Specifjcation and Implementation of Replicated List The Jupiter - - PowerPoint PPT Presentation

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Specifjcation and Implementation of Replicated List

— The Jupiter Protocol Revisited (OPODIS’2018)

Hengfeng Wei, Yu Huang, Jian Lu

Nanjing University

December 17, 2018

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The Main Contribution

The Jupiter protocol [Nichols et al., 1995]a for replicated list satisfjes the weak list specifjcation [Attiya et al., 2016]b.

aDavid A. Nichols et al. (1995). “High-latency, Low-bandwidth

Windowing in the Jupiter Collaboration System”. In: Proceedings of the 8th Annual ACM Symposium on User Interface and Software Technology. UIST ’95. ACM, pp. 111–120.

bHagit Attiya et al. (2016). “Specifjcation and complexity of

collaborative text editing”. In: Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing. PODC ’16. ACM, pp. 259–268.

This was proposed as a conjecture in a PODC paper [Attiya et al., 2016].

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The Main Contribution

The Jupiter protocol [Nichols et al., 1995]a for replicated list satisfjes the weak list specifjcation [Attiya et al., 2016]b.

aDavid A. Nichols et al. (1995). “High-latency, Low-bandwidth

Windowing in the Jupiter Collaboration System”. In: Proceedings of the 8th Annual ACM Symposium on User Interface and Software Technology. UIST ’95. ACM, pp. 111–120.

bHagit Attiya et al. (2016). “Specifjcation and complexity of

collaborative text editing”. In: Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing. PODC ’16. ACM, pp. 259–268.

This was proposed as a conjecture in a PODC paper [Attiya et al., 2016].

Hengfeng Wei (Nanjing University) Replicated List (Jupiter) December 17, 2018 2 / 32

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Outline

• 1. Why do we care about replicated list?
• 2. What is the weak list specifjcation

weak?

• 3. How does the Jupiter protocol work?
• 4. How to prove that Jupiter satisfjes

weak?

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Outline

• 1. Why do we care about replicated list?
• 2. What is the weak list specifjcation

weak?

• 3. How does the Jupiter protocol work?
• 4. How to prove that Jupiter satisfjes

weak?

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Outline

• 1. Why do we care about replicated list?
• 2. What is the weak list specifjcation Aweak?
• 3. How does the Jupiter protocol work?
• 4. How to prove that Jupiter satisfjes

weak?

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Outline

• 1. Why do we care about replicated list?
• 2. What is the weak list specifjcation Aweak?
• 3. How does the Jupiter protocol work?
• 4. How to prove that Jupiter satisfjes

weak?

Hengfeng Wei (Nanjing University) Replicated List (Jupiter) December 17, 2018 3 / 32

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Outline

• 1. Why do we care about replicated list?
• 2. What is the weak list specifjcation Aweak?
• 3. How does the Jupiter protocol work?
• 4. How to prove that Jupiter satisfjes Aweak?

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Replicated List

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Replicated Collaborative Text Editing Systems

(a) Google Docs (b) Apache Wave (c) Wikipedia (d) L

A

T EX Editor

Replicas are required to respond to user operations immediately. Updates are propagated to other replicas asynchronously.

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Replicated list object: to model the core functionality

Ins(a, p) : Insert a at position p. Del(p) : Delete the element at position p. Read : Return the list.

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Weak List Specifjcation

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Defjnition (Weak List Specifjcation Aweak [Attiya et al., 2016]) Informally, Aweak requires the ordering between elements that are not deleted to be consistent across the system.

Specify a global property on all states across the system.

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We show that Aweak can be rephrased as

Defjnition (Pairwise State Compatibility Property) For any pair of list states, there cannot be two elements a and b such that a precedes b in one state but b precedes a in the other.

σ0 : ab σ1 : ba a b σ0 : ab σ1 : ba

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Jupiter

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Jupiter adopts the client-server architecture [Nichols et al., 1995]: (n + 1) replicas ≜ (n) Client + (1) Server

S C1 C2 C3 User

Issue Ops Respond Immed.

Client

FIFO Updates

Server

FIFO Updates

Other Clients

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Jupiter adopts the client-server architecture [Nichols et al., 1995]: (n + 1) replicas ≜ (n) Client + (1) Server

S C1 C2 C3

1 2 3 4

2 2 1 1 3 3 4 4

User

Issue Ops

− − − − − − − − − − − →

Respond Immed.

