Shape Analysis by Graph Decomposition

1
Heap Decomposition for Concurrent Shape Analysis
R. ManevichT. Lev-Ami Tel Aviv University
G. Ramalingam MSR India
J. Berdine MSR Cambridge
2
Overview

• Challenge precise and efficient shape analyses
  for concurrent programs
• Coarse-grained / fine-grained parallelism
• Prove safety properties
• Absence of nullderef
• Absence of memory leaks
• Data structure invariants
• Observation
• Threads operate on part of state
• Correlations between different sub-states often
  irrelevant to prove safety properties
• Our approach develop abstraction for sub-heaps
• Abstract correlations between sub-states of
  different threads
• Reduce exponential state space

3
Example non-blocking stack
1 void push(Stack S, data_type v) 2
Node x alloc(sizeof(Node))3 x-gtd
v4 do 5 Node t S-gtTop6
x-gtn t7 while
(!CAS(S-gtTop,t,x))8
9 data_type pop(Stack S)10 do 11
Node t S-gtTop12 if (t
NULL)13 return EMPTY14
Node s t-gtn15 data_type r
s-gtd16 while (!CAS(S-gtTop,t,s))1
7 return r18
4
Full state
prod1
cons1
Top
t
t
n
x
n
s
t
s
n
n
t
x
n
prod2
cons2
5
Sub-states
prod1
cons1
Top
Top
Top
Top
t
prod2
t
cons2
x
n
n
n
n
t
n
s
n
s
x
n
n
n
n
t
n
6
Full states
H2
H1
prod1
prod2
cons1
cons2
Top
Top
t
t
t
t
x
x
n
s
n
n
s
n
cons2
cons1
prod2
prod1
s
t
n
s
t
n
n
t
n
t
x
x
n
n
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Sub-states 1 ? Sub-states 2
prod1
Top
cons1
Top
Top
Top
t
t
cons2
prod2
n
n
s
n
x
n
n
s
t
n
n
n
n
t
x
n
n
?
?
?
Top
prod2
Top
cons2
Top
Top
t
prod1
n
t
cons1
x
n
t
n
n
s
n
n
n
s
x
n
n
t
n
n
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Main results

• New parametric abstraction for heaps
• Heap decomposition Cartesian product
• Family of sound transformers for Cartesian
  abstractions with multiple components
• Implementation in HeDec
• Heap Decomposition Canonical abstraction
• Used to prove interesting properties of
  heap-manipulating programs withfine-grained
  parallelism
• Linearizability
• Exponential state space reduction

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Empirical results

• Exponential time/space reduction
• Non-blocking stack linearizability

10
Future/on-going work

• Extend analysis for an unbounded number of
  threads
• Extend ideas to non-shape analyses
• Combine with interprocedural analysis

11
The End
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Formal details

• For each thread t define a sub-heap h(t)
• By defining a location-selection predicate ?(H,v)
• project(H, ?) keeps only locations in Hselected
  by ?
• Abstraction for t is ?t(H) bound(
  project(H, ?) )
• bound is some finitary heap abstraction
• Final abstraction for threads t1,,tn
  ?(XH) ?t1(XH) ? ? ?tn(XH)

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Abstract sub-states
prod1
cons1
Top
Top
Top
Top
t
prod2
t
cons2
x
n
n
n
n
t
n
s
n
s
x
n
n
n
n
t
n