Comparison of schemes for encoding unobservability in translation to SAT

• Authors: Miroslav N. Velev
• Venue: Proceedings of the 2005 Asia and South Pacific Design Automation Conference
• Year: 2005

Compared are seven schemes for encoding unobservability of logic blocks in Boolean-to-CNF translation. Four of the schemes are based on merging of logic blocks with adjacent gates toward the primary output. Two are based on using CNF unobservability variables to encode the unobservability of logic blocks. Also explored is a hybrid scheme. Encoding the unobservability of logic blocks accelerated the SAT-solving of Boolean formulas from formal verification of complex micro-processors, while allowing us to use a conventional CNF-based SAT-solver. On unsatisfiable CNF formulas, best was the strategy of merging logic blocks with adjacent gates on the only path from the block output to the primary output, with a resulting speedup of up to 16x for CNF formulas with hundreds of thousands of variables, millions of clauses, and tens of millions of literals. Furthermore, the speedup is relative to an already very efficient Boolean-to-CNF translation. On satisfiable CNF formulas, best was the strategy of merging logic blocks with leaf gates and with adjacent gates on the only path to the primary output, as well as exploiting the polarity of gates and logic blocks to reduce the number of their clauses. The presented optimizations are general and applicable to other classes of Boolean formulas.