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Sep 01, 2023 268 likes •644 views

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slide-1
SLIDE 1

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

❖✈❡r❧❛♣ ❛♥❞ ■♥❞❡♣❡♥❞❡♥❝❡ ✐♥ ▼✉❧t✐s❡t ❈♦♠♣r❡❤❡♥s✐♦♥ P❛tt❡r♥s

❊❞♠✉♥❞ ❙✳▲✳ ▲❛♠ ■❧✐❛♥♦ ❈❡r✈❡s❛t♦

s❧❧❛♠❅q❛t❛r✳❝♠✉✳❡❞✉ ✐❧✐❛♥♦❅❝♠✉✳❡❞✉

❙✉♣♣♦rt❡❞ ❜② ◗◆❘❋ ❣r❛♥ts ◆P❘P ✹✲✶✺✾✸✲✶✲✷✻✵ ❛♥❞ ✹✲✸✹✶✲✶✲✵✺✾

❏✉♥❡ ✷✵✶✻

slide-2
SLIDE 2

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

❖✉t❧✐♥❡

✶

❚❤❡ ❈♦♥t❡①t

✷

❚❤❡ Pr♦❜❧❡♠

✸

❚❤❡ ✭P❛rt✐❛❧✮ ❙♦❧✉t✐♦♥

✹

❚❤❡ ❈♦♥❝❧✉s✐♦♥s

slide-3
SLIDE 3

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

❈♦♠✐♥❣❧❡

❆ ♣r♦❣r❛♠♠✐♥❣ ❧❛♥❣✉❛❣❡ ❢♦r ❞✐str✐❜✉t❡❞ ♠♦❜✐❧❡ ❛♣♣s

❉❡s✐❣♥❡❞ t♦ ✐♠♣❧❡♠❡♥t ♠♦❜✐❧❡ ❛♣♣s t❤❛t r✉♥ ❛❝r♦ss ❆♥❞r♦✐❞ ❞❡✈✐❝❡s ❊♥❛❜❧❡s ❤✐❣❤✲❧❡✈❡❧ s②st❡♠✲❝❡♥tr✐❝ ❛❜str❛❝t✐♦♥ s♣❡❝✐✜❡s ❞✐str✐❜✉t❡❞ ❝♦♠♣✉t❛t✐♦♥s ❛s ♦♥❡ ❞❡❝❧❛r❛t✐✈❡ ♣r♦❣r❛♠ ❝♦♠♣✐❧❡s ✐♥t♦ ♥♦❞❡✲❝❡♥tr✐❝ ❢r❛❣♠❡♥ts✱ ❡①❡❝✉t❡❞ ❜② ❡❛❝❤ ♥♦❞❡ ❚②♣❡❞ ♠✉❧t✐s❡t r❡✇r✐t✐♥❣ ✇✐t❤ ❞❡❝❡♥tr❛❧✐③❛t✐♦♥ ❝♦♠♣r❡❤❡♥s✐♦♥ ♣❛tt❡r♥s t✐♠❡ s②♥❝❤r♦♥✐③❛t✐♦♥ ♠♦❞✉❧❛r✐t② ❉❡❝❧❛r❛t✐✈❡✱ ❝♦♥❝✐s❡✱ r♦♦ts ✐♥ ❧✐♥❡❛r ❧♦❣✐❝

slide-4
SLIDE 4

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

❈♦♠✐♥❣❧❡

❆ ♣r♦❣r❛♠♠✐♥❣ ❧❛♥❣✉❛❣❡ ❢♦r ❞✐str✐❜✉t❡❞ ♠♦❜✐❧❡ ❛♣♣s

❉❡s✐❣♥❡❞ t♦ ✐♠♣❧❡♠❡♥t ♠♦❜✐❧❡ ❛♣♣s t❤❛t r✉♥ ❛❝r♦ss ❆♥❞r♦✐❞ ❞❡✈✐❝❡s ❊♥❛❜❧❡s ❤✐❣❤✲❧❡✈❡❧ s②st❡♠✲❝❡♥tr✐❝ ❛❜str❛❝t✐♦♥ s♣❡❝✐✜❡s ❞✐str✐❜✉t❡❞ ❝♦♠♣✉t❛t✐♦♥s ❛s ♦♥❡ ❞❡❝❧❛r❛t✐✈❡ ♣r♦❣r❛♠ ❝♦♠♣✐❧❡s ✐♥t♦ ♥♦❞❡✲❝❡♥tr✐❝ ❢r❛❣♠❡♥ts✱ ❡①❡❝✉t❡❞ ❜② ❡❛❝❤ ♥♦❞❡ ❚②♣❡❞ ♠✉❧t✐s❡t r❡✇r✐t✐♥❣ ✇✐t❤ ❞❡❝❡♥tr❛❧✐③❛t✐♦♥ ❝♦♠♣r❡❤❡♥s✐♦♥ ♣❛tt❡r♥s t✐♠❡ s②♥❝❤r♦♥✐③❛t✐♦♥ ♠♦❞✉❧❛r✐t② ❉❡❝❧❛r❛t✐✈❡✱ ❝♦♥❝✐s❡✱ r♦♦ts ✐♥ ❧✐♥❡❛r ❧♦❣✐❝

