On Maximal Merging of Information in Boolean Computations
We prove that in any computation by logical operations of a Boolean function f which merges information of size 2n (for instance ) there exist at least n node-disjoint pairs of merging paths. Given a directed acyclic graph with max indegree 2 then the size of any cut which breaks all pairs of merging paths is a lower bound for the twofold maximal size of any set of node-disjoint pairs of merging paths. These lower bounds for the number of node-disjoint pairs of merging paths cannot be improved.
KeywordsBoolean Function Directed Acyclic Graph Turing Machine Logical Operation Labelling Procedure
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