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Register a new userPairing Functions, Boolean Evaluation and Binary Decision Diagrams in Prolog
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Added by
Paul Tarau
Publication date
2009
fields
Informatics Engineering
and research's language is
English
Authors
Paul Tarau
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A pairing function J associates a unique natural number z to any two natural numbers x,y such that for two unpairing functions K and L, the equalities K(J(x,y))=x, L(J(x,y))=y and J(K(z),L(z))=z hold. Using pairing functions on natural number representations of truth tables, we derive an encoding for Binary Decision Diagrams with the unique property that its boolean evaluation faithfully mimics its structural conversion to a a natural number through recursive application of a matching pairing function. We then use this result to derive {em ranking} and {em unranking} functions for BDDs and reduced BDDs. The paper is organized as a self-contained literate Prolog program, available at http://logic.csci.unt.edu/tarau/research/2008/pBDD.zip Keywords: logic programming and computational mathematics, pairing/unpairing functions, encodings of boolean functions, binary decision diagrams, natural number representations of truth tables
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