slide-5
SLIDE 5

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

❊①❛♠♣❧❡✿ ❙✇❛♣ ❉❛t❛ ❜❡t✇❡❡♥ X ❛♥❞ Y ✉♣ t♦ ❚❤r❡s❤♦❧❞ P

■♥ ♠❛t❤✿

♣✐✈♦t❙✇❛♣ ❳ s✇❛♣ ❨ P ❳ ✐t❡♠ ❉ ❉ P

❉ ❳s

❨ ✐t❡♠ ❉ ❉ P

❉ ❨s

❨ ✐t❡♠ ❉

❉ ❳s

❳ ✐t❡♠ ❉

❉ ❨s

■♥ ❝♦❞❡✿

slide-6
SLIDE 6

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

❊①❛♠♣❧❡✿ ❙✇❛♣ ❉❛t❛ ❜❡t✇❡❡♥ X ❛♥❞ Y ✉♣ t♦ ❚❤r❡s❤♦❧❞ P

■♥ ♠❛t❤✿

♣✐✈♦t❙✇❛♣ : [❳]s✇❛♣(❨ , P) [❳]✐t❡♠(❉) | ❉ ≥ P❉❳s [❨ ]✐t❡♠(❉) | ❉ ≤ P❉❨s ⊸ [❨ ]✐t❡♠(❉)❉❳s [❳]✐t❡♠(❉)❉❨s

■♥ ❝♦❞❡✿

slide-7
SLIDE 7

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

❊①❛♠♣❧❡✿ ❙✇❛♣ ❉❛t❛ ❜❡t✇❡❡♥ X ❛♥❞ Y ✉♣ t♦ ❚❤r❡s❤♦❧❞ P

■♥ ♠❛t❤✿

♣✐✈♦t❙✇❛♣ : [❳]s✇❛♣(❨ , P) [❳]✐t❡♠(❉) | ❉ ≥ P❉❳s [❨ ]✐t❡♠(❉) | ❉ ≤ P❉❨s ⊸ [❨ ]✐t❡♠(❉)❉❳s [❳]✐t❡♠(❉)❉❨s

■♥ ❝♦❞❡✿

predicate swap :: (loc,int) -> trigger. predicate item :: int -> fact. predicate display :: (string,A) -> actuator. rule pivotSwap :: [X]swap(Y,P), {[X]item(D)|D->Xs. D >= P}, {[Y]item(D)|D->Ys. D <= P}

  • -o [X]display(Msg,size(Ys),Y), {[X]item(D)|D<-Ys},

[Y]display(Msg,size(Xs),X), {[Y]item(D)|D<-Xs} where Msg = "Received %s items from %s".

slide-8
SLIDE 8

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

❊①❛♠♣❧❡✿ pivotSwap ❊①❡❝✉t✐♦♥

[X]swap(Y,P) {[X]item(D)|D->Xs.D>=P} --o [X]display(Msg,size(Ys),Y), {[X]item(D)|D<-Ys} {[Y]item(D)|D->Ys.D<=P} [Y]display(Msg,size(Xs),X), {[Y]item(D)|D<-Xs} where Msg = "Received %s items from %s".

▲❡t s = swap✱ i = item ❛♥❞ d = display

Node: n✶

s(n✷, ✺), i(✹), i(✻), i(✽)

Node: n✷

i(✸), i(✷✵)

Node: n✸

s(n✷, ✶✵), i(✶✽) ✶ ✶ ✷ ✸ ✹ ✷ ✷ ✶ ✻ ✽ ✷✵ ✸ ✷ ✶✵ ✶✽ ✶ ✶ ✷ ✹ ✸ ✷ ✷ ✶ ✶ ✸ ✶✽ ✷✵ ✸ ✷ ✷ ✻ ✽

slide-9
SLIDE 9

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

❊①❛♠♣❧❡✿ pivotSwap ❊①❡❝✉t✐♦♥

[X]swap(Y,P) {[X]item(D)|D->Xs.D>=P} --o [X]display(Msg,size(Ys),Y), {[X]item(D)|D<-Ys} {[Y]item(D)|D->Ys.D<=P} [Y]display(Msg,size(Xs),X), {[Y]item(D)|D<-Xs} where Msg = "Received %s items from %s".

▲❡t s = swap✱ i = item ❛♥❞ d = display

Node: n✶

s(n✷, ✺), i(✹), i(✻), i(✽)

  • Node: n✷

i(✸), i(✷✵)

Node: n✸

s(n✷, ✶✵), i(✶✽) ✶ ✶ ✷ ✸ ✹ ✷ ✷ ✶ ✻ ✽ ✷✵ ✸ ✷ ✶✵ ✶✽ ✶ ✶ ✷ ✹ ✸ ✷ ✷ ✶ ✶ ✸ ✶✽ ✷✵ ✸ ✷ ✷ ✻ ✽

slide-10
SLIDE 10

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

❊①❛♠♣❧❡✿ pivotSwap ❊①❡❝✉t✐♦♥

[X]swap(Y,P) {[X]item(D)|D->Xs.D>=P} --o [X]display(Msg,size(Ys),Y), {[X]item(D)|D<-Ys} {[Y]item(D)|D->Ys.D<=P} [Y]display(Msg,size(Xs),X), {[Y]item(D)|D<-Xs} where Msg = "Received %s items from %s".