Client

FIFO

− − − − − − − →

Updates

Server

FIFO

− − − − − − − →

Updates

Other Clients

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Challenge: Confmicts caused by concurrent operations

(The server is not drawn.)

efecte efecte

Ins Del

efgecte efect

Ins Del

efgece efgect efecte efecte

Ins Del

efgecte efect

Ins Del

efgect efgect Solution: Operational Transformation (OT) [Ellis and Gibbs, 1989]

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Challenge: Confmicts caused by concurrent operations

(The server is not drawn.)

efecte

C1

efecte

C2

Ins Del

efgecte efect

Ins Del

efgece efgect efecte efecte

Ins Del

efgecte efect

Ins Del

efgect efgect Solution: Operational Transformation (OT) [Ellis and Gibbs, 1989]

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Challenge: Confmicts caused by concurrent operations

(The server is not drawn.)

efecte

C1

efecte

C2

• 1 = Ins(f, 1)
• 2 = Del(5)

efgecte efect

Ins Del

efgece efgect efecte efecte

Ins Del

efgecte efect

Ins Del

efgect efgect Solution: Operational Transformation (OT) [Ellis and Gibbs, 1989]

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Challenge: Confmicts caused by concurrent operations

(The server is not drawn.)

efecte

C1

efecte

C2

• 1 = Ins(f, 1)
• 2 = Del(5)

efgecte efect

• ′

1 = Ins(f, 1)

• ′

2 = Del(5)

efgece efgect efecte efecte

Ins Del

efgecte efect

Ins Del

efgect efgect Solution: Operational Transformation (OT) [Ellis and Gibbs, 1989]

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Challenge: Confmicts caused by concurrent operations

(The server is not drawn.)

efecte

C1

efecte

C2

• 1 = Ins(f, 1)
• 2 = Del(5)

efgecte efect

• ′

1 = Ins(f, 1)

• ′

2 = Del(5)

efgece efgect efecte

C1

efecte

C2

• 1 = Ins(f, 1)
• 2 = Del(5)

efgecte efect

Ins Del

efgect efgect Solution: Operational Transformation (OT) [Ellis and Gibbs, 1989]

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Challenge: Confmicts caused by concurrent operations

(The server is not drawn.)

efecte

C1

efecte

C2

• 1 = Ins(f, 1)
• 2 = Del(5)

efgecte efect

• ′

1 = Ins(f, 1)

• ′

2 = Del(5)

efgece efgect efecte

C1

efecte

C2

• 1 = Ins(f, 1)
• 2 = Del(5)

efgecte efect

• ′

1 = Ins(f, 1)

• ′

2 = Del(6)

efgect efgect Solution: Operational Transformation (OT) [Ellis and Gibbs, 1989]

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σ

• 1
• 2
• ′

2 = OT(o2, o1)

• ′

1 = OT(o1, o2)

Commutative:

σ; o1; o′

2 ≡ σ; o2; o′ 1

[Ellis and Gibbs, 1989]

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Q : What if replicas diverge by ≥ 2 steps?

0123 123 13

Del(0) Del(1) Del(3) Del Del Del Del

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Q : What if replicas diverge by ≥ 2 steps?

0123 123 13

Del(0) Del(1)

012

Del(3) Del Del Del Del

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Q : What if replicas diverge by ≥ 2 steps?

0123 123 13

Del(0) Del(1)

012

Del(3)

12

Del(2) Del(0) Del Del

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Q : What if replicas diverge by ≥ 2 steps?

0123 123 13

Del(0) Del(1)

012

Del(3)

1 12

Del(2) Del(0) Del(1) Del(1)

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Key Challenge to Solve: When a replica r receives an operation o from another replica redirected by the server, how should o be transformed?

Transformed with which operations and in what order?

Key Ideas:

• 1. With concurrent operations previously executed at
• 2. In the serialization order of operations established at the server

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Key Challenge to Solve: When a replica r receives an operation o from another replica redirected by the server, how should o be transformed?

Transformed with which operations and in what order?

Key Ideas:

• 1. With concurrent operations previously executed at
• 2. In the serialization order of operations established at the server

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Key Challenge to Solve: When a replica r receives an operation o from another replica redirected by the server, how should o be transformed?

Transformed with which operations and in what order?

Key Ideas:

• 1. With concurrent operations previously executed at r
• 2. In the serialization order of operations established at the server

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Jupiter uses 2D state spaces

[Xu, Sun, and Li, 2014]

to manage the procedure of performing OTs [Ellis and Gibbs, 1989].

0123 123 13 1 012 12

Del(0) Del(1) Del(3) Del(2) Del(0) Del(1) Del(1)

• Edges are labeled with operations.

Local Dimension: For operations generated by the client Global Dimension: For operations generated by others

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Jupiter uses 2D state spaces

[Xu, Sun, and Li, 2014]

to manage the procedure of performing OTs [Ellis and Gibbs, 1989].

0123 123 13 1 012 12

Del(0) Del(1) Del(3) Del(2) Del(0) Del(1) Del(1)

• Edges are labeled with operations.

Local Dimension: For operations generated by the client Global Dimension: For operations generated by others

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Each client maintains a 2D state space.

C1 C2 C3 S

C1 C2 C3

The server maintains n (= 3) 2D state spaces, one for each client.

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Mismatch!

Global property on all replica states specifjed by Aweak Local view each replica maintains in Jupiter

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CJupiter (Compact Jupiter)

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CJupiter maintains an n-ary ordered state space for each replica.

ϵ 1 x

1: Ins(x, 0)

12 ϵ 13 ax 123 a

2: Del(x, 0) 3: Ins(a, 0) 3: Ins(a, 0) 2: Del(x, 1)

124 b

4: Ins(b, 0)

1234 ba

3 : I n s ( a , 1 ) 4: Ins(b, 0)

14 xb

4 : I n s ( b , 1 ) 2 : D e l ( x , )

There can be more than two edges coming from the same node. Edges from the same node are totally ordered according to the serialization order of associated operations.

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CJupiter maintains an n-ary ordered state space for each replica.

ϵ 1 x

1: Ins(x, 0)

12 ϵ 13 ax 123 a

2: Del(x, 0) 3: Ins(a, 0) 3: Ins(a, 0) 2: Del(x, 1)

124 b

4: Ins(b, 0)

1234 ba

3 : I n s ( a , 1 ) 4: Ins(b, 0)

14 xb

4 : I n s ( b , 1 ) 2 : D e l ( x , )

There can be more than two edges coming from the same node. Edges from the same node are totally ordered according to the serialization order of associated operations.

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Theorem (Equivalence of CJupiter and Jupiter) Under the same schedule, the behaviors of corresponding replicas in CJupiter and Jupiter are the same. Schedule: Issue, Send, and Receive of operations Behavior: A sequence of replica states

Equivalence from the perspectives of both the server and clients.

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Theorem (Equivalence of CJupiter and Jupiter) Under the same schedule, the behaviors of corresponding replicas in CJupiter and Jupiter are the same. Schedule: Issue, Send, and Receive of operations Behavior: A sequence of replica states

Equivalence from the perspectives of both the server and clients.

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At the server side:

Proposition (n ↔ 1 (Informal)) The single n-ary ordered state space at the server side in CJupiter is a union of n 2D state spaces at the server side in Jupiter.

At the client side:

Proposition ( (Informal)) Jupiter is slightly optimized in implementation at clients by eliminating redundant OTs in CJupiter.

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At the server side:

Proposition (n ↔ 1 (Informal)) The single n-ary ordered state space at the server side in CJupiter is a union of n 2D state spaces at the server side in Jupiter.

At the client side:

Proposition (1 ↔ 1 (Informal)) Jupiter is slightly optimized in implementation at clients by eliminating redundant OTs in CJupiter.

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Proposition (Compactness of CJupiter (Informal))

At a high level, CJupiter maintains only one n-ary ordered state space.

ϵ 1 x

1: Ins(x, 0)

12 ϵ 13 ax 123 a

2 : D e l ( x , ) 3 : I n s ( a , ) 3 : I n s ( a , ) 2 : D e l ( x , 1 )

124 b

4: Ins(b, 0)

1234 ba

3 : I n s ( a , 1 ) 4 : I n s ( b , )

14 xb

4: Ins(b, 1) 2 : D e l ( x , )

All replica states are represented in a single data structure. Each replica behavior corresponds to a path going through this state space.

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Proposition (Compactness of CJupiter (Informal))

At a high level, CJupiter maintains only one n-ary ordered state space.

