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

초록

Modified Condition/Decision Coverage (MC/DC) is a mandatory structural coverage criterion for safety-critical software. Among its variants, Unique-Cause MC/DC provides a strong independence guarantee, but minimal test generation remains challenging for general Boolean decisions. This paper focuses on Singular Boolean Expressions (SBEs), a practically dominant decision class in avionics software in which each condition appears exactly once. We propose Robin's Rule, a deterministic direct-construction method that builds an N+1 Unique-Cause MC/DC suite for SBEs without solver search, BDD path extraction, or 2(N) truth-table enumeration. The method uses structural decomposition, Relation Table (RT) context selection, and exception handling. We provide explicit composition invariants, RT-preservation lemmas, an exception-handling contract, and a phase-by-phase O(N-2) complexity analysis. We evaluate 25 benchmark SBEs, consisting of 15 TCAS-II-derived SBE expressions and 10 randomly generated SBEs, using VectorCAST as an external coverage oracle and compare the results with fixed-configuration BDD and SAT baselines. We also report a separate checker-validated scalability stress test for synthetic SBEs with N=25,50,75,100,150 , and 200 conditions. Robin's Rule constructs exact N+1 suites for all evaluated SBEs, achieves full VectorCAST-validated Unique-Cause MC/DC coverage on the 25 benchmark SBEs, and satisfies all independently checked witness-pair obligations in the scalability test. The contribution is a transparent and reproducible construction procedure for SBE-focused safety-critical verification, rather than a universal replacement for solver-based MC/DC generators.

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