▲❡t s = swap✱ i = item ❛♥❞ d = display

Node: n✶

s(n✷, ✺), i(✹), i(✻), i(✽)

  • Node: n✷

i(✸), i(✷✵)

Node: n✸

s(n✷, ✶✵), i(✶✽)

→

Node: n✶

d(”✶ from n✷”) i(✸), i(✹)

Node: n✷

d(”✷ from n✶”) i(✻), i(✽), i(✷✵)

Node: n✸

s(n✷, ✶✵), i(✶✽) ✶ ✶ ✷ ✹ ✸ ✷ ✷ ✶ ✶ ✸ ✶✽ ✷✵ ✸ ✷ ✷ ✻ ✽

slide-11
SLIDE 11

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

❊①❛♠♣❧❡✿ pivotSwap ❊①❡❝✉t✐♦♥

[X]swap(Y,P) {[X]item(D)|D->Xs.D>=P} --o [X]display(Msg,size(Ys),Y), {[X]item(D)|D<-Ys} {[Y]item(D)|D->Ys.D<=P} [Y]display(Msg,size(Xs),X), {[Y]item(D)|D<-Xs} where Msg = "Received %s items from %s".

▲❡t s = swap✱ i = item ❛♥❞ d = display

Node: n✶

s(n✷, ✺), i(✹), i(✻), i(✽)

  • Node: n✷

i(✸), i(✷✵)

Node: n✸

s(n✷, ✶✵), i(✶✽)

→

Node: n✶

d(”✶ from n✷”) i(✸), i(✹)

Node: n✷

d(”✷ from n✶”) i(✻), i(✽), i(✷✵)

Node: n✸

s(n✷, ✶✵), i(✶✽)

  • ✶

✶ ✷ ✹ ✸ ✷ ✷ ✶ ✶ ✸ ✶✽ ✷✵ ✸ ✷ ✷ ✻ ✽

slide-12
SLIDE 12

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

❊①❛♠♣❧❡✿ pivotSwap ❊①❡❝✉t✐♦♥

[X]swap(Y,P) {[X]item(D)|D->Xs.D>=P} --o [X]display(Msg,size(Ys),Y), {[X]item(D)|D<-Ys} {[Y]item(D)|D->Ys.D<=P} [Y]display(Msg,size(Xs),X), {[Y]item(D)|D<-Xs} where Msg = "Received %s items from %s".

▲❡t s = swap✱ i = item ❛♥❞ d = display

Node: n✶

s(n✷, ✺), i(✹), i(✻), i(✽)

  • Node: n✷

i(✸), i(✷✵)

Node: n✸

s(n✷, ✶✵), i(✶✽)

→

Node: n✶

d(”✶ from n✷”) i(✸), i(✹)

Node: n✷

d(”✷ from n✶”) i(✻), i(✽), i(✷✵)

Node: n✸

s(n✷, ✶✵), i(✶✽)

  • →

Node: n✶

d(”✶ from n✷”) i(✹), i(✸)

Node: n✷

d(”✷ from n✶”) d(”✶ from n✸”) i(✶✽), i(✷✵)

Node: n✸

d(”✷ from n✷”) i(✻), i(✽)

slide-13
SLIDE 13

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

❚r② ✐t ❨♦✉rs❡❧❢✦

❉♦✇♥❧♦❛❞ ❢r♦♠

https://github.com/sllam/comingle ❙❤♦✇ ②♦✉r s✉♣♣♦rt✱ ♣❧❡❛s❡ ❙❚❆❘ ❈♦♠✐♥❣❧❡ ●✐t❍✉❜ r❡♣♦s✐t♦r②✦

◆❡t✇♦r❦✐♥❣ ♦✈❡r ❲✐✜✲❉✐r❡❝t✱ ◆❋❈✱ ▲❆◆ ❛♥❞ ❇❧✉❡t♦♦t❤

s✉♣♣♦rt ❢♦r ❞r♦♣✲✐♥✴❞r♦♣✲♦✉t

Pr♦♦❢✲♦❢✲❝♦♥❝❡♣t ❛♣♣s

❉r❛❣ ❘❛❝✐♥❣ ✖ ❘❛❝✐♥❣ ❝❛rs ❛❝r♦ss ♠♦❜✐❧❡ ❞❡✈✐❝❡s ❇❛tt❧❡s❤✐♣ ✖ ❚r❛❞✐t✐♦♥❛❧ ♠❛r✐t✐♠❡ ✇❛r ❣❛♠❡✱ ♠✉❧t✐✲♣❛rt② ❲✐✜✲❉✐r❡❝t ❞✐r❡❝t♦r② ✖ ▼❛✐♥t❛✐♥✐♥❣ ■P t❛❜❧❡ ❢♦r ❲✐✜✲❉✐r❡❝t ▼✉s✐❝❛❧ s❤❛r❡s ✖ ❇♦✉♥❝❡ ❛ ♠✉s✐❝❛❧ ♣✐❡❝❡ ❜❡t✇❡❡♥ ❞❡✈✐❝❡s ❙✇❛r❜❜❧❡ ✖ ❘❡❛❧✲t✐♠❡ t❡❛♠✲❜❛s❡❞ s❝r❛❜❜❧❡ ▼❛✜❛ ✖ ❚r❛❞✐t✐♦♥❛❧ ♣❛rt② ❣❛♠❡✱ ✇✐t❤ ❛ ♠♦❜✐❧❡ t✇✐st ❈♦❉♦♦❞❧❡ ✖ ■♥t❡r❛❝t✐✈❡ ♣r❡s❡♥t❛t✐♦♥ t♦♦❧