ϵ 1 x

1: Ins(x, 0)

12 ϵ 13 ax 123 a

2 : D e l ( x , ) 3 : I n s ( a , ) 3 : I n s ( a , ) 2 : D e l ( x , 1 )

124 b

4: Ins(b, 0)

1234 ba

3 : I n s ( a , 1 ) 4 : I n s ( b , )

14 xb

4: Ins(b, 1) 2 : D e l ( x , )

All replica states are represented in a single data structure. Each replica behavior corresponds to a path going through this state space.

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Proposition (Compactness of CJupiter (Informal))

At a high level, CJupiter maintains only one n-ary ordered state space.

ϵ 1 x

1: Ins(x, 0)

12 ϵ 13 ax 123 a

2 : D e l ( x , ) 3 : I n s ( a , ) 3 : I n s ( a , ) 2 : D e l ( x , 1 )

124 b

4: Ins(b, 0)

1234 ba

3 : I n s ( a , 1 ) 4 : I n s ( b , )

14 xb

4: Ins(b, 1) 2 : D e l ( x , ) S, C1 C2 C3

All replica states are represented in a single data structure. Each replica behavior corresponds to a path going through this state space.

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CJupiter Satisfjes the Weak List Specifjcation

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We focus on a single n-ary ordered state space.

ϵ 1 x

1: Ins(x, 0)

12 ϵ 13 ax 123 a

2: Del(x, 0) 3: Ins(a, 0) 3: Ins(a, 0) 2: Del(x, 1)

124 b

4: Ins(b, 0)

1234 ba

3 : I n s ( a , 1 ) 4: Ins(b, 0)

14 xb

4 : I n s ( b , 1 ) 2 : D e l ( x , ) S, C1 C2 C3

We show the pairwise state compatibility property in three steps.

By Contradiction, By Induction, and By Case Analysis.

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1 Take any two nodes/states v1 and v2. Lemma (LCA (Lowest Common Ancestor)) Each pair of states in the n-ary ordered state space has a unique LCA.

v0 v1 v2

v0 = LCA(v1, v2)

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2 Consider the paths to v1 and v2 from their LCA v0. Lemma (Disjoint Paths) The set of operations Ov0❀v1 along Pv0❀v1 is disjoint from the set of

• perations Ov0❀v2 along Pv0❀v2.

v0 v1 v2

Pv0⇝v1 Pv0⇝v2

v0 = LCA(v1, v2)

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3 Consider the states in these two paths. Lemma (Compatible Paths) Each pair of states consisting of one state v in Pv0❀v1 and the other v′ in Pv0❀v2 are compatible.

v0 v v′ v1 v2

Pv0⇝v1 Pv

0⇝v 2

v0 = LCA(v1, v2) In particular, v1 and v2 are compatible.

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The Main Contribution

The Jupiter protocol [Nichols et al., 1995]a for replicated list satisfjes the weak list specifjcation [Attiya et al., 2016]b.

aDavid A. Nichols et al. (1995). “High-latency, Low-bandwidth

Windowing in the Jupiter Collaboration System”. In: Proceedings of the 8th Annual ACM Symposium on User Interface and Software Technology. UIST ’95. ACM, pp. 111–120.

bHagit Attiya et al. (2016). “Specifjcation and complexity of

collaborative text editing”. In: Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing. PODC ’16. ACM, pp. 259–268.

This was proposed as a conjecture in a PODC paper [Attiya et al., 2016].

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Model checking/verifying a family of Jupiter protocols using TLA+/TLAPS

AbsJupiter (Wei@TR’18) CJupiter (Wei@OPODIS’18) XJupiter (Xu@CSCW’14) AJupiter (Attiya@PersonalComm’17)

Refjnement

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Attiya, Hagit et al. (2016). “Specifjcation and complexity of collaborative text editing”. In: Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing. PODC ’16. ACM, pp. 259–268. Ellis, C. A. and S. J. Gibbs (1989). “Concurrency Control in Groupware Systems”. In: Proceedings of the 1989 ACM SIGMOD International Conference on Management of Data. SIGMOD ’89. ACM, pp. 399–407. Nichols, David A. et al. (1995). “High-latency, Low-bandwidth Windowing in the Jupiter Collaboration System”. In: Proceedings of the 8th Annual ACM Symposium on User Interface and Software Technology. UIST ’95. ACM,

• pp. 111–120.

Roh, Hyun-Gul et al. (Mar. 2011). “Replicated Abstract Data Types: Building Blocks for Collaborative Applications”. In: J. Parallel Distrib. Comput. 71.3,

• pp. 354–368.

