In computer science, symbolic execution (also symbolic evaluation or symbex) is a means of analyzing a program to determine what inputs cause each part of a program to execute. An interpreter follows the program, assuming symbolic values for inputs rather than obtaining actual inputs as normal execution of the program would. It thus arrives at expressions in terms of those symbols for expressions and variables in the program, and constraints in terms of those symbols for the possible outcomes of each conditional branch. Finally, the possible inputs that trigger a branch can be determined by solving the constraints.

The field of symbolic simulation applies the same concept to hardware. Symbolic computation applies the concept to the analysis of mathematical expressions.

Example

Consider the program below, which reads in a value and fails if the input is 6.

<syntaxhighlight lang="c">

  1. include <stdio.h>

// reads an integer from somewhere and returns it

int read();

int main() {

int y = read();

int z = y * 2;

if (z == 12) {

perror("Program failed!");

return 1;

} else {

printf("OK");

return 0;

}

}

</syntaxhighlight>

During a normal execution ("concrete" execution), the program would read a concrete input value (e.g., 5) and assign it to <code>y</code>. Execution would then proceed with the multiplication and the conditional branch, which would evaluate to false and print <code>OK</code>.

During symbolic execution, the program reads a symbolic value (e.g., <code>λ</code>) and assigns it to <code>y</code>. The program would then proceed with the multiplication and assign <code>λ * 2</code> to <code>z</code>. When reaching the <code>if</code> statement, it would evaluate <code>λ * 2 == 12</code>. At this point of the program, <code>λ</code> could take any value, and symbolic execution can therefore proceed along both branches, by "forking" two paths. Each path gets assigned a copy of the program state at the branch instruction as well as a path constraint. In this example, the path constraint is <code>λ * 2 == 12</code> for the <code>if</code> branch and <code>λ * 2 != 12</code> for the <code>else</code> branch. Both paths can be symbolically executed independently. When paths terminate (e.g., as a result of executing <code>fail()</code> or simply exiting), symbolic execution computes a concrete value for <code>λ</code> by solving the accumulated path constraints on each path. These concrete values can be thought of as concrete test cases that can, e.g., help developers reproduce bugs. In this example, the constraint solver would determine that in order to reach the <code>fail()</code> statement, <code>λ</code> would need to equal 6 or (if <code>int</code> is a 32-bit two's complement integer and integer overflow is taken into account) -2147483642.

Limitations

Path explosion

Symbolically executing all feasible program paths does not scale to large programs. The number of feasible paths in a program grows exponentially with an increase in program size and can even be infinite in the case of programs with unbounded loop iterations. Solutions to the path explosion problem generally use either heuristics for path-finding to increase code coverage, reduce execution time by parallelizing independent paths, or by merging similar paths. One example of merging is veritesting, which "employs static symbolic execution to amplify the effect of dynamic symbolic execution".

Program-dependent efficiency

Symbolic execution is used to reason about a program path-by-path which is an advantage over reasoning about a program input-by-input as other testing paradigms use (e.g. dynamic program analysis). However, if few inputs take the same path through the program, there is little savings over testing each of the inputs separately.

Memory aliasing

Symbolic execution is harder when the same memory location can be accessed through different names (aliasing). Aliasing cannot always be recognized statically, so the symbolic execution engine can't recognize that a change to the value of one variable also changes the other.

Arrays

Since an array is a collection of many distinct values, symbolic executors must either treat the entire array as one value or treat each array element as a separate location. The problem with treating each array element separately is that a reference such as "A[i]" can only be specified dynamically, when the value for i has a concrete value. Cloud9, and Otter take this approach by implementing models for file system operations, sockets, IPC, etc.

Forking the entire system state. Symbolic execution tools based on virtual machines solve the environment problem by forking the entire VM state. For example, in S2E each state is an independent VM snapshot that can be executed separately. This approach alleviates the need for writing and maintaining complex models and allows virtually any program binary to be executed symbolically. However, it has higher memory usage overheads (VM snapshots may be large).