slide-14
SLIDE 14

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

❖✉t❧✐♥❡

✶

❚❤❡ ❈♦♥t❡①t

✷

❚❤❡ Pr♦❜❧❡♠

✸

❚❤❡ ✭P❛rt✐❛❧✮ ❙♦❧✉t✐♦♥

✹

❚❤❡ ❈♦♥❝❧✉s✐♦♥s

slide-15
SLIDE 15

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

❙②♥t❛①

✭❆ ❈♦♠✐♥❣❧❡ ♣r♦❣r❛♠ P ✐s ❛ s❡t ♦❢ r✉❧❡s r : ¯ E | g ⊸ B ✇❤❡r❡ B ✐s ❛❧s♦ ❛ ♠✉❧t✐s❡ts ♦❢ ❡①♣r❡ss✐♦♥s❀ ✇❡ ❛r❡ ❛❧s♦ ✐❣♥♦r✐♥❣ ❧♦❝❛t✐♦♥s ❛♥❞ t②♣❡s✮

❆ ❤❡❛❞ ♣❛tt❡r♥ ¯ E | g ❝♦♥s✐sts ♦❢

❛ ♠✉❧t✐s❡t ♦❢ ❡①♣r❡ss✐♦♥s ¯ E ❛ ❇♦♦❧❡❛♥ ❣✉❛r❞ g

❆♥ ❡①♣r❡ss✐♦♥ E ✐s ❡✐t❤❡r

❛ ❢❛❝t✿ p( t) ❛ ❝♦♠♣r❡❤❡♥s✐♦♥✿ p( t) | g

xT

▼✉❧t✐s❡t ♦❢ ❛❧❧ p( t) ✐♥ t❤❡ st❛t❡ t❤❛t s❛t✐s❢② g

  • x ❜♦✉♥❞ ✐♥ g ❛♥❞

t ❈♦♠♣r❡❤❡♥s✐♦♥ r❛♥❣❡ T ✐s t❤❡ ♠✉❧t✐s❡t ♦❢ ❛❧❧ ❜✐♥❞✐♥❣s x

slide-16
SLIDE 16

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

▼❛t❝❤✐♥❣ ❙❡♠❛♥t✐❝s

❆ st❛t❡ ❙t ✐s ❛ ♠✉❧t✐s❡t ♦❢ ❣r♦✉♥❞ ❢❛❝ts ▼❛t❝❤✐♥❣ ❛ ❤❡❛❞ ♣❛tt❡r♥ H = ¯ E | g ❛❣❛✐♥st ❛ st❛t❡ ❙t ✇✐t❤ r❡s✐❞✉❛❧ ❙t−✿ ❙t

H

  • → ❙t−

❍♦❧❞s ✐❢ ❙t = ❙t+, ❙t− ❛♥❞ t❤❡r❡ ✐s ❛ ❣r♦✉♥❞ s✉❜st✐t✉t✐♦♥ θ s✉❝❤ t❤❛t

θ ¯ E ♠❛t❝❤❡s ❙t+ ❙t− ❞♦❡s ♥♦t ♠❛t❝❤ ❛♥② ❝♦♠♣r❡❤❡♥s✐♦♥ ✐♥ θ ¯ E θg ✐s ✈❛❧✐❞

θ ¯ E head ❙t+ θ ¯ E ¬

head ❙t−

| = θg ❙t+, ❙t−

¯ E|g

  • −

− → ❙t−

❈♦♠♣r❡❤❡♥s✐♦♥s ✐♥ ¯ E | g ♠❛t❝❤ ♠❛①✐♠❛❧ ♣♦rt✐♦♥s ♦❢ ❙t

slide-17
SLIDE 17

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

P❛tt❡r♥ ■♥t❡r❛❝t✐♦♥s

❲❤❡♥ ❞♦ t✇♦ ❤❡❛❞ ♣❛tt❡r♥s ✐♥t❡r❢❡r❡ ✇✐t❤ ❡❛❝❤ ♦t❤❡r❄

❯s❡❢✉❧ ❢♦r

❞❡❜✉❣❣✐♥❣ ✐♠♣❧❡♠❡♥t❛t✐♦♥ r❡❛s♦♥✐♥❣ ❝♦st ❛♥❛❧②s✐s

■♥t❡r❢❡r❡♥❝❡❄

❖♥❡✬s ❝♦♥s✉♠❡❞ ❢❛❝ts ♠❛② ♣r❡✈❡♥t t❤❡ ♦t❤❡r ❢r♦♠ ❜❡✐♥❣ ❛♣♣❧✐❝❛❜❧❡ ✳ ✳ ✳ ♣♦ss✐❜❧② ❝♦♥❝✉rr❡♥t❧②

