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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)

http//research.microsoft.com/zing

Lecture I Outline

- Software Model Checking
- Overview of ZING

Software Validation

- Large scale reliable software is hard to build

and test. - Different groups of programmers write different

components. - Integration testing is a nightmare.

Property Checking

- Programmer provides redundant partial

specifications - Code is automatically checked for consistency
- Different from proving whole program correctness
- Specifications are not complete

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

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

Why bother?

- Just because a problem is undecidable, it doesnt

go away!

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

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

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

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

- 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

N1,N2 turn0

N noncritical, T trying, C critical

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?

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

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)

- 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

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

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?

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)

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

- What is the key design challenge in a model

checker for software? - It is the model!

Model Checking Hardware

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

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

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

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

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

Traditional approach

model checker

FSM

Finite state machines

Source code

Sequential C program

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,

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)

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

Lecture I Outline

- Software Model Checking
- Overview of ZING

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

Zing Object Model Internal StateView

State

Globals simple types refs

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

- 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 !

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

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

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

Architecture Communication

Server

Reachable states

Frontier

Trace

Reached States

Frontier States

Model Checker

Model Checker

Model Checker

Model Checker

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

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

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

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

Transaction

Lipton 75 any sequence (RB) (N?) (LB)

is a transaction

Other threads need not be scheduled in the middle

of a transaction

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

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?)

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

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,

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

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

Assertion checking for concurrent programs

- There is no algorithm for assertion checking of

concurrent boolean programs, even with only two

threads Ramalingam 00

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

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

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

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)?

Iterative refinement, ala SLAM

Harness

SLIC Rule

Iterative refinement in Zing

Zing program

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

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

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

http//research.microsoft.com/zing