An Efficient Algorithm for Generating Minimal Unique-Cause MC/DC Test cases for Singular Boolean Expressions

Abstract

Modified Condition/Decision Coverage (MC/DC) is a mandatory structural coverage criterion for assuring the reliability of safety-critical software. Among its variants, Unique-Cause MC/DC provides the strongest assurance, yet efficient and scalable test generation for Unique-Cause MC/DC remains underexplored. This gap is particularly important because large-scale avionics studies report that 99.7% of conditional decisions are Singular Boolean Expressions (SBEs), for which Unique-Cause obligations can be precisely characterized. We propose Robin's Rule, a deterministic, direct-construction algorithm that generates a provably minimal test suite of N+1 test cases to guarantee 100% Unique-Cause MC/DC for SBEs with N conditions, without enumerating the 2^N truth table. The algorithm runs in O(N^2) time by explicitly constructing an (N+1)xN test table. To evaluate the approach, we build a benchmark of 25 SBEs consisting of 15 TCAS-II-derived conditions and 10 randomly generated SBEs with diverse operators and nesting. We validate achieved coverage using VectorCAST as an oracle and compare against state-of-the-art baseline paradigms using BDD and SAT. Across all benchmarks, Robin's Rule consistently achieves 100% Unique-Cause MC/DC with the theoretical minimum number of tests, while providing stable and efficient generation time. This work offers a practical and provably optimal solution for Unique-Cause MC/DC test generation on SBEs, improving both rigor and scalability for safety-critical verification.