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Generalized Symbolic Execution for Model Checking and Testing

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Generalized Symbolic Execution for Model Checking and Testing

SarfrazKhurshid, Corina S. Păsăreanu, and Willem Visser

TACAS 2003

- Introduction
- General Methodology
- Background
- Symbolic Execution

- Two-fold Generalization of Symbolic Execution
- Lazy initialization
- Instrumentation

- Implementations
- Applications
- Conclusion

- Modern software systems are concurrent and manipulate complex dynamically allocated data structures (e.g., linked lists or binary trees)
- Two common techniques for checking correctness of software
- Testing
- widely used but doesn’t give us an assurance
- is not good at finding errors related to concurrent behavior

- Model Checking
- is automatic and good at analyzing concurrent systems
- suffers from state-space explosion problem and typically requires a closed system, i.e., bound on input sizes

- Testing

Symbolic execution

+

model checking

- Symbolic execution
- well-known program analysis
- traditionally arose in the context of checking sequential programs with a fixed number of integer variables
- requires dedicated tools to perform the analyses and do not handle concurrent systems with complex inputs

Generalization of traditional symbolic execution

Source to source translation to instrument a model checkable program

Novel symbolic execution algorithm for handling dynamically allocated structures (e.g., lists and trees)

Decision

Procedure

continue/backtrack

Code

Instrumentation

Model

Checking

Instrumented

Program

Source

Program

Counter example

Correctness

specification

precondition/ postcondition

- Symbolic Execution
- The main idea is to use symbolic values, instead of actual data, as input values, and to represent the value of program variables as expressions
- The state of a symbolically executed program includes the symbolic values of program variables and a path condition (pc)
- A symbolic execution tree characterizes the execution paths followed during the symbolic execution of a program

x : =A y := B

PC := true

- Symbolic Execution (Example)

1

1

int x, y;

1: if (x > y){

2: x = x + y ;

3: y = x – y ;

4: x = x – y ;

5: if (x – y > 0)

6: assert(false);

}

x : = A y := B

PC := A>B

x : =A y := B

PC := A<=B

2

x : =A+B, y :=B

PC := A>B

3

x : =A+B, y :=A

PC := A>B

4

x : =B, y :=A

PC := A>B

5

5

x : =B, y :=A

PC := A>B & B-A>0

FALSE!

x : =B, y :=A

PC := A>B & B-A <=0

- Lazy initialization
- is an algorithm for generalizing traditional symbolic execution to support advanced constructs of modern programming languages, such as Java and C++
- A key feature of the lazy initialization algorithm is that it starts execution of the method on inputs with uninitialized fields and use lazy initialization to assign values to these field, i.e., it initialize fields when they are first accessed during the method’s symbolic execution

- Lazy initialization

decision procedure

: checks the path condition is

satisfied. If not, backtracks

if ( F is uninitialized ) {

if ( F is a reference field of user-defined type T ) {

nondeterministically initialize F to

1. null

2. a new object of class T (with uninitialized field values)

3. an object created during a prior initialization of a field

of type T

if ( method precondition is violated )

backtrack();

}

if ( F is a primitive field )

initialize F to a new symbolic value of appropriate type

}

next

?

Two-fold Generalization of symbolic execution (3/9)

next field not accessed

- Lazy initialization (example)

class Node {intelem;Node next;Node swapNode() {1: if (next != null)2: if (elem > next.elem) {3: Node t = next;4: next = t.next;5: t.next = this;6: return t; } return this;}

}

Node instance with uninitialized element

next

?

next

next

next

next

?

?

?

?

?

?

next

Two-fold Generalization of symbolic execution (4/9)

consider executing1: if (next != null)

Precondition: acyclic list

1

next

next

next

next

next

next

next

next

next

next

E0

E0

?

E0

E0

?

?

E1

E1

E1

Two-fold Generalization of symbolic execution (5/9)

consider executing2: if (elem - next.elem>0)

} initialize “elem”

} initialize “next.elem”

2

2

1

PC : E0 <= E1,

PC : E0 > E1,

next

next

E0

E1

t

next

next

Precondition: acyclic list

next

next

next

E0

E1

?

E0

E1

t

t

next

next

next

E0

E1

next

E0

E1

null

t

t

next

next

next

next

next

E0

E1

null

E0

E1

?

t

t

Two-fold Generalization of symbolic execution (6/9)

consider executing

4: next = t.next;

- Instrumentation
- Two steps
- The integer fields and operations are instrumented
- The declared type of integer fields of input objects is changed to Expression, which is a library class for manipulation of symbolic integer expression

- The field accesses are instrumented
- Field reads are replaced by get method, get methods implement the lazy initialization
- Filed updates are replaced by set method

- The integer fields and operations are instrumented

- Two steps

- Instrumentation (example)

class Node {

Expression elem;

Node next;

boolean _next_is_initialized;

boolean _elem_is_initialized;

Node swapNode () {

if(_get_next() != null)

if(Expression._pc._update_GT(

_get_elem()._minus(

_get_next()._get_elem()) ,

new IntegerConstant(0) ) {

Node t = _get_next();

_set_next(t._get_next());

t._set_next(this);

return t;

}

return this; } }

class Node {

intelem;

Node next;

Node swapNode () {

if (next !=null)

if (elem – next.elem) >0) {

Node t = next;

next = t.next;

t.next = this;

return t;

}

return this;

}

}

- Instrumentation (example)

pc

class Expression {

static PathCondition _pc;

Expression _minus(Expression e) {

…

}

}

class PathCondition {

Constraints c;

boolean _update_GT(Expression e1, Expression e2) {

boolean result = choose_boolean();

if (result)

c.add_constraint_GT(e1, e2);

else

c.add_constraint_LE(e1, e2);

if (!c.is_satisfiable())

backtrack();

return result; }}

nondeterministic choice

add (e1 > e2)

to the path condition

add (e1 <= e2)

to the path condition

decision procedure

- Code instrumentation
- build on the Korat tool

- Model checking
- Java PathFinder (JPF)

- Decision procedure
- Java implementation of the Omega library

- Checking multithreaded programs with inputs

distributed sorting

method

- The implementation to symbolically execute distributed sort took 11 seconds to analyze the method’s correctness and it produced a counterexample

input list : [X] [Y] [Z] such that X > Y > Z

Thread- 1 : swaps X and Y

Thread -2 : swaps X and Z

resulting list : [Y] [Z] [X] ; Y and Z out of order

- Novel framework based on symbolic execution, for automated checking of concurrent software systems that manipulate complex data structures
- Two-fold generalization
- Future work
- Plan to integrate different constraints solvers that will allow us to handle floats and non-linear constraints
- Symbolic execution during model checking is powerful but we don’t know how well it scales to real applications