Task Computability in Unreliable Anonymous Networks Nayuta Yanagisawa DeNA Co., Ltd. Petr Kuznetsov Telecom ParisTech
I am here to talk about ... the computability issues of failure-prone anonymous broadcast models.
Anonymous Model Anonymous model: Processes have no unique IDs, i.e. processes execute an identical program. systems are anonymous by design or may choose anonymity for the sake of privacy. of unique identifiers affects the computational power of distributed systems. • Some sensor networks and peer-to-peer file sharing • It is theoretically interesting to study how the existence
Existing Works t = 0 t > 0 Shared-memory Attiya et al. ’02 Guerraoui and Ruppert ’07 Yanagisawa ’17 Delporte et al. ’18a, b Message-passing Angluin ‘80 Aspnes et al ’06 Existing works concerning the anonymous and asynchronous computation, where t is the number of failures:
Anonymous Broadcast Model and asynchronous processes. via a fully connected reliable FIFO network. We assume that a process cannot detect through which link a message has been received. • A distributed system consists of a set of anonymous • At most t<n/2 processes are prone to crash failures. • Processes communicate by broadcasting messages
Overview of Our Results linearizable implementation if t>0. object is implementable if 0≦t<n/2. solvable in the anonymous broadcast model iff it is t-resiliently solvable in the non-anonymous broadcast model, where 0≦t<n/2. • Impossibility: Any non-trivial object type has no • Possibility: A sequentially-consistent add-only set • Characterization: A colorless task is t-resiliently
Impossibility Any non-trivial object type has no linearizable implementation if t>0.
Non-commuting Operation read() legal 0 read() ack write(1) 0 [ ] Definition 1 [ ] [ ] o 1 r 1 o 2 r 2 o 1 r 1 is not legal. for all responses r 1 ,r 2 ∈ R s.t. o 1 r 1 o 2 r 2 is legal, operations o 1 ,o 2 ∈ O are weakly-non-commutative if, not legal Let T = (Q,q 0 ,O,R, ∆ ) be an object type. We say that
Impossibility Theorem 1 There is no 1-resilient linearizable implementation of an object type with weakly-non-commutative operations in the anonymous broadcast model. [Aspnes et al. ’06] An atomic register has 0-resilient linearizable implementation in the anonymous broadcast model.
Proof Sketch [ ] read() 0 [ ] write(1) ack p 1 p n 0 [ ] read() … p 2 zzz... …
Possibility A sequentially-consistent add-only set object is implementable if 0≦t<n/2.
Add-Only Set Definition 2 An add-only set stores a set of values, initially ∅, and exports operations add(v) (v∈V) and get(). add(v) adds a value v to the set. get() returns the current snapshot of the set. add(v) and get() are weakly-non-commutative and thus the add-only set has no 1-resilient linearizable implementation.
Sequential-Consistency ack write(1) 0 read() [ ] [ ] 0 read() [ ] write(1) [ ] 0 read() [ ] [ ] sequentially-consistent linearizable 0 read() ack
Possibility Theorem 2 An add-only set has a sequentially-consistent t- resilient implementation in the anonymous broadcast model, where 0≦t<n/2. Collorary 1 A snapshot object has a sequentially-consistent implementation in the anonymous broadcast model, where 0≦t<n/2.
Implementation of the set and a round number. estimate, broadcast it with the round number, and increment the round number. more than n/2 of other processes’ estimate with the same round number. If all the estimated sets are identical, then the process return the set. Otherwise, it increments the round number and tries to collect other processes’ estimated sets again. • Each process keeps its local estimate of the content • To add a value v, a process insert v into its local • To get the content of the set, a process collects
Characterization A colorless task is t-resiliently solvable in the anonymous broadcast model if and only if it is t-resiliently solvable in the non-anonymous model, where 0≦t<n/2.
Colorless Task Definition 3 A colorless task is defined through a set I of input sets, a set O of output sets, and a total relation of possible output sets. Consensus, k-set agreement, and loop agreement are all colorless tasks. ∆ : I ︎ → 2 O that associates each input set with a set
Characterization Theorem 3 A colorless task T is t-resiliently solvable in the anonymous broadcast model if and only if it is t-resiliently solvable in the non-anonymous broadcast model.
Proof Sketch: If Part T is t-resiliently solvable in the non-anonymous broadcast model. ⇒ T is t-resilient solvable in the non-anonymous shared-memory model [Attiya et al. ’95]. ⇒ T is t-resilient solvable in the anonymous shared- memory model [Delporte et.al. ’18]. ⇒ T is t-resilient solvable in the anonymous broadcast model (Collorary 1).
Existing Works t = 0 t > 0 Shared-memory Attiya et al. ’02 Guerraoui and Ruppert ’07 Yanagisawa ’17 Delporte et al. ’18a Delporte et al. ’18b Message-passing Angluin ‘80 Impossibility Possibility Characterization Aspnes et al ’06
Future Work of distributed decision tasks. consistency. • Extending our characterization to a general class • Consistency conditions stronger than sequential-
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