ZING Systematic State Space Exploration of Concurrent Software

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ZING Systematic State Space Exploration of
Concurrent Software

• Jakob Rehof
• Microsoft Research
• http//research.microsoft.com/rehof
• http//research.microsoft.com/zing
• Joint work with
• Tony Andrews (MS)
• Shaz Qadeer (MSR)
• Sriram K. Rajamani (MSR)

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http//research.microsoft.com/zing
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Lecture I Outline

• Software Model Checking
• Overview of ZING

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Software Validation

• Large scale reliable software is hard to build
  and test.
• Different groups of programmers write different
  components.
• Integration testing is a nightmare.

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Property Checking

• Programmer provides redundant partial
  specifications
• Code is automatically checked for consistency
• Different from proving whole program correctness
• Specifications are not complete

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Interface Usage Rules

• Rules in documentation
• Incomplete, unenforced, wordy
• Order of operations data access
• Resource management
• Disobeying rules causes bad behavior
• System crash or deadlock
• Unexpected exceptions
• Failed runtime checks

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Does a given usage rule hold?

• Checking this is computationally impossible!
• Equivalent to solving Turings halting problem
  (undecidable)
• Even restricted computable versions of the
  problem (finite state programs) are prohibitively
  expensive

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Why bother?

• Just because a problem is undecidable, it doesnt
  go away!

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Automatic property checking Study of tradeoffs

• Soundness vs completeness
• Missing errors vs reporting false alarms
• Annotation burden on the programmer
• Complexity of the analysis
• Local vs Global
• Precision vs Efficiency
• Space vs Time

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Broad classification

• Underapproximations
• Testing
• After passing testing, a program may still
  violate a given property
• Overapproximations
• Type checking
• Even if a program satisfies a property, the type
  checker for the property could still reject it

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Current trend

• Confluence of techniques from different fields
• Model checking
• Automatic theorem proving
• Program analysis
• Significant emphasis on practicality
• Several new projects in academia and industry

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Model Checking

• Algorithmic exploration of state space of the
  system
• Several advances in the past decade
• symbolic model checking
• symmetry reductions
• partial order reductions
• compositional model checking
• bounded model checking using SAT solvers
• Most hardware companies use a model checker in
  the validation cycle

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• enum N, T, C state1..2
• int turn
• init
• state1 N state2 N
• turn 0
• trans
• statei N turn 0 -gt
  statei T turn i
• statei N turn !0 -gt
  statei T
• statei T turn i -gt
  statei C
• statei C state2-i1 N -gt
  statei N
• statei C state2-i1 ! N -gt
  statei N turn 2-i1

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N1,N2 turn0
N noncritical, T trying, C critical
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Model Checking

• Strengths
• Fully automatic (when it works)
• Computes inductive invariants
• I such that F(I) ? I
• Provides error traces
• Weaknesses
• Scale
• Operates only on models
• How do you get from the program to the model?

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Theorem proving

• Early theorem provers were proof checkers
• They were built to support assertional reasoning
  in the Hoare style
• Cumbersome and hard to use
• Greg Nelsons thesis in early 80s paved the way
  for automatic theorem provers
• Theory of equality with uninterpreted functions
• Theory of lists
• Theory of linear arithmetic
• Combination of the above !
• Automatic theorem provers based on Nelson-Oppen
  method are widely used
• ESC
• Proof Carrying Code

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Theory of Equality.

• Symbols , ¹, f, g,
• Axiomatically defined

E E
E2 E1
E1 E2
E1 E2 E2 E3
E1 E3
E1 E2
f(E1) f(E2)

• Example of a satisfiability problem
• g(g(g(x)) x ? g(g(g(g(g(x))))) x
  ? g(x) ¹ x
• Satisfiability problem decidable in O(n log n)

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• a array 1..len of int
• int max -MAXINT
• i 1
• ? 1 ? j ? i. aj ? max
• while (i ? len)
• if( ai gt max)
• max ai
• i i1
• endwhile
• ? 1 ? j ? len. aj ? max

( ? 1 ? j ? i. aj ? max) ? ( i gt len) ? (?
1 ? j ? len. aj ? max
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Automatic theorem proving

• Strengths
• Handles unbounded domains naturally
• Good implementations for
• equality with uninterpreted functions
• linear inequalities
• combination of theories
• Weaknesses
• Hard to compute fixpoints
• Requires inductive invariants
• Pre and post conditions
• Loop invariants

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Program analysis

• Originated in optimizing compilers
• constant propagation
• live variable analysis
• dead code elimination
• loop index optimization
• Type systems use similar analysis
• Are the type annotations consistent?

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Program analysis

• Strengths
• Works on code
• Pointer aware
• Integrated into compilers
• Precision efficiency tradeoffs well studied
• flow (in)sensitive
• context (in)sensitive
• Weakenesses
• Abstraction is hardwired and done by the designer
  of the analysis
• Not targeted at property checking (traditionally)

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Model Checking, Theorem Proving and Program
Analysis

• Very related to each other
• Different histories
• different emphasis
• different tradeoffs
• Complementary, in some ways
• Combination can be extremely powerful

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• What is the key design challenge in a model
  checker for software?
• It is the model!

