Key insights: a path can be encoded by a concrete test input; a set of paths can be encoded by a pair of paths (all paths lexicographically between the two paths).

These insights enable *ranged symbolic execution*: partitioning the search space into a number of
ranges.
The only redundant work performed when using this approach to partition the set of paths is
redundant exploration of the boundaries between sets (i.e., the limits of the ranges).
This is most useful when doing a exhaustive exploration of all paths because it requires
a fixed branch exploration ordering which conflicts with use of search heuristics used
for partial explorations.

Some uses:

- Resumable symbolic execution: pausing SE at any time and restarting later.
- Parallel symbolic execution.
- Dynamic range refinement that performs parallel symbolic execution using work stealing.

Notes:

- When comparing two paths, it is best to exploit their common prefix to avoid repeating that work.
- Turning test inputs into paths seems to have some of the flavour of concolic execution.
- There is a restriction involving finite paths - not sure this is fundamental though.
- Evaluation
- Implemented in KLEE, evaluated on standard KLEE testsuite of CoreUtils using the 71 programs where KLEE hits more than 100 paths in ten minutes.
- Results are the min, max and (arithmetic?) average of five runs running on
ten cores.
- Average speedup (arithmetic? geometric?) on 10 cores is 6.6x. Peak speedup is 17.7x due to improved hit rates in KLEE’s internal caches.

- To explore scaling on 1, 5, 10 and 20 cores, they use a subset of 5 worst,
5 median, 5 best programs based on the ten core results.
- The worst don’t show any scaling, the best exhibit the same superlinear scaling and reach up to 22x.
- Eyeballing the data, there seems to be an obvious knee in the curves around 8 cores.

Future work suggests other uses of *ranged symbolic execution* such as

- Using binary search to find the range of paths that encloses some code change
- Creating ensemble analysis tools that use paths to communicate what work each tool has succeeded or failed at so that tools can try where others have failed.
- Applying the technique to software model checking to divide the space “vertically” instead of the “horizontal” divisions used in bounded model checking.

The conclusion makes the following interesting observation

But [symbolic execution normally explores the connection between symbolic execution and tests] in just one direction: from symbolic execution to tests. The key novelty of our work is to establish the connection in the opposite direction—from a test input to symbolic execution—specifically, to use a test input to encode the state of a run of symbolic execution—and show how this direction enables a number of novel approaches for more effective symbolic execution for test input generation.

## Notes related to Scaling symbolic execution using ranged analysis

Swarm verification, Symbolic execution, Verification performance of code, Verifier performance

## Papers related to Scaling symbolic execution using ranged analysis

- A synergistic approach for distributed symbolic execution using test ranges [qiu:icse:2017]