On Beyond Registers: WaitFree Readable Objects

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On Beyond Registers Wait-Free Readable Objects

• Maurice Herlihy
• Brown University

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Leslies Contribution

• First to ask fundamental questions
• Synchronization
• Communication
• Registers
• Reading and writing shared memory
• Without locking

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Register Constructions
readers
Atomic snapshot
writers
Dozens of researchers
Register algorithm space
Register size
1-bit 1-reader, 1-writer
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Register Research Today?

• Claim
• the answers come and go
• but the questions live on
• Premise
• properly interpreted, LLs original questions
  remain productive

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One Approach

• Hilbert-like list of open problems
• Advantage solemn
• Disadvantage not serious

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Another Approach

• Look at one subarea (of many)
• Continuation of LL program
• LL citations everywhere you turn
• Survey some past work
• Express opinionated views

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Premise

• Not enough to read LL opus, must also interpret
• Narrow, fundamentalist interpretations not
  promising

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Devils Advocate

• Real memory doesnt act like read/write registers
• Weird correctness conditions total store
  ordering, processor consistency,
• Exotic operations memory barriers, inconsistent
  reads and writes

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Devils Advocate

• Real memory hardware is different
• No safe bits
• Elaborate cache-coherence protocols
• Complicated, not complex

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Devils Advocate

• Read/Write synchronization
• Mutual exclusion
• Not that you would, but you could?
• Use read-modify-write operations instead
• Lock-free or wait-free
• Mostly impossible
• Some exotic exceptions

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Nevertheless

• Fundamental questions
• about synchronization and communication
• live on
• Lamports original inspiration still rocks
• Proof by rambling example

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Registers vs Objects

• No reason to privilege read/write registers
• Rather the reverse
• Wait-free objects have been studied
• Focus on replacing writes
• What about read operations?

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Shared Objects
Set of operations
Set of states
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Sequential Objects
Abstract Object
Refinement Map
0010
Implementation
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Concurrent Objects
1

• It is universally acknowledged that
• People not good at concurrent reasoning
• Concurrent correctness is some kind of
  equivalence to sequential executions
• Sectarian differences exist on nature of
  equivalence

1. or it should be
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Concurrent Objects

• Sequential Consistency Lamport 79
• Reorder concurrent operations
• Linearizability HerlihyWing 90
• Also respect real-time order

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Question

• A logical snapshot atomically reads and returns
  an objects state
• SC or linearizable (take your pick)
• Call such an object
• Snapshootable? Nah
• Readable!

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Question

• For which objects can we implement wait-free or
  lock-free logical snapshots?
• What does it mean if we can or cant?

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A One-Banana Problem?

• Objects are bits in memory
• Use a known atomic snapshot scan algorithm to
  capture the bits

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Snapshot Scan
Afek et al. 90
Anderson 90
Multi-reader/multi-writer shared memory
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Snapshot Scan
Instantaneous picture of array in a consistent
state
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Atomic Snapshots

• A collect
• Read bits one-by-one (non-atomically)
• May overlap with operations that modify memory
• A clean collect
• Does not overlap with modifying operations

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Atomic Snapshots

• Lock-free
• Detect a clean collect
• Return results
• Wait-free
• Memory-modifying threads help collector
• Eventually clean collect occurs

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Memory Operations

• Notion of clean collect does not require write
  operations
• Can snapshot against any operations
• Test-and-set
• Compare-and-swap
• Fetch-and-mumble

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Opinionated Aside

• Can atomic snapshots be made truly practical?
• Software seems implausible
• Architecture?
• Modify cache coherence protocols
• Minor hardware support

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Problem Solved?

• No, snapshot of underlying bits may not be a
  snapshot of object
• Proof by PowerPoint

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PO-Set Object
last
first
last
last
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PO-Set Enqueue
last
first
last
last
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PO-Set Dequeue
last
gone
last
last
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Correctness

• Operations take time
• Operations respect Lamports happens before
  order
• Non-overlapping PO_Enq operations leave
  totally-ordered items in queue
• Not a SC spec!
• Can be made so, however

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FIFO Queue Implementation
Linearizable Implementation
FIFO queue
PO-set
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Claims

• FIFO_Enq is PO_Enq
• FIFO_Deq is PO_Deq
• Claim
• Linearizable implementation
• Deterministic sequential spec
• Non-determinism absorbed by linearizability
  condition

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The Consensus Task
Before private inputs
After agree on one input
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Claim

• PO-set registers
• Cannot solve 3-process consensus
• Usual FLP-style proof
• Under the influence
• Therefore neither can FIFO queue registers

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Claim

• FIFO queue snapshot
• Solves consensus for any number of processes
• Algorithm
• Enqueue your id
• Take snapshot
• Take winners value

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Consequence

• Example of wait-free linearizable FIFO queue
  implementation
• Cannot implement snapshots
• See HerlihyWing 86 for less contrived
  construction using swap, fetchinc.

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Refinement Maps

• Snapshot operations closely related to refinement
  maps
• Snapshot is an algorithm
• Refinement map is a mathematical construct

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Abadi-Lamport 91

• Refinement maps always exist, given
• History variables
• Record the past
• Prophecy variables
• Predict the future
• some minor technicalities

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Implications

• Refinement map does not imply snapshot
• Cant implement prophecy variables
• Cant always implement history variables in
  concurrent settings?

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Opinion

• Need Abadi-Lamport theorem for snapshot
  operations
• Characterize when they exist
• How to implement them

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Consensus Theory

• Robustness Jayanti
• Can objects with low consensus numbers be
  combined to reach a higher consensus number?

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Consensus Theory

• Readable Objects Ruppert
• Objects with snapshots are robust
• Consensus numbers computable for finite-state
  objects

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Open Question

• What are implications of snapshot operations for
  consensus hierarchy?

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Open Questions

• Snapshots enable fault-tolerance
• Checkpoints
• Roll-backs
• Atomic transactions
• Implications for fault-tolerant computation?

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Clip Art