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Model Checking Hardware

• Primitive values are booleans
• States are boolean vectors of fixed size
• Models are finite state machines !!

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Characteristics of Software

• Primitive values are more complicated
• Pointers
• Objects
• Control flow (transition relation) is more
  complicated
• Functions
• Function pointers
• Exceptions
• States are more complicated
• Unbounded graphs over values
• Variables are scoped
• Locals
• Shared scopes
• Much richer modularity constructs
• Functions
• Classes

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Computing power doubles every 18
months -Gordon Moore

• When I use a model checker, it runs and runs for
  ever and never comes back when I use a static
  analysis tool, it comes back immediately and says
  I dont know
• - Patrick Cousot

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Problem

• Check if programs written in common programming
  languages (C, C, C, Java) satisfy certain
  safety properties
• Examples of properties
• API usage rules ordering of calls
• Absence of races
• Absence of deadlocks
• Protocol (state machines) on objects
• Language-based safety properties

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Approach

• Extract abstract model from the program that
  captures all relevant portions of the program
  with respect to property of interest
• Systematically explore the state space of the
  extracted model.
• Example SLAM
• Check if a sequential C program uses an interface
  correctly as specified by a safety property,
  using boolean program models

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Traditional approach
model checker
FSM
Finite state machines
Source code
Sequential C program
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Software model checking
SLAM
model checker
Data flow analysis implemented using BDDs
Finite state machines
Push down model
FSM
Boolean program
abstraction
C data structures, pointers, procedure calls,
parameter passing, scoping,control flow
Source code
Sequential program in rich programming language
(eg. C)
Related work BLAST, MAGIC,
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Zing
model checker
Rich control constructs thread creation,
function call, exception, objects, dynamic
allocation Model checking is undecidable!
abstraction
Source code
Device driver (taking concurrency into account),
web services code, transaction management system
(2pc)
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Zing
model checker

• 3 core constructs
• Procedure calls with call-stack
• Objects with dynamic allocation
• Threads with dynamic creation
• Inter-process communication
• Shared memory
• Channels with blocking-receives, non-blocking
  sends, FIFO

abstraction
Source code
Concurrent program in rich programming language
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Lecture I Outline

• Software Model Checking
• Overview of ZING

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Zing Challenges and Approach

• Handling programming language features
• Compile Zing to an intermediate object model
  (ZOM)
• Build model checker on top of ZOM
• State explosion
• Expose program structure in ZOM
• Exploit program structure to do efficient model
  checking

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Zing Object Model Internal StateView
State
Globals simple types refs
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Zing Object Model External State View

• Simplified view to query and update state
• How many processes?
• Is process(i) runnable?
• Are two states equal?
• Execute process(i) for one atomic step
• Can write simple DFS search in 10 lines

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• private void doDfs()
• while(stateStack.Count gt 0)
• State s (State) stateStack.Peek()
• bool foundSuccessor false
• // find the next process to execute and
  execute it
• for (int p s.LastProcessExplored 1 p lt
  s.NumProcesses p)
• if(s.RunnableProcessesp
  
• State newS s.Execute(p)
• if (!stateHash.contains(newS))
• stateHash.add(newS)
• stateStack.push(newS)
• foundSuccessor true
• break
• if(!foundSuccessor)

DOESNT SCALE NEED TO EXPLOIT PROGRAM STRUCTURE !
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Optimizations to make model checking scale

• Exploring states efficiently
• Finger-printing
• State-delta
• Parallel model checking with multiple nodes
• Exploring fewer states (using mathematical
  properties)
• Reduction
• Summarization
• Symbolic execution
• Iterative Refinement
• Compositional conformance checking

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Saving storage

• Only states on the checkers stack are stored
• For states not on the stack only a fingerprint is
  stored
• Store only deltas from previous states

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State reduction

• Abstract notion of equality between states
• Avoid exploring similar states several times
• Exploit structure and do this fully automatically
  while computing the fingerprint
• s1 ? s2 ? f(s1) f(s2)

Heap1
100
200
a
b
0
ptr
Heap2
ptr
150
300
b
0
a
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Architecture Communication
Server
Reachablestates
Frontier
Trace
Reached States
Frontier States
ModelChecker
Model Checker
ModelChecker
Model Checker
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Optimizations to make model checking scale

• Exploring states efficiently
• Finger-printing
• State-delta
• Parallel model checking with multiple nodes
• Exploring fewer states (using mathematical
  properties)
• Reduction
• Summarization
• Symbolic execution
• Iterative Refinement
• Compositional conformance checking

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Racy program need to explore all interleavings!
//initialize int x 0
local int z 0 x x 1 x x 1 x
x 1 x x 1 assert(x div 4) z
z1 z z1

