Symbolic execution

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.

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

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.

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.

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