ZING Systematic State Space

Exploration of Concurrent Software

Jakob RehofMicrosoft Research

http://research.microsoft.com/~rehofhttp://research.microsoft.com/zing

Joint work withTony 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 Turing’s 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 doesn’t 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} state[1..2]

int turn

init

state[1] = N; state[2] = N

turn = 0

trans

state[i]= N & turn = 0 -> state[i] = T; turn = i

state[i] = N & turn !=0 -> state[i] = T

state[i] = T & turn = i -> state[i] = C

state[i] = C & state[2-i+1] = N -> state[i] = N

state[i] = C & state[2-i+1] != N -> state[i] = N; turn = 2-i+1

N1,N2turn=0

T1,N2turn=1

T1,T2turn=1

C1,N2turn=1

C1,T2turn=1

N1,T2turn=2

T1,T2turn=2

N1,C2turn=2

T1,C2turn=2

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 Nelson’s 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: =, , 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) x

• Satisfiability problem decidable in O(n log n)

a : array [1..len] of int;

int max := -MAXINT;i := 1;{ 1 j i. a[j] max}while (i len)

if( a[i] > max) max := a[i];

i := i+1;endwhile{ 1 j len. a[j] max}

( 1 j i. a[j] max) ( i > len)

( 1 j len. a[j]

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

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 don’t know”

- Patrick Cousot

Computing power doubles every 18 months

-Gordon Moore

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

Sequential C program

Finite state machines

Source code

FSM

modelchecker

Traditional approach

Sequential program in rich programming language (eg. C)

Finite state machines

Source code

FSM

abstraction

modelchecker

C data structures, pointers,procedure calls, parameter passing,scoping,control flow

Software model checking

Boolean program

Data flow analysis implemented using BDDs

SLAM

Push down model

Related work: BLAST, MAGIC,…

Source code

abstraction

modelchecker

Zing

Rich control constructs: thread creation, function call, exception, objects, dynamic allocation

Model checking is undecidable!

Device driver (taking concurrency into account), web services code, transaction management system (2pc)

Source code

abstraction

modelchecker

Zing

3 core constructs:

1. Procedure calls with call-stack

2. Objects with dynamic allocation

3. Threads with dynamic creation

Inter-process communication:

1. Shared memory

2. Channels with blocking-receives, non-blocking sends, FIFO

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

State

Heap: complex types

…

ProcessProcess

Process

…Processes

Zing Object Model: Internal StateView

Globals: simple types & refs

Stack

IPLocalsParams

IPLocalsParams

…

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 > 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 < s.NumProcesses; p++) {

if(s.RunnableProcesses[p] {

State newS = s.Execute(p); if (!stateHash.contains(newS)){ stateHash.add(newS);

stateStack.push(newS); foundSuccessor = true;

break; }

} } if(!foundSuccessor) stateStack.Pop(); }}

DOESN’T 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

a

100

b 0

200

Heap2

b 0

150

a

300

ptr

ptr

Architecture & Communication

ModelChecker

ModelChecker

ModelChecker

ModelChecker

Reachablestates Frontier

Trac

e

Reach

ed S

tate

s

Fron

tier S

tate

s

Server

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!

local int y = 0; x := x + 1; x := x + 1; x := x + 1; x := x +1;

assert(x div 4);

y = y+1;y = y+1;

//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 = z+1;z = z+1;

Race-free program: need to explore two interleavings!

local int y;acquire (m); x := x + 1; x := x + 1; x := x + 1; x := x +1;

assert(x div 4);release (m);

y = y+1;y = y+1;

//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 = z+1;z = z+1;

Four atomicitiesS0 S1 S2

acq(this) x

S0 T1 S2

x acq(this)

S7T6S5

rel(this) z

S7S6S5

rel(this)z

S2 S3 S4

r=bal y

S2 T3 S4

r=baly

S2 T3 S4

r=bal x

S2 S3 S4

r=balx

• 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

S0. S5

R* N L*x Y. . .

S0. S5

R* N L*x Y. . .

Other threads need not be scheduled in the middle of a transaction

Lipton ‘75: any sequence (R+B)*; (N+) ; (L+B)* is a transaction

Recall example:each thread has one transaction!

local int y;acquire (m); x := x + 1; x := x + 1; x := x + 1; x := x +1;

assert(x div 4);release (m);

y = y+1;y = y+1;

//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 = z+1;z = z+1;

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

int x;

void incr_by_2() { x++; x++;}

void main() { … x = 0; incr_by_2(); … x = 0; incr_by_2(); … x = 1; incr_by_2(); …}

x x’

0 21 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(g+m)

), 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 Zing’s 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

#include <ntddk.h>

C2BPpredicate abstraction

booleanprogram

Newtonfeasibility

check

Bebopreachability

check

HarnessSLICRule

+

refinementpredicates

errorpath

Iterative refinement in Zing

Pointerabstraction

AbstractZing

program

PointerRefinement

ZingMC

Zingprogram +

hint

errorpath

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 < Q? Does one model (P, implementation) conform

to another (Q, specification)?

• Compositional– P < Q => C[P] < C[Q]

• 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