Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: BDDs Naturally Represent Boolean Functions, and ZDDs Naturally Represent
  Sets of Sets   This paper studies a difference between Binary Decision Diagrams (BDDs) and
Zero-suppressed BDDs (ZDDs) from a conceptual point of view. It is commonly
understood that a BDