ComputerAssisted Construction of Efficient Concurrent Algorithms

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Computer-Assisted Construction of
Efficient Concurrent Algorithms
Martin Vechev, Eran Yahav, Maged Michael,
Hagit Attiya, Greta Yorsh
IBM T.J. Watson Research Center
Technion
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Construction Challenge Lets suppose
I want a concurrent set that is correct
efficient portable QUICKLY
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Now what
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The result
Harris (DISC01)
Heller et al. (OPODIS05)
Michael (PODC02)
Vechev Yahav (PLDI08)
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Another Domain Concurrent Garbage Collection
Yuasa 90
Steele(C) 75
Dijkstra(C) 78
FAMILY
Ben-Ari Base 84
Doligez(C) 93
Boehm 91
Azatchi 03
Ben-Ari Extended 84
Barabash 03
ALGORITHMS
Domani 03
Ben-Ari Base 84
Doligez 94
Pixley 88
PROOFS
THEOREM PROVING
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What if an assumption/requirement changes ?

• Examples
• Synchronization primitives are missing
• Automatic memory management is missing
• Allow obstruction-free instead of lock-free
• Effort is per-algorithm each time
• Construction
• Verification

CONSTRUCTION
VERIFICATION
Why verify this arbitrary algorithm ?!
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Awkward disconnected spaces

• Concurrent Data Structures
• Sets, Queues, Weak Queues
• Concurrent (and real-time, parallel) garbage
  collection
• (Java) Virtual machines and processor simulators
  
• Concurrent memory allocators
• Real-time OS kernels

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Core Challenges

• Commonalities
• Share construction and verification effort
  across algorithms
• Comparison
• Define formally what is better, more
  efficient
• Representation
• Expose dependencies
• Find Transformations
• Support assumption changes

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Commonalities Example Concurrent Sets
Sequential
Intermediate Algorithm
Published Algorithm
Priority Queue


Stack
DCAS
DCAS
CAS/DCAS
Trieber Stack
Vechev Yahav (PLDI08)
Michael (PODC02)
Heller et al. (OPODIS05)
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Commonalities Example One Instantiation
Implementations
Common Algorithm
bool remove(int key) Entry pred,curr,r
restart locate(pred,curr,key) k
(curr-gtkey ? key) if (k) return false
curr-gtmarked true r curr-gtnext atomic mp
?pred-gtmarked val(pred-gtnextcurr) ? mp
if (?val) goto restart pred-gtnext r return
true
CAS (if bit in pointer supported)
LOCKS and TRY-LOCKS
REENTRANT LOCKS and TRY-LOCKS
LOCKS
DCAS
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Commonalities Example Concurrent Sets
Sequential
Intermediate Algorithm
Published Algorithm
Share construction and verification effort across
algorithms
Priority Queue


Stack
DCAS
DCAS
CAS/DCAS
Trieber Stack
Vechev Yahav (PLDI08)
Michael (PODC02)
Heller et al. (OPODIS05)
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Comparison
Which algorithm is better ? What does
more concurrent mean ?
Harris (DISC01)
Heller et al. (OPODIS05)
Maged (PODC02)
Vechev Yahav (PLDI08)
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Comparison starting dimensions

• Problem is finding the right dimensions

Sequential
Concurrent
Space
Space
Synchronization
Time
Time
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Concurrent Sets Breaking atomicity
bool remove(int key) atomic Entry
pred,curr,r
locate(pred,curr,key) k
(curr-gtkey ? key) if (k) return false r
curr-gtnext pred-gtnext r return true
bool remove(int key) Entry pred,curr,r
restart locate(pred,curr,key) k
(curr-gtkey ? key) if (k) return false
curr-gtmarked true r curr-gtnext atomic mp
?pred-gtmarked val(pred-gtnextcurr)? mp if
(?val) goto restart pred-gtnext r return
true
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Concurrent Garbage Collectors Breaking atomicity
mutate(source, fld, new) old source.fld e
source.E_fld source.fld new s source.S_fld
if (s) val gc_state atomic if (val
TRACE) new.MC else new.MC max
val new.inLog if (!val) new.inLog
true atomic candnextcand new
atomic if (e) old.MC
mutate(source, field, new)
atomic old source.field w
source.field.WF w ? new.MC w ? log log U
new w ? old.MC-- source.fld new
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Comparison existing work

• Concurrent Garbage Collection (PLDI06)
• Precision formalizes expected intuition
• Tailored to a specific domain
• Linked List algorithms (Attiya Hillel,
  DISC06)
• A measure of locality
• Based on worst-case
• Concurrent GC, Data structures (PLDI07,
  PLDI08)
• Subset of traces simple and intuitive
• Many algorithms are incomparable (that should be)

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Central Problem Representation

• Concurrency not explicit

bool remove(int key) Entry pred,curr,r
restart locate(pred,curr,key)
k (curr-gtkey ? key) if
(k) return false ltr,mgt curr-gtnext
lvalCAS(curr-gtnext, ?r,m?,?r,1?) if (?lval)
goto restart pvalCAS(pred-gtnext,
?curr,0?,?r,0?) if (?pval) goto restart return
true
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Representation Expressing an algorithm

• Gap between theory and practice
• Need to allow explicit description of concurrency
  
• Should capture commonalities
• Should enable concurrency transformations

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Summary Practical Systematic Construction

• Representation of Fundamental Algorithms
• Concurrent Garbage Collection, new algorithms
  PLDI06
• Semi-Automated Reduction of Atomicity
• Concurrent Collectors, new algorithms PLDI07
• Concurrent Sets, new algorithms PLDI08
• Practically Beneficial
• Results were surprising even to algorithmic
  experts
• Explore space of algorithms, understand design
  space
• Expose commonalities and tradeoffs between
  algorithms
• Naturally leads to new algorithms

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