♥✜♥✐t❡ ✇♦r❞s✳ ✳ Pr❡❧✐♠✐♥❛r✐❡s ❙✐♠♣❧✐❢✐❝❛t✐♦♥ ✭❇✐✮s✐♠✉❧❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥ ■♥ t❤✐s t❛❧❦✳✳✳ Pr❡s❤❡❛✈❡s ❛s s❡♠❛♥t✐❝ ♠♦❞❡❧s ♦❢ ❞②♥❛♠✐❝❛❧ s②st❡♠✳ ✺ ✴ ✸✽

❘❡✜♥❡♠❡♥t ♦❢ ❜❡❤❛✈✐♦✉r ✭s✐♠✉❧❛t✐♦♥✮ ❛s ♣r❡s❤❡❛❢ ♠♦r♣❤✐s♠✳ ❇✐s✐♠✉❧❛t✐♦♥ ♠❛♣s ❛r❡ s♣❡❝✐❛❧ ♣r❡s❤❡❛❢ ♠♦r♣❤✐s♠s✳ str♦♥❣ ❜✐s✐♠✉❧❛t✐♦♥ ✲❢❛✐r ❜✐s✐♠✉❧❛t✐♦♥ ❜r❛♥❝❤✐♥❣ ❜✐s✐♠✉❧❛t✐♦♥ ❘❡❝❛❧❧ t❤❛t ✐s t❤❡ ♣♦s❡t ♦❢ ✜♥✐t❡ ✇♦r❞s✳ ✐s t❤❡ ♣♦s❡t ♦❢ ✐♥✜♥✐t❡ ✇♦r❞s✳ ✳ Pr❡❧✐♠✐♥❛r✐❡s ❙✐♠♣❧✐❢✐❝❛t✐♦♥ ✭❇✐✮s✐♠✉❧❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥ ■♥ t❤✐s t❛❧❦✳✳✳ Pr❡s❤❡❛✈❡s ❛s s❡♠❛♥t✐❝ ♠♦❞❡❧s ♦❢ ❞②♥❛♠✐❝❛❧ s②st❡♠✳ ❇❡❤❛✈✐♦✉r ✐s ❣✐✈❡♥ ❜② ❝♦❧❧❡❝t✐♦♥ ♦❢ ❡①❡❝✉t✐♦♥s✳ ❆ ♣r❡s❤❡❛❢ r❡❝♦r❞s ❡①❡❝✉t✐♦♥s ♦❢ ❛ s②st❡♠✳ ✻ ✴ ✸✽

❇✐s✐♠✉❧❛t✐♦♥ ♠❛♣s ❛r❡ s♣❡❝✐❛❧ ♣r❡s❤❡❛❢ ♠♦r♣❤✐s♠s✳ str♦♥❣ ❜✐s✐♠✉❧❛t✐♦♥ ✲❢❛✐r ❜✐s✐♠✉❧❛t✐♦♥ ❜r❛♥❝❤✐♥❣ ❜✐s✐♠✉❧❛t✐♦♥ ❘❡❝❛❧❧ t❤❛t ✐s t❤❡ ♣♦s❡t ♦❢ ✜♥✐t❡ ✇♦r❞s✳ ✐s t❤❡ ♣♦s❡t ♦❢ ✐♥✜♥✐t❡ ✇♦r❞s✳ ✳ Pr❡❧✐♠✐♥❛r✐❡s ❙✐♠♣❧✐❢✐❝❛t✐♦♥ ✭❇✐✮s✐♠✉❧❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥ ■♥ t❤✐s t❛❧❦✳✳✳ Pr❡s❤❡❛✈❡s ❛s s❡♠❛♥t✐❝ ♠♦❞❡❧s ♦❢ ❞②♥❛♠✐❝❛❧ s②st❡♠✳ ❇❡❤❛✈✐♦✉r ✐s ❣✐✈❡♥ ❜② ❝♦❧❧❡❝t✐♦♥ ♦❢ ❡①❡❝✉t✐♦♥s✳ ❆ ♣r❡s❤❡❛❢ r❡❝♦r❞s ❡①❡❝✉t✐♦♥s ♦❢ ❛ s②st❡♠✳ ❘❡✜♥❡♠❡♥t ♦❢ ❜❡❤❛✈✐♦✉r ✭s✐♠✉❧❛t✐♦♥✮ ❛s ♣r❡s❤❡❛❢ ♠♦r♣❤✐s♠✳ ✼ ✴ ✸✽