slide-18
SLIDE 18

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

❖✈❡r❧❛♣ ❛♥❞ ■♥❞❡♣❡♥❞❡♥❝❡

H✶ = ¯ E✶ | g✶ ❛♥❞ H✷ = ¯ E✷ | g✷ ✇✐t❤♦✉t ✈❛r✐❛❜❧❡s ✐♥ ❝♦♠♠♦♥

♦✈❡r❧❛♣ ✐❢ t❤❡r❡ ✐s ❛ st❛t❡ ❙t s✉❝❤ t❤❛t

❙t

H✶

  • −

→ ❙t✶ ❢♦r s♦♠❡ ❙t✶ ❛♥❞ ❙t

H✷

  • −

→ ❙t✷ ❢♦r s♦♠❡ ❙t✷✱

❜✉t t❤❡r❡ ✐s ♥♦ ❙t′ s✉❝❤ t❤❛t ❙t

H✶H✷

  • −

− − → ❙t′✳

❊✳❣✳✱ H✶ = p(a, X), q(X) ❛♥❞ H✷ = p(Y , Y ), r(Z) ❚❛❦❡ ❙t = (a, a), q(a), r(b)

❛r❡ ✐♥❞❡♣❡♥❞❡♥t ✐❢ t❤❡② ❞♦♥✬t ♦✈❡r❧❛♣

❊✳❣✳✱ H✶ ❛♥❞ H′

✷ = p(b, Y ), r(Z)

❆r❡ t❤❡r❡ ❛❧❣♦r✐t❤♠✐❝ ❝r✐t❡r✐❛❄

slide-19
SLIDE 19

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

❖✉t❧✐♥❡

✶

❚❤❡ ❈♦♥t❡①t

✷

❚❤❡ Pr♦❜❧❡♠

✸

❚❤❡ ✭P❛rt✐❛❧✮ ❙♦❧✉t✐♦♥

✹

❚❤❡ ❈♦♥❝❧✉s✐♦♥s

slide-20
SLIDE 20

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

❈❛s❡✿ P❧❛✐♥ ▼✉❧t✐s❡ts

H = ¯ F✿ ❡♠♣t② ❣✉❛r❞ ❛♥❞ ♥♦ ❝♦♠♣r❡❤❡♥s✐♦♥s H✶ ❛♥❞ H✷ ♦✈❡r❧❛♣ ✐✛ ♦♥❡ ❝♦♥t❛✐♥s ❛ ❢❛❝t ✉♥✐✜❛❜❧❡ ✐♥ t❤❡ ♦t❤❡r✿

H✶ = p( t✶), ¯ F ′

✶

H✷ = p( t✷), ¯ F ′

✷

t❤❡r❡ ✐s θ s✉❝❤ t❤❛t θ t✶ = θ t✷

◆♦t❡s✿

p( t✶) ❛♥❞ p( t✷) ♠❛② ♥♦t ❜❡ ✉♥✐q✉❡ P♦❧②♥♦♠✐❛❧ ❝♦♠♣❧❡①✐t② ✳ ✳ ✳ ❢♦r ✇❡❧❧✲❜❡❤❛✈❡❞ t❡r♠ ❧❛♥❣✉❛❣❡s ■♠♣❧❡♠❡♥t❡❞ ✉s✐♥❣ t❡r♠✲❧❛♥❣✉❛❣❡ ✉♥✐✜❝❛t✐♦♥

slide-21
SLIDE 21

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

❈❛s❡✿ ●✉❛r❞❡❞ ▼✉❧t✐s❡ts

H = ¯ F | g✿ ♥♦ ❝♦♠♣r❡❤❡♥s✐♦♥s ✖ ❢♦✉♥❞ ✐♥ ♠♦st r✉❧❡✲❜❛s❡❞ ❧❛♥❣✉❛❣❡s H✶ ❛♥❞ H✷ ♦✈❡r❧❛♣ ✐✛

H✶ = p( t✶), ¯ F ′

✶

H✷ = p( t✷), ¯ F ′

✷

t❤❡r❡ ✐s θ s✉❝❤ t❤❛t θ t✶ = θ t✷ ❛♥❞ | = θg✶ ❛♥❞ | = θg✷

❊①❛♠♣❧❡s✿

H✶ = p(X) | X > ✸ ❛♥❞ H✷ = p(Y ) | Y < ✶✵ ♦✈❡r❧❛♣

❊✳❣✳✱ ✐♥ st❛t❡ p(✼)

H✶ ❛♥❞ H′

✷ = p(Y ) | Y < ✸ ❛r❡ ✐♥❞❡♣❡♥❞❡♥t

■♠♣❧❡♠❡♥t❛t✐♦♥✿ ❝♦♠♣✉t❡ ✉♥✐✜❡rs θ ❢♦r p( t✶) ❛♥❞ p( t✷)✱ ❛♥❞ t❤❡♥ ♣❛ss θg✶ ❛♥❞ θg✷ t♦ ❛♥ ❙▼❚ s♦❧✈❡r

slide-22
SLIDE 22

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

❈❛s❡✿ ❖♣❡♥✲❡♥❞❡❞ ▼✉❧t✐s❡ts

H = ¯ E | g✿ ❝♦♠♣r❡❤❡♥s✐♦♥ r❛♥❣❡s ✐s ♥❡✈❡r ✉s❡❞

p(X), p(x) | x > ✵x❳s ❜✉t ♥♦t p(X), p(x) | x > ✵x❳s | s✐③❡(❳s) = ✵

H✶ ❛♥❞ H✷ ♦✈❡r❧❛♣ ❡①❛❝t❧② ❛s ✐♥ ❧❛st ❝❛s❡✦

❖♣❡♥✲❡♥❞❡❞ ❝♦♠♣r❡❤❡♥s✐♦♥s ❝❛♥ ♥❡✈❡r ❢❛✐❧ ❆t ♠♦st r❡t✉r♥ t❤❡ ❡♠♣t② ♠✉❧t✐s❡t ❈♦♥s✐❞❡r H✶ = p(X) ❛♥❞ H✷ = p(x)x❳s✿

p(a)