• local int y 0
• x x 1
• x x 1
• x x 1
• x x 1
• assert(x div 4)
• y y1
• y y1

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Race-free program need to explore two
interleavings!
//initialize int x 0 mutex m
local int z acquire (m) x x 1 x
x 1 x x 1 x x 1 assert(x div
4) release (m) z z1 z z1

• local int y
• acquire (m)
• x x 1
• x x 1
• x x 1
• x x 1
• assert(x div 4)
• release (m)
• y y1
• y y1

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Four atomicities

• R right movers
• lock acquire
• L left movers
• lock release
• B both right left movers
• variable access holding lock
• N non-movers
• access unprotected variable

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Transaction
Lipton 75 any sequence (RB) (N?) (LB)
is a transaction
Other threads need not be scheduled in the middle
of a transaction
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Recall exampleeach thread has one transaction!
//initialize int x 0 mutex m
local int z acquire (m) x x 1 x
x 1 x x 1 x x 1 assert(x div
4) release (m) z z1 z z1

• local int y
• acquire (m)
• x x 1
• x x 1
• x x 1
• x x 1
• assert(x div 4)
• release (m)
• y y1
• y y1

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Transaction-based reduction

• ZOM extended to expose mover-ness of each
  action
• Model checker maintains a state machine to track
  the phase of each transaction
• Continues scheduling one thread as long as it is
  inside a transaction!
• Current implementation
• Classifies all heap accesses as non-movers
• Can improve the scalability using better analysis
  (ownership?)

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Optimizations to make model checking scale

• Exploring states efficiently
• Finger-printing
• State-delta
• Parallel model checking with multiple nodes
• Exploring fewer states (using mathematical
  properties)
• Reduction
• Summarization
• Symbolic execution
• Iterative Refinement
• Compositional conformance checking

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Summarization for sequential programs

• Procedure summarization (Sharir-Pnueli 81,
  Reps-Horwitz-Sagiv 95) is the key to efficiency

int x void incr_by_2() x x
void main() x 0 incr_by_2()
x 0 incr_by_2()

• Bebop, ESP, Moped, MC, Prefix,

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What is a summary in sequential programs?

• Summary of a procedure P
• Set of all (pre-state ? post-state) pairs
  obtained by invocations of P

x ? x 0 ? 2 1 ? 3
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Assertion checking for sequential programs

• Boolean program with
• g number of global vars
• m max. number of local vars in any scope
• k size of the CFG of the program
• Complexity is O( k ? 2 O(gm) ), linear in the
  size of CFG
• Summarization enables termination in the presence
  of recursion

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Assertion checking for concurrent programs

• There is no algorithm for assertion checking of
  concurrent boolean programs, even with only two
  threads Ramalingam 00

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Our approach

• Precise semi-algorithm for verifying properties
  of concurrent programs
• based on model checking
• procedure summarization for efficiency
• Termination for a large class of concurrent
  programs with recursion and shared variables
• Generalization of precise interprocedural
  dataflow analysis for sequential programs

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What is a summary in concurrent programs?

• Unarticulated so far
• Naïve extension of summaries for sequential
  programs do not work
• Qadeer, Rajamani, Rehof. POPL 2004

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Optimizations to make model checking scale

• Exploring states efficiently
• Finger-printing
• State-delta
• Parallel model checking with multiple nodes
• Exploring fewer states (using mathematical
  properties)
• Reduction
• Summarization
• Symbolic execution
• Iterative Refinement
• Compositional conformance checking

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Symbolic execution

• Go from closed to open programs
• Can think about this as delayed case-split
• Integrating Zings state exploration engine with
  Zap theorem prover from TVM group
• States are now extended to have a concrete part
  and symbolic part
• Concrete part is fingerprinted
• Symbolic part is manipulated by theorem prover
• How do we handle symbolic references (pointers)?

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Iterative refinement, ala SLAM

Harness
SLIC Rule
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Iterative refinement in Zing
Zing program

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Optimizations to make model checking scale

• Exploring states efficiently
• Finger-printing
• State-delta
• Parallel model checking with multiple nodes
• Exploring fewer states (using mathematical
  properties)
• Reduction
• Summarization
• Symbolic execution
• Iterative Refinement
• Compositional conformance checking

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Conformance

• Conformance theory
• P lt Q? Does one model (P, implementation) conform
  to another (Q, specification)?
• Compositional
• P lt Q gt CP lt CQ
• Theory developed for CCS
• Fournet, Rajamani, Hoare, Rehof. CAV 2004
• Implemented modularly on top of ZING (ZOM)
• Used in integrated checker for message-passing
  programs

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Context-bounded model checking

• Motivation Many concurrency bugs manifest within
  relatively few context switches (5-10)
• If we bound the number of context switches, we
  can explore (unbounded) concurrent stack machines
  completely, up to the bound
• Qadeer, Rehof. TACAS 2005

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http//research.microsoft.com/zing