The inclusion-exclusion principle is a well-known property of set cardinality and probability measures, that is instrumental to solve some problems such as the evaluation of systems reliability or of uncertainty over Boolean formulas. However, when using sets and probabilities conjointly, this principle no longer holds in general. It is therefore useful to know in which cases it is still valid....

The inclusion-exclusion principle is a well-known mathematical principle used to count the number of elements in the union of a collection of sets in terms of intersections of sub-collections. We present an algorithm for counting the number of solutions of a given k-SAT formula using the inclusion-exclusion principle. The key contribution of our work consists of a novel subsumption pruning tech...

Many data mining algorithms make use of the well-known Inclusion-Exclusion principle. As a consequence, using this principle efficiently is crucial for the success of all these algorithms. Especially in the context of condensed representations, such as NDI, and in computing interesting measures, a quick inclusion-exclusion algorithm can be crucial for the performance. In this paper, we give an ...

Abstract We present two fast algorithms which apply inclusion–exclusion principle to sum over the bosonic diagrams in bare diagrammatic quantum Monte Carlo and inchworm method, respectively. In case of Carlo, proposed algorithm gives an extension work [2018 Inclusion–exclusion for many-body diagrammatics Phys. Rev. B 98 115152] from fermionic systems. prove that reduce computational complexity ...