Tools

{| class="wikitable sortable"

|-

! Tool

! Target

! URL

! Can anybody use it/ Open source/ Downloadable

|-

| angr

| libVEX based (supporting x86, x86-64, ARM, AARCH64, MIPS, MIPS64, PPC, PPC64, and Java)

| http://angr.io/

|

|-

| BE-PUM

| x86

| https://github.com/NMHai/BE-PUM

|

|-

|BINSEC

|x86, ARM, RISC-V (32 bits)

|http://binsec.github.io

|

|-

|crucible

|LLVM, JVM, etc

|https://github.com/GaloisInc/crucible

|

|-

| ExpoSE

| JavaScript

| https://github.com/ExpoSEJS/ExpoSE

|

|-

| FuzzBALL

| VineIL / Native

| http://bitblaze.cs.berkeley.edu/fuzzball.html

|

|-

| GenSym

| LLVM

| https://github.com/Generative-Program-Analysis/GenSym

|

|-

| Jalangi2

| JavaScript

| https://github.com/Samsung/jalangi2

|

|-

| janala2

|Java

| https://github.com/ksen007/janala2

|

|-

| JaVerT

| JavaScript

| https://www.doc.ic.ac.uk/~pg/publications/FragosoSantos2019JaVerT.pdf

|

|-

| JBSE

|Java

| https://github.com/pietrobraione/jbse

|

|-

| jCUTE

|Java

| https://github.com/osl/jcute

|

|-

| KeY

|Java

| http://www.key-project.org/

|

|-

| Kite

| LLVM

| http://www.cs.ubc.ca/labs/isd/Projects/Kite/

|

|-

| KLEE

| LLVM

| https://klee.github.io/

|

|-

| Kudzu

| JavaScript

| http://webblaze.cs.berkeley.edu/2010/kudzu/kudzu.pdf

|

|-

|MPro

|Ethereum Virtual Machine (EVM) / Native

|https://sites.google.com/view/smartcontract-analysis/home

|

|-

| Maat

| Ghidra P-code / SLEIGH

| https://maat.re/

|

|-

| Manticore

| x86-64, ARMv7, Ethereum Virtual Machine (EVM) / Native

| https://github.com/trailofbits/manticore/

|

|-

| Mayhem

| Binary

| http://forallsecure.com

|

|-

| Mythril

| Ethereum Virtual Machine (EVM) / Native

| https://github.com/ConsenSys/mythril

|

|-

| Otter

| C

| https://bitbucket.org/khooyp/otter/overview

|

|-

| Owi

| C, C++, Rust, WebAssembly, Zig

| https://github.com/ocamlpro/owi

|

|-

| Oyente-NG

| Ethereum Virtual Machine (EVM) / Native

| http://www.comp.ita.br/labsca/waiaf/papers/RafaelShigemura_paper_16.pdf

|

|-

| Pathgrind

| Native 32-bit Valgrind-based

| https://github.com/codelion/pathgrind

|

|-

| Pex

| .NET Framework

| http://research.microsoft.com/en-us/projects/pex/

|

|-

| pysymemu

| x86-64 / Native

| https://github.com/feliam/pysymemu/

|

|-

| Rosette

| Dialect of Racket

| https://emina.github.io/rosette/

|

|-

| Rubyx

| Ruby

| http://www.cs.umd.edu/~avik/papers/ssarorwa.pdf

|

|-

| S2E

| x86, x86-64, ARM / User and kernel-mode binaries

| http://s2e.systems/

|

|-

| Symbolic PathFinder (SPF)

| Java Bytecode

| https://github.com/SymbolicPathFinder

|

|-

| SymDroid

| Dalvik bytecode

| http://www.cs.umd.edu/~jfoster/papers/symdroid.pdf

|

|-

| SymJS

| JavaScript

| https://core.ac.uk/download/pdf/24067593.pdf

|

|-

| SymCC

| LLVM

| https://www.s3.eurecom.fr/tools/symbolic_execution/symcc.html

|

|-

| Triton

| x86, x86-64, ARM and AArch64

| https://triton.quarkslab.com

|

|-

| Verifast

| C, Java

| https://people.cs.kuleuven.be/~bart.jacobs/verifast

|

|-

|}

Earlier versions of the tools

  1. EXE is an earlier version of KLEE. The EXE paper can be found here.

History

The concept of symbolic execution was introduced academically in the 1970s with descriptions of: the Select system,

the EFFIGY system,

the DISSECT system,

and Clarke's system.

See also

  • Abstract interpretation
  • Symbolic simulation
  • Symbolic computation
  • Concolic testing
  • Control-flow graph
  • Dynamic recompilation

References