Analysis of Concurrent Software Models Using Partial Order Views
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Analysis of Concurrent Analysis of Concurrent Software Models Using Software Models Using Partial Order Views Partial Order Views Qiang Sun, [email protected] Yuting Chen, [email protected] Jianjun Zhao, [email protected] Shanghai Jiaotong University Jun 16, 2022
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Analysis of Concurrent Software Models Using Partial Order Views. Qiang Sun, [email protected] Yuting Chen, [email protected] Jianjun Zhao, [email protected] Shanghai Jiaotong University 22-Aug-14. Outline. Motivation - PowerPoint PPT Presentation
Transcript of Analysis of Concurrent Software Models Using Partial Order Views
Analysis of Concurrent Software Analysis of Concurrent Software Models Using Partial Order ViewsModels Using Partial Order Views
Qiang Sun, [email protected] Chen, [email protected] Jianjun Zhao, [email protected]
Shanghai Jiaotong University Apr 22, 2023
OutlineOutline
• Motivation
• An approach to analysis of concurrent software models using partial order views
• Some simple examples
MotivationMotivation
• Checking and analyzing the software design model become crucial
• Analysis of concurrent software behavioural models still faces challenges– Data races, atomicity violations, bugs
• A number of analyses are on the basis of state models– A process can be modeled as a state machine in which the transitions
are atomic or indivisible actions executed by the process. – LTS: Labeled Transition Systems – FSP (Finite State Processes), CCS, CSP
• Analyzing a state model usually faces difficulties– Combination of state models leads to state space explosion
Solution?Solution?
• Modeling concurrency using partial ordersModeling concurrency using partial orders– Partial order viewPartial order view
• Extraction of partial orders of interest events from state machines– Partial orders can also be extracted from partial behavioral models.
• BiG provides the mechanism of the model transformation and synchronization.– State machine ↔ Pomset model
Labeled Partial Order (LPO)Labeled Partial Order (LPO)
– A partial order is a pair (E, <), where < is an irreflexive transitive binary relation on the vertex set E.
– A labeled partial order (lpo) is a structure (E, ∑, μ, <), where (E, <) is a partial order, and μ : E→∑ labels the vertices of E with elements of the set ∑.
– (E, ∑, μ, <) and (E’, ∑’, μ’, <’) over the same set of labels ∑ are isomorphic if
– there exists a bijection τ: E→E’ such that for all u, v ∈ E, μ(u)= μ’(τ(u)), and u < v iff τ(u) <’ τ(v).
Partial Order Multi-Set (Pomset)Partial Order Multi-Set (Pomset)
• A pomset [E, ∑, μ, <] is the isomorphism class of an lpo (E, ∑, μ, <). – A pomset [E, ∑, μ, <] is finite if E is finite.– Two pomsets [E, ∑, μ, <] and [E’, ∑’, μ’, <’] are
isomorphic if • there exist bijections τ : E→E’ and ν: ∑ → ∑’, such
that for all u, v ∈ E and for all a ∈ ∑, μ(u) = a iff μ’ (μ(u)) = ν(a), and u < v iff τ(u) <’τ(v).
Two OperationsTwo Operations
• Let – p = [E, ∑, <, μ] – p' = [E’, ∑, <’, μ’] – E ∩ E' =Φ.
• Series operation– p;p’ = [E∪E’, ∑, (< <’ (∪ ∪ E×E’)), μ ∪μ’]
• Parallel operation– p||p’ = [E∪E’, ∑, (< <’)∪ , μ ∪μ’]
• Pomset Model– Actions & events
• An action may occur more than once. ∑• An occurrence of an action is an event. E
• Pomset model helps analyze and understand the behaviors of concurrent software better.– Happens-before relationship for the events of interest– Calculating the possible traces– Pomset model can avoid state space explosion; the increment of the
events is linear.
A B
Analysis of Concurrent Software Models Analysis of Concurrent Software Models Using Partial Order ViewsUsing Partial Order Views
• To extract pomset model– Computing the partial order of events within one process.– Merging partial orders of different processes through parallel
operation.
• To analyze pomset model and check event traces • To revisit state model whether we detect abnormal event
traces• Bidirectional Graph Transformation technique provides with
support in transforming state model to pomset model and keeping model synchronization.– The result can be easily mapped back to the original LTS.
SMALL EXAMPLESSMALL EXAMPLES
Semaphore Semaphore
• Semaphore LTS
• Loop
-1 0 1
up
up down
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up
down
critical 1 0
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up
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critical 2
Begin
up
up
critical 1 down
critical 2 down
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Elevator SystemElevator System
• Outer request– FLOOR × {UP, DOWN}
• Inner request– FLOOR TO GO TO
• Controller of elevators– Out requests: accessing request queue– Inner requests: message passing
5 floors and 2 elevators
0 send
Outer request queue
0 1 3
send send
receive receive
-1
send
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send
receive
User in elevator
Inner request buffer
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getREQ receive
response
response response
response
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elevator
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send
receive
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remove
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elevator
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Two elevatorsTwo elevators
Outer request queue
0 1 2 3 4
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response
response response
response
1’receive receive receive
get remove
Elevator 1
0 1 2 3 4
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response
response response
response
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get remove
Elevator 2
Begin
get1 get2
remove1 remove2
get1 → get2 → remove1 → remove2
Lock & UnlockLock & Unlock
Begin
lock lock
get1 get2
remove1 remove2
unlock unlock
Begin
lock lock
get1 get2
remove1 remove2
unlock unlock
Outer request queue
0 1 2 3 4
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response
response response
response
1’
receive receive receive
get remove
Elevator 1
1’’ 1’’’
unlocklock
0 1 2 3 4
5
response
response response
response
1’
receive receive receive
get remove
Elevator 2
1’’ 1’’’
unlocklock
• Partial order event model provides engineers with – A different view about the events occurring in the concurrent software
system and their order.– Bidirectional model transformation technique helps transform state model
to partial order event model
• Detection of potential errors is possible from taking advantage of information about partial order event model– To detect data races by associating the events to accessing the shared
memory – To detect atomicity violations by associating actions to accessing resources– Determination of the real bugs usually relies on human judgements – Bidirectional model transformation technique helps reveal the bugs in the
state model if any abnormal event traces are found
ConclusionsConclusions
• State model is widely used in practice
• Pomset model can avoid state space explosion
• An approach to checking and analyzing state model using pomset model
• BiG provides the mechanism of model transformation and bug elimination
Future WorkFuture Work
• A systematic approach
• Correctness of the approach– Case studies and experiments
• Tool Support
