Distributed Symbolic Model Checking

1
Distributed Symbolic Model Checking

• Tamir Heyman
• Advisors
• Orna Grumberg and Assaf Schuster
• Technion Haifa

2
The Size Problem

• Model Checking takes a model and a specification
• This presentation focus on the sub problem known
  as reachability analysis (RA)
• The number of states/vertices is exponential in
  the number of model variables

3
The Sequential Solution

• Symbolic Model Checking
• Computation is done over sets of states, usually
  represented as BDDs
• Representation size may be polynomial
• Memory requirements still a problem
• limits model size to 300 state variables (Bits)

4
Distributed Method

• The goal is to solve verification problems that
  cannot fit into the memory of a single machine
• We use a large cluster of nodes as if they were
  one big node.
• Each node contributes a local memory and a
  processor

5
Distributed Challenges

• What Distributed has to do with NP problems?
• We keep the representation efficient as in the
  sequential algorithm therefore works on
  polynomial problems.
• Why not a single node with larger memory?
• The clusters memory capacity is proportional to
  the cluster CPU power.
• What is required in order to handle any size?
• Keep the efficiency while the system is growing.

6
Distributed Symbolic Method

• A Complete set of window functions W1Wn,
  defines for each process the part of the state
  space it owns
• S is partitioned to SiS/\Wi
• The parts Si are smaller than the whole set S

7
Elements of Distributed Symbolic Model Checking
HGGS CAV00

• Developed for reachability analysis, extended to
  full model checking
• Slicing algorithm
• Exchange algorithm
• Balance algorithm

8
Slicing algorithm

• Given a set S, the slicing algorithm computes
  window functions

S
9
Slicing algorithm

• Slicing S according to window functions

S1
S2
P1
P2
10
Exchange algorithm

• During a calculation, states may be found that
  belong to other window
• Exchange a set according to window functions

11
Memory balance

• During calculation, the sets that distributed
  based on current window function may be
  unbalanced
• Balance window functions and exchange the set
  accordingly

12
What a Researcher Needs?

• Get a Sequential model checker, implement message
  passing interface, implement transmission of
  objects, implement transmission of sets of states
  represented as BDDs
• Or
• Use the Division system ,under construction.
• By Tamir Heyman and Amnon Heyman

13
What is in the Division?

• Open source
• Platform for research
• General system
• Supporting distributed model checking
• Special support in distributed symbolic model
  checking

14
The Divisions Structure
Model Checking Mu-Calculus
Basic Model Checking Operations
Distributed Tool Kit
Standard Building Blocks
Infrastructure
15
Infrastructure

• Operating system
• Communication
• Distributed files system

16
Standard Building Blocks

• Message Passing Interface (MPI)
• Standard Template Library (STL)
• Symbolic Model Checker (SMC)
• Interface implemented by the SMC

MPI STL SMC Standard Building
Blocks
DTK Interface
17
Division tool kit

• Collection of independent tools for
• Distributed computation
• Distributed model checking
• Distributed symbolic model checking

18
Basic Model Checking Operation

• Exchange
• Termination detection
• Split

19
Model Checking Mu-calculus

• Distributed fixpoint
• Distributed Reachability analysis
• Distributed Full Mu-Calculus

20
Focus on DTK
Model Checking Mu-Calculus
Basic Model Checking Operations
Distributed Tool Kit
Standard Building Blocks
Infrastructure
21
DTK for distributed Algorithm

• Distributed output
• Collected from many processes
• Filtered
• Transmission of objects
• Like in CORBA
• Transmission of commands
• Executing remote code

22
DTK for Model Checking

• Interface for model checking engine
• Simple, short, hid the complexity
• Manager for Pool of processes
• Response to partners requests
• Collect Idle processes calls

23
DTK for Symbolic MC

• Transmitting BDDs
• Save/load BDD from Disk
• Set of states that uses BDD
• Implicit mark/release BDD
• Implementation of operators ,-,,,!,

24
Results

• Slicing is effective at least with 512 slices
• Model checking is effective at least using 32
  machines
• Finds bugs that could not be found by single
  machine running the sequential algorithm

25
Future work

• Massive parallelism using hundreds of nodes
• Including known orthogonal optimizations to
  further reduce memory requirements
• Improve speedup, by further optimizations

26
Future Development

• Distributed Reorder
• Force the same order in all process
• Let Each process choose locally
• Do something in between
• New fixpoint algorithm
• To better utilize O(100) nodes