Shapiro, Marc et al. (2011). “Confmict-free Replicated Data Types”. In: Proceedings

• f the 13th International Conference on Stabilization, Safety, and Security of

Distributed Systems. SSS’11. Springer-Verlag, pp. 386–400. Xu, Yi, Chengzheng Sun, and Mo Li (2014). “Achieving Convergence in Operational Transformation: Conditions, Mechanisms and Systems”. In: Proceedings of the 17th ACM Conference on Computer Supported Cooperative Work. CSCW ’14. ACM, pp. 505–518.

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Backup

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Does Jupiter satisfy the weak list specifjcation?

Yes, it does.

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Replication (for availability)

Updates

Replicas respond to user operations immediately Updates are propagated asynchronously

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Defjnition (Eventual Convergence [Ellis and Gibbs, 1989]) The lists are identical at all replicas at quiescence, i.e., all update

• perations have been executed at all replicas.

Defjnition (Strong Eventual Consistency [Shapiro et al., 2011]) The lists are identical at all replicas whenever after executing the same set of update operations.

Specify little on intermediate states going through by replicas.

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Defjnition (Eventual Convergence [Ellis and Gibbs, 1989]) The lists are identical at all replicas at quiescence, i.e., all update

• perations have been executed at all replicas.

Defjnition (Strong Eventual Consistency [Shapiro et al., 2011]) The lists are identical at all replicas whenever after executing the same set of update operations.

Specify little on intermediate states going through by replicas.

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Defjnition (Eventual Convergence [Ellis and Gibbs, 1989]) The lists are identical at all replicas at quiescence, i.e., all update

• perations have been executed at all replicas.

Defjnition (Strong Eventual Consistency [Shapiro et al., 2011]) The lists are identical at all replicas whenever after executing the same set of update operations.

Specify little on intermediate states going through by replicas.

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Strong/weak list specifjcation [Attiya et al., 2016]

Specify global properties on all states across the system. Proved: RGA [Roh et al., 2011] satisfjes the strong list specifjcation. Conjecture: Jupiter [Nichols et al., 1995] satisfjes the weak list specifjcation.

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It is still challenging to achieve convergence despite the server. S C1 C2 C3

1

1

1 1 2

2

2 2 3

3

3 3 4

4

4 4

Serializability may not be desirable. It does not imply that clients process operations in the same order.

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∀σ, σ′ : a, b ∈ σ ∩ σ′ = ⇒ (a ≺σ b ⇐ ⇒ a ≺σ′ b) (σ, σ′ : list; a, b : element; ≺σ: precedes)

σ0 : ab σ1 : ba a b σ : a b σ1 : ba

σ0 : ax σ1 : xb σ2 : ba a x b σ0 : a x σ1 : xb σ

2

: b a

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OT functions for a replicated list object [Ellis and Gibbs, 1989]

OT

(

Ins(a1, p1, pr1), Ins(a2, p2, pr2)

)

=

                    

Ins(a1, p1, pr1) p1 < p2 Ins(a1, p1 + 1, pr1) p1 > p2 NOP p1 = p2 ∧ a1 = a2 Ins(a1, p1 + 1, pr1) p1 = p2 ∧ a1 ̸= a2 ∧ pr1 > pr2 Ins(a1, p1, pr1) p1 = p2 ∧ a1 ̸= a2 ∧ pr1 ≤ pr2 OT

(

Ins(a1, p1, pr1), Del(_, p2, pr2)

)

=

  

Ins(a1, p1, pr1) p1 ≤ p2 Ins(a1, p1 − 1, pr1) p1 > p2 OT

(

Del(_, p1, pr1), Ins(a2, p2, pr2)

)

=

  

Del(_, p1, pr1) p1 < p2 Del(_, p1 + 1, pr1) p1 ≥ p2 OT

(

Del(_, p1, pr1), Del(_, p2, pr2)

)

=

        

Del(_, p1, pr1) p1 < p2 Del(_, p1 − 1, pr1) p1 > p2 NOP p1 = p2

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Consider a replicated system with n (= 3) clients.

S C1 C2 C3

1

1

I n s ( x , )

1 1 2

2

D e l ( )

2 2 3

3

Ins(a, 0)

3 3 4

4

I n s ( b , 1 )

4 4 Hengfeng Wei (Nanjing University) Replicated List (Jupiter) December 17, 2018 9 / 9