str♦♥❣ ❜✐s✐♠✉❧❛t✐♦♥ ✲❢❛✐r ❜✐s✐♠✉❧❛t✐♦♥ ❜r❛♥❝❤✐♥❣ ❜✐s✐♠✉❧❛t✐♦♥ ❘❡❝❛❧❧ t❤❛t ✐s t❤❡ ♣♦s❡t ♦❢ ✜♥✐t❡ ✇♦r❞s✳ ✐s t❤❡ ♣♦s❡t ♦❢ ✐♥✜♥✐t❡ ✇♦r❞s✳ ✳ Pr❡❧✐♠✐♥❛r✐❡s ❙✐♠♣❧✐❢✐❝❛t✐♦♥ ✭❇✐✮s✐♠✉❧❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥ ■♥ t❤✐s t❛❧❦✳✳✳ Pr❡s❤❡❛✈❡s ❛s s❡♠❛♥t✐❝ ♠♦❞❡❧s ♦❢ ❞②♥❛♠✐❝❛❧ s②st❡♠✳ ❇❡❤❛✈✐♦✉r ✐s ❣✐✈❡♥ ❜② ❝♦❧❧❡❝t✐♦♥ ♦❢ ❡①❡❝✉t✐♦♥s✳ ❆ ♣r❡s❤❡❛❢ r❡❝♦r❞s ❡①❡❝✉t✐♦♥s ♦❢ ❛ s②st❡♠✳ ❘❡✜♥❡♠❡♥t ♦❢ ❜❡❤❛✈✐♦✉r ✭s✐♠✉❧❛t✐♦♥✮ ❛s ♣r❡s❤❡❛❢ ♠♦r♣❤✐s♠✳ ❇✐s✐♠✉❧❛t✐♦♥ ♠❛♣s ❛r❡ s♣❡❝✐❛❧ ♣r❡s❤❡❛❢ ♠♦r♣❤✐s♠s✳ ✽ ✴ ✸✽

Pr❡❧✐♠✐♥❛r✐❡s ❙✐♠♣❧✐❢✐❝❛t✐♦♥ ✭❇✐✮s✐♠✉❧❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥ ■♥ t❤✐s t❛❧❦✳✳✳ Pr❡s❤❡❛✈❡s ❛s s❡♠❛♥t✐❝ ♠♦❞❡❧s ♦❢ ❞②♥❛♠✐❝❛❧ s②st❡♠✳ ❇❡❤❛✈✐♦✉r ✐s ❣✐✈❡♥ ❜② ❝♦❧❧❡❝t✐♦♥ ♦❢ ❡①❡❝✉t✐♦♥s✳ ❆ ♣r❡s❤❡❛❢ r❡❝♦r❞s ❡①❡❝✉t✐♦♥s ♦❢ ❛ s②st❡♠✳ ❘❡✜♥❡♠❡♥t ♦❢ ❜❡❤❛✈✐♦✉r ✭s✐♠✉❧❛t✐♦♥✮ ❛s ♣r❡s❤❡❛❢ ♠♦r♣❤✐s♠✳ ❇✐s✐♠✉❧❛t✐♦♥ ♠❛♣s ❛r❡ s♣❡❝✐❛❧ ♣r❡s❤❡❛❢ ♠♦r♣❤✐s♠s✳ PSh ( A ⋆ ) str♦♥❣ ❜✐s✐♠✉❧❛t✐♦♥ PSh ( A ∞ ) ∀ ✲❢❛✐r ❜✐s✐♠✉❧❛t✐♦♥ PSh ( A ⋆ τ ) ❜r❛♥❝❤✐♥❣ ❜✐s✐♠✉❧❛t✐♦♥ ¯ ❘❡❝❛❧❧ t❤❛t A ⋆ ✐s t❤❡ ♣♦s❡t ♦❢ ✜♥✐t❡ ✇♦r❞s✳ A ω ✐s t❤❡ ♣♦s❡t ♦❢ ✐♥✜♥✐t❡ ✇♦r❞s✳ A ∞ = A ⋆ ∪ A ω ✳ ✾ ✴ ✸✽