Abstract
We present an algorithm for computing both functional dependency and unateness of combinational and sequential Boolean functions represented as logic networks. The algorithm uses SAT-based techniques from Combinational Equivalence Checking (CEC) and Automatic Test Pattern Generation (ATPG) to compute the dependency matrix of multi-output Boolean functions. Additionally, the classical dependency definitions are extended to sequential functions and a fast approximation is presented to efficiently yield a sequential dependency matrix. Extensive experiments show the applicability of the methods and the improved robustness compared to existing approaches.
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Notes
- 1.
We also performed a structural check for each input-output pair if there potentially exists an inverting path between them. If this is not the case, the additionally SAT-call to check for unateness may be skipped. However, the performance impact was insignificant and hence we did not employ this optimization.
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- 3.
In [29] shift-left and shift-right are considered separately. Since these operations are equivalent under permutation, the measured numbers in the experiment also do not differ.
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Acknowledgments
The authors wish to thank Robert Brayton and Alan Mishchenko for many helpful discussions. This research was partially financed by H2020-ERC-2014-ADG 669354 CyberCare and the Baden-Württemberg Stiftung gGmbH Stuttgart within the scope of its IT security research programme.
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Soeken, M., Raiola, P., Sterin, B., Becker, B., De Micheli, G., Sauer, M. (2016). SAT-Based Combinational and Sequential Dependency Computation. In: Bloem, R., Arbel, E. (eds) Hardware and Software: Verification and Testing. HVC 2016. Lecture Notes in Computer Science(), vol 10028. Springer, Cham. https://doi.org/10.1007/978-3-319-49052-6_1
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