Negation is powerless for Boolean slice functions
SIAM Journal on Computing
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A new algorithm for optimal 2-constraint satisfaction and its implications
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Finding Efficient Circuits Using SAT-Solvers
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
The Conflict-Driven Answer Set Solver clasp: Progress Report
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
New upper bounds on the Boolean circuit complexity of symmetric functions
Information Processing Letters
A note on designing logical circuits using SAT
ICES'03 Proceedings of the 5th international conference on Evolvable systems: from biology to hardware
Improving exhaustive search implies superpolynomial lower bounds
Proceedings of the forty-second ACM symposium on Theory of computing
On the possibility of faster SAT algorithms
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Fast zeta transforms for lattices with few irreducibles
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
March_eq: implementing additional reasoning into an efficient look-ahead SAT solver
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
Known algorithms on graphs of bounded treewidth are probably optimal
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Synthesizing shortest linear straight-line programs over GF(2) using SAT
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
On moderately exponential time for SAT
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
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Given a Boolean function as input, a fundamental problem is to find a Boolean circuit with the least number of elementary gates (AND, OR, NOT) that computes the function. The problem generalises naturally to the setting of multiple Boolean functions: find the smallest Boolean circuit that computes all the functions simultaneously. We study an NP-complete variant of this problem titled Ensemble Computation and, especially, its relationship to the Boolean satisfiability (SAT) problem from both the theoretical and practical perspectives, under the two monotone circuit classes: OR-circuits and SUM-circuits. Our main result relates the existence of nontrivial algorithms for CNF-SAT with the problem of rewriting in subquadratic time a given OR-circuit to a SUM-circuit. Furthermore, by developing a SAT encoding for the ensemble computation problem and by employing state-of-the-art SAT solvers, we search for concrete instances that would witness a substantial separation between the size of optimal OR-circuits and optimal SUM-circuits. Our encoding allows for exhaustively checking all small witness candidates. Searching over larger witness candidates presents an interesting challenge for current SAT solver technology.