H✶

  • −

→ ∅ p(a)

H✷

  • −

→ ∅ p(a)

H✶H✷

  • −

− − → ∅ ❜❡❝❛✉s❡ ∅

H✷

  • −

→ ∅

slide-23
SLIDE 23

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

  • ❡♥❡r❛❧ ❈❛s❡

❯♥s♦❧✈❡❞✦

✶ ❳s

❳s ❛♥❞

✷

❛r❡ ♦✈❡r❧❛♣♣✐♥❣✿

❙✉❝❝❡❡❞ s❡♣❛r❛t❡❧② ♦♥ ❙t ❈♦♠♣♦s✐t✐♦♥ ❢❛✐❧s ❛s ❣✉❛r❞ ♦❢

✷ ❢❛✐❧s

❇✉t

✶

✸

❳s

❳s ❛♥❞

✷

✺ ❛r❡ ✐♥❞❡♣❡♥❞❡♥t✿

❜❡❝❛✉s❡ ♥♦ ❢❛❝t ❝❛♥ ♠❛t❝❤ ❜♦t❤ ♣❛tt❡r♥s

slide-24
SLIDE 24

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

  • ❡♥❡r❛❧ ❈❛s❡

❯♥s♦❧✈❡❞✦ H✶ = p(x)x❳s, q(Y ) | Y ∈ ❳s ❛♥❞ H✷ = p(Z) ❛r❡ ♦✈❡r❧❛♣♣✐♥❣✿

❙✉❝❝❡❡❞ s❡♣❛r❛t❡❧② ♦♥ ❙t = p(a), q(a) ❈♦♠♣♦s✐t✐♦♥ ❢❛✐❧s ❛s ❣✉❛r❞ ♦❢ H✷ ❢❛✐❧s

❇✉t

✶

✸

❳s

❳s ❛♥❞

✷

✺ ❛r❡ ✐♥❞❡♣❡♥❞❡♥t✿

❜❡❝❛✉s❡ ♥♦ ❢❛❝t ❝❛♥ ♠❛t❝❤ ❜♦t❤ ♣❛tt❡r♥s

slide-25
SLIDE 25

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

  • ❡♥❡r❛❧ ❈❛s❡

❯♥s♦❧✈❡❞✦ H✶ = p(x)x❳s, q(Y ) | Y ∈ ❳s ❛♥❞ H✷ = p(Z) ❛r❡ ♦✈❡r❧❛♣♣✐♥❣✿

❙✉❝❝❡❡❞ s❡♣❛r❛t❡❧② ♦♥ ❙t = p(a), q(a) ❈♦♠♣♦s✐t✐♦♥ ❢❛✐❧s ❛s ❣✉❛r❞ ♦❢ H✷ ❢❛✐❧s

❇✉t H✶ = p(x) | x < ✸x❳s, q(Y ) | Y ∈ ❳s ❛♥❞ H✷ = p(Z) | Z > ✺ ❛r❡ ✐♥❞❡♣❡♥❞❡♥t✿

❜❡❝❛✉s❡ ♥♦ ❢❛❝t p(n) ❝❛♥ ♠❛t❝❤ ❜♦t❤ ♣❛tt❡r♥s

slide-26
SLIDE 26

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

  • ❡♥❡r❛❧ ❈❛s❡

H✶ = p(x)x❳s | s✐③❡(❳s) > ✵ ❛♥❞ H✷ = p(Z) ❛r❡ ♦✈❡r❧❛♣♣✐♥❣✿

❙✉❝❝❡❡❞ s❡♣❛r❛t❡❧② ♦♥ ❙t ❈♦♠♣♦s✐t✐♦♥ ❢❛✐❧s ❛s ❳s s❡t t♦ ✱ ✈✐♦❧❛t✐♥❣ ❣✉❛r❞

❇✉t

✶ ❳s

s✐③❡ ❳s ✽ ❛♥❞

✷

❛r❡ ✐♥❞❡♣❡♥❞❡♥t✿

❜❡❝❛✉s❡ ✐t ❤❛s ❛♥ ✉♣♣❡r ❜♦✉♥❞ ♦♥ t❤❡ ❝♦♠♣r❡❤❡♥s✐♦♥ r❛♥❣❡✱ ♥♦t ❛ ❧♦✇❡r ❜♦✉♥❞

◆❡❣❛t✐♦♥✲❛s✲❛❜s❡♥❝❡✿

✶ ❳s

s✐③❡ ❳s ✵ ❛♥❞

✷

slide-27
SLIDE 27

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

  • ❡♥❡r❛❧ ❈❛s❡

H✶ = p(x)x❳s | s✐③❡(❳s) > ✵ ❛♥❞ H✷ = p(Z) ❛r❡ ♦✈❡r❧❛♣♣✐♥❣✿

❙✉❝❝❡❡❞ s❡♣❛r❛t❡❧② ♦♥ ❙t = p(a) ❈♦♠♣♦s✐t✐♦♥ ❢❛✐❧s ❛s ❳s s❡t t♦ ∅✱ ✈✐♦❧❛t✐♥❣ ❣✉❛r❞

