Symbolic execution

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In computer science, symbolic execution (also symbolic evaluation) 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, a case of abstract interpretation. 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.

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

Example[edit]

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

 1 int f() {
 2   ...
 3   y = read();
 4   z = y * 2;
 5   if (z == 12) {
 6     fail();
 7   } else {
 8     printf("OK");
 9   }
10 }

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

During symbolic execution, the program reads a symbolic value (e.g., λ) and assigns it to y. The program would then proceed with the multiplication and assign λ * 2 to z. When reaching the if statement, it would evaluate λ * 2 == 12. At this point of the program, λ could take any value, and symbolic execution can therefore proceed along both branches, by "forking" two paths. Each path get assigned a copy of the program state at the branch instruction as well as a path constraint. In this example, the path constraint is λ * 2 == 12 for the then branch and λ * 2 != 12 for the else branch. Both paths can be symbolically executed independently. When paths terminate (e.g., as a result of executing fail() or simply exiting), symbolic execution computes a concrete value for λ 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 fail() statement, λ would need to equal 6.

Limitations[edit]

Path Explosion[edit]

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.[1] Solutions to the path explosion problem generally use either heuristics for path-finding to increase code coverage,[2] reduce execution time by parallelizing independent paths,[3] or by merging similar paths.[4]

Program-Dependent Efficacy[edit]

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.

Environment Interactions[edit]

Programs interact with their environment by performing system calls, receiving signals, etc. Consistency problems may arise when execution reaches components that are not under control of the symbolic execution tool (e.g., kernel or libraries). Consider the following example:

 1 int main()
 2 {
 3   FILE *fp = fopen("doc.txt");
 4   ...
 5   if (condition) {
 6     fputs("some data", fp);
 7   } else {
 8     fputs("some other data", fp);
 9   }
10   ...
11   data = fgets(..., fp);
12 }

This program opens a file and, based on some condition, writes different kind of data to the file. It then later reads back the written data. In theory, symbolic execution would fork two paths at line 5 and each path from there on would have its own copy of the file. The statement at line 11 would therefore return data that is consistent with the value of "condition" at line 5. In practice, file operations are implemented as system calls in the kernel, and are outside the control of the symbolic execution tool. The main approaches to address this challenge are:

Executing calls to the environment directly. The advantage of this approach is that it is simple to implement. The disadvantage is that the side effects of such calls will clobber all states managed by the symbolic execution engine. In the example above, the instruction at line 11 would return "some datasome other data" or "some other datasomedata" depending on the sequential ordering of the states.

Modeling the environment. In this case, the engine instruments the system calls with a model that simulates their effects and that keeps all the side effects in per-state storage. The advantage is that one would get correct results when symbolically executing programs that interact with the environment. The disadvantage is that one needs to implement and maintain many potentially complex models of system calls. Tools such as KLEE[5] and Cloud9 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[6] 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[edit]

Tool It can analyze Arch/Lang url Can anybody use it/ Open source/ Downloadable
KLEE LLVM http://klee.github.io/ yes
FuzzBALL VineIL / Native http://bitblaze.cs.berkeley.edu/fuzzball.html yes
JPF Java http://babelfish.arc.nasa.gov/trac/jpf yes
jCUTE Java https://github.com/osl/jcute yes
janala2 Java https://github.com/ksen007/janala2 yes
KeY Java http://www.key-project.org/ yes
S2E x86, x86-64, ARM / User and kernel-mode binaries http://s2e.epfl.ch yes
Pathgrind[7] Native 32-bit Valgrind-based https://github.com/codelion/pathgrind yes
Mayhem Binary http://forallsecure.com/mayhem.html no
Otter C https://bitbucket.org/khooyp/otter/overview yes
SymDroid Dalvik bytecode http://www.cs.umd.edu/~jfoster/papers/symdroid.pdf no
Rubyx Ruby http://www.cs.umd.edu/~avik/papers/ssarorwa.pdf no
Pex .NET Framework http://research.microsoft.com/en-us/projects/pex/ no
SymJS JavaScript http://www.cs.utah.edu/~ligd/publications/SymJS-FSE14.pdf no
Jalangi2 JavaScript https://github.com/Samsung/jalangi2 yes
Kite LLVM http://www.cs.ubc.ca/labs/isd/Projects/Kite/ yes
pysymemu x86-64 / Native https://github.com/feliam/pysymemu/ yes
Triton x86 and x86-64 http://triton.quarkslab.com yes
angr libVEX based http://angr.io/ yes

History[edit]

The concept of symbolic execution was introduced academically with descriptions of: the Select system,[8] the EFFIGY system,[9] the DISSECT system,[10] and Clarke's system.[11] See a bibliography of more technical papers published on symbolic execution.

See also[edit]

References[edit]

  1. ^ Anand, Saswat; Patrice Godefroid; Nikolai Tillmann (2008). "Demand-Driven Compositional Symbolic Execution". Tools and Algorithms for the Construction and Analysis of Systems, Lecture Notes in Computer Science 4963: 367–381. Retrieved 2013-04-03. 
  2. ^ Ma, Kin-Keng; Khoo Yit Phang; Jeffrey S. Foster; Michael Hicks (2011). "Directed Symbolic Execution". Proceedings of the 18th International Conference on Statis Analysis: 95–111. Retrieved 2013-04-03. 
  3. ^ Staats, Matt; Corina Pasareanu (2010). "Parallel symbolic execution for structural test generation". Proceedings of the 19th international symposium on Software testing and analysis: 183–194. Retrieved 2011-04-03. 
  4. ^ Kuznetsov, Volodymyr; Kinder, Johannes; Bucur, Stefan; Candea, George (2012-01-01). "Efficient State Merging in Symbolic Execution". Proceedings of the 33rd ACM SIGPLAN Conference on Programming Language Design and Implementation. PLDI '12 (New York, NY, USA: ACM): 193–204. doi:10.1145/2254064.2254088. ISBN 978-1-4503-1205-9. 
  5. ^ Cadar, Cristian; Dunbar, Daniel; Engler, Dawson (2008-01-01). "KLEE: Unassisted and Automatic Generation of High-coverage Tests for Complex Systems Programs". Proceedings of the 8th USENIX Conference on Operating Systems Design and Implementation. OSDI'08 (Berkeley, CA, USA: USENIX Association): 209–224. 
  6. ^ Chipounov, Vitaly; Kuznetsov, Volodymyr; Candea, George (2012-02-01). "The S2E Platform: Design, Implementation, and Applications". ACM Trans. Comput. Syst. 30 (1): 2:1–2:49. doi:10.1145/2110356.2110358. ISSN 0734-2071. 
  7. ^ "Exploiting Undefined Behaviors for Efficient Symbolic Execution". ICSE 2014. Retrieved 2014-12-02. 
  8. ^ Robert S. Boyer and Bernard Elspas and Karl N. Levitt SELECT--a formal system for testing and debugging programs by symbolic execution, Proceedings of the International Conference on Reliable Software, 1975,page 234--245, Los Angeles, California
  9. ^ James C. King,Symbolic execution and program testing, Communications of the ACM, volume 19, number 7, 1976, 385--394
  10. ^ William E. Howden, Experiments with a symbolic evaluation system, Proceedings, National Computer Conference, 1976.
  11. ^ Lori A. Clarke, A program testing system, ACM 76: Proceedings of the Annual Conference, 1976, pages 488-491, Houston, Texas, United States

External links[edit]