Abstract
Sums-of-products provide a basis for describing certain computational problems, particularly problems related to constraint satisfaction including SAT, MAX SAT, and #SAT. They also can be used to describe many problems arising from graph theory. By modeling a problem as a sum-of-products problem, the concept of “subproblem independence” takes on a clear meaning. Subproblem independence has immediate computational implications since it can be used to create programs with reduced levels of nesting and programs which exploit memoization. The concept of subproblem independence also extends to quantified sums.
Subproblem independence can be linked directly to structural concepts associated with tree decompositions for graphs and the closely related structure trees for algebraic problems. Thus methods of finding tree decompositions apply directly to finding independent subproblems.
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Stearns, R.E., Hunt, H.B. (2009). Sums-of-Products and Subproblem Independence. In: Ravi, S.S., Shukla, S.K. (eds) Fundamental Problems in Computing. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9688-4_11
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DOI: https://doi.org/10.1007/978-1-4020-9688-4_11
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