❇✉t

✶ ❳s

s✐③❡ ❳s ✽ ❛♥❞

✷

❛r❡ ✐♥❞❡♣❡♥❞❡♥t✿

❜❡❝❛✉s❡ ✐t ❤❛s ❛♥ ✉♣♣❡r ❜♦✉♥❞ ♦♥ t❤❡ ❝♦♠♣r❡❤❡♥s✐♦♥ r❛♥❣❡✱ ♥♦t ❛ ❧♦✇❡r ❜♦✉♥❞

◆❡❣❛t✐♦♥✲❛s✲❛❜s❡♥❝❡✿

✶ ❳s

s✐③❡ ❳s ✵ ❛♥❞

✷

slide-28
SLIDE 28

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

  • ❡♥❡r❛❧ ❈❛s❡

H✶ = p(x)x❳s | s✐③❡(❳s) > ✵ ❛♥❞ H✷ = p(Z) ❛r❡ ♦✈❡r❧❛♣♣✐♥❣✿

❙✉❝❝❡❡❞ s❡♣❛r❛t❡❧② ♦♥ ❙t = p(a) ❈♦♠♣♦s✐t✐♦♥ ❢❛✐❧s ❛s ❳s s❡t t♦ ∅✱ ✈✐♦❧❛t✐♥❣ ❣✉❛r❞

❇✉t H✶ = p(x)x❳s | s✐③❡(❳s) ≤ ✽ ❛♥❞ H✷ = p(Z) ❛r❡ ✐♥❞❡♣❡♥❞❡♥t✿

❜❡❝❛✉s❡ ✐t ❤❛s ❛♥ ✉♣♣❡r ❜♦✉♥❞ ♦♥ t❤❡ ❝♦♠♣r❡❤❡♥s✐♦♥ r❛♥❣❡✱ ♥♦t ❛ ❧♦✇❡r ❜♦✉♥❞

◆❡❣❛t✐♦♥✲❛s✲❛❜s❡♥❝❡✿

✶ ❳s

s✐③❡ ❳s ✵ ❛♥❞

✷

slide-29
SLIDE 29

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

  • ❡♥❡r❛❧ ❈❛s❡

H✶ = p(x)x❳s | s✐③❡(❳s) > ✵ ❛♥❞ H✷ = p(Z) ❛r❡ ♦✈❡r❧❛♣♣✐♥❣✿

❙✉❝❝❡❡❞ s❡♣❛r❛t❡❧② ♦♥ ❙t = p(a) ❈♦♠♣♦s✐t✐♦♥ ❢❛✐❧s ❛s ❳s s❡t t♦ ∅✱ ✈✐♦❧❛t✐♥❣ ❣✉❛r❞

❇✉t H✶ = p(x)x❳s | s✐③❡(❳s) ≤ ✽ ❛♥❞ H✷ = p(Z) ❛r❡ ✐♥❞❡♣❡♥❞❡♥t✿

❜❡❝❛✉s❡ ✐t ❤❛s ❛♥ ✉♣♣❡r ❜♦✉♥❞ ♦♥ t❤❡ ❝♦♠♣r❡❤❡♥s✐♦♥ r❛♥❣❡✱ ♥♦t ❛ ❧♦✇❡r ❜♦✉♥❞

◆❡❣❛t✐♦♥✲❛s✲❛❜s❡♥❝❡✿

✶ ❳s

s✐③❡ ❳s ✵ ❛♥❞

✷

slide-30
SLIDE 30

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

  • ❡♥❡r❛❧ ❈❛s❡

H✶ = p(x)x❳s | s✐③❡(❳s) > ✵ ❛♥❞ H✷ = p(Z) ❛r❡ ♦✈❡r❧❛♣♣✐♥❣✿

❙✉❝❝❡❡❞ s❡♣❛r❛t❡❧② ♦♥ ❙t = p(a) ❈♦♠♣♦s✐t✐♦♥ ❢❛✐❧s ❛s ❳s s❡t t♦ ∅✱ ✈✐♦❧❛t✐♥❣ ❣✉❛r❞

❇✉t H✶ = p(x)x❳s | s✐③❡(❳s) ≤ ✽ ❛♥❞ H✷ = p(Z) ❛r❡ ✐♥❞❡♣❡♥❞❡♥t✿

❜❡❝❛✉s❡ ✐t ❤❛s ❛♥ ✉♣♣❡r ❜♦✉♥❞ ♦♥ t❤❡ ❝♦♠♣r❡❤❡♥s✐♦♥ r❛♥❣❡✱ ♥♦t ❛ ❧♦✇❡r ❜♦✉♥❞

◆❡❣❛t✐♦♥✲❛s✲❛❜s❡♥❝❡✿ H✶ = p(x)x❳s | s✐③❡(❳s) = ✵ ❛♥❞ H✷ = p(Z)

slide-31
SLIDE 31

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

  • ❡♥❡r❛❧ ❈❛s❡

H✶ = p(x)x❳s, q(y)y❳s ❛♥❞ H✷ = p(Z) ❛r❡ ♦✈❡r❧❛♣♣✐♥❣✿

❙✉❝❝❡❡❞ s❡♣❛r❛t❡❧② ♦♥ ❙t = p(a), q(a) ❈♦♠♣♦s✐t✐♦♥ ❢❛✐❧s

✶ ❳s

❳s

❨s

❛♥❞

✷

❛r❡ ✐♥❞❡♣❡♥❞❡♥t✿

❜❡❝❛✉s❡ ✐t ✜❧t❡rs ♦✉t ✈❛❧✉❡s ❢♦r ❨s r❛t❤❡r t❤❛♥ r❡q✉✐r✐♥❣ t❤❛t s♦♠❡ t❡r♠s ❜❡ ♣r❡s❡♥t

slide-32
SLIDE 32

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

  • ❡♥❡r❛❧ ❈❛s❡

H✶ = p(x)x❳s, q(y)y❳s ❛♥❞ H✷ = p(Z) ❛r❡ ♦✈❡r❧❛♣♣✐♥❣✿

❙✉❝❝❡❡❞ s❡♣❛r❛t❡❧② ♦♥ ❙t = p(a), q(a) ❈♦♠♣♦s✐t✐♦♥ ❢❛✐❧s

H✶ = p(x)x❳s, q(y) | y ∈ ❳sy❨s ❛♥❞ H✷ = p(Z) ❛r❡ ✐♥❞❡♣❡♥❞❡♥t✿

❜❡❝❛✉s❡ ✐t ✜❧t❡rs ♦✉t ✈❛❧✉❡s ❢♦r ❨s r❛t❤❡r t❤❛♥ r❡q✉✐r✐♥❣ t❤❛t s♦♠❡ t❡r♠s ❜❡ ♣r❡s❡♥t

slide-33
SLIDE 33

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

❖✉t❧✐♥❡

✶

❚❤❡ ❈♦♥t❡①t

✷

❚❤❡ Pr♦❜❧❡♠

✸

❚❤❡ ✭P❛rt✐❛❧✮ ❙♦❧✉t✐♦♥

✹

❚❤❡ ❈♦♥❝❧✉s✐♦♥s

slide-34
SLIDE 34

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

❋✉t✉r❡ ❲♦r❦

▲♦ts ♠♦r❡ ✇♦r❦ t♦ ❜❡ ❞♦♥❡✦

slide-35
SLIDE 35

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

◗✉❡st✐♦♥s❄

slide-36
SLIDE 36

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

❈♦♠✐♥❣❧❡ ❊①❛♠♣❧❡✿ ❉r❛❣ ❘❛❝✐♥❣

■♥s♣✐r❡❞ ❜② ❈❤r♦♠❡ ❘❛❝❡r ✭www.chrome.com/racer✮ ❘❛❝❡ ❛❝r♦ss ❛ ❣r♦✉♣ ♦❢ ♠♦❜✐❧❡ ❞❡✈✐❝❡s P✉r❡❧② ❧♦❝❛❧ ❝♦♠♠✉♥✐❝❛t✐♦♥s

slide-37
SLIDE 37

❈♦♥t❡①t Pr♦❜❧❡♠ ❙♦❧✉t✐♦♥ ❈♦♥❝❧✉s✐♦♥s

■♠♣❧❡♠❡♥t✐♥❣ ❉r❛❣ ❘❛❝✐♥❣ ✐♥ ❈♦♠✐♥❣❧❡

rule init :: [I]initRace(Ls)

  • -o {[A]next(B)|(A,B)<-Cs}, [E]last(),

{[I]has(P), [P]all(Ps), [P]at(I), [P]rendTrack(Ls) | P<-Ps} where (Cs,E) = makeChain(I,Ls), Ps = list2mset(Ls). rule start :: [X]all(Ps) \ [X]startRace() --o {[P]release()|P<-Ps}. rule tap :: [X]at(Y) \ [X]sendTap() --o [Y]recvTap(X). rule trans :: [X]next(Z) \ [X]exiting(Y), [Y]at(X) --o [Z]has(Y), [Y]at(Z). rule win :: [X]last() \ [X]all(Ps), [X]exiting(Y) --o {[P]decWinner(Y) | P <- Ps}.

✰ ✽✻✷ ❧✐♥❡s ♦❢ ♣r♦♣❡r❧② ✐♥❞❡♥t❡❞ ❏❛✈❛ ❝♦❞❡

✼✵✵++ ❧✐♥❡s ♦❢ ❧♦❝❛❧ ♦♣❡r❛t✐♦♥s ✭❡✳❣✳✱ ❞✐s♣❧❛② ❛♥❞ ❯■ ♦♣❡r❛t✐♦♥s✮ < ✶✵✵ ❧✐♥❡s ❢♦r ✐♥✐t✐❛❧✐③✐♥❣ ❈♦♠✐♥❣❧❡ r✉♥✲t✐♠❡