NFA universality is an important problem in formal verification, since it is an effective proxy for complementation of NFAs - a key operation that underlies most verification algorithms. However, because complemented automata are extremely large, many modern tools use symbolic representations to perform complementation and universality checking. One state-of-the-art tool for NFA universality, ALASKA, symbolically represents automata using binary decision diagrams (BDDs) to more efficiently complement them with the subset construction.

The algorithm usually only represents a small number of subset-constructed states at a time, relative to the vast state space. Zero-suppressed decision diagrams (ZDDs) have the same semantics as BDDs, but are more efficient when representing sparse solution sets. We used this advantage in constructing a new ZDD-based tool, ALASKA-ZDD, which completely replaces ALASKA's symbolic representation with a ZDD-based one. We then experimentally compared it with ALASKA, using random automata generated with the widely-used Tabakov-Vardi (T-V) random model due to a lack of practical benchmarks. We found that ALASKA-ZDD is more efficient on automata with sparse transition relations.

But how do we know the T-V model gives robust results? The model was originally adopted due to lack of practical benchmarks, but this also prevents checking its reliability against real examples. While it statistically guarantees certain universality properties about the automata it produces, no further work has been done to verify its results. Therefore, it is unclear if tests on the T-V model are sufficient. In graph theory, many different random models are used for representing different problems - would that be an appropriate approach for verification? We introduce three new random models, and show that their results for the NFA universality question are the same as T-V. We also compare multiple solutions to the Buechi universality problem on these models, and find that their results are the same as T-V. Therefore, in addition to showing ALASKA-ZDD is competitive, we show that T-V can be used as a robust random model for verification, across multiple problems, verifying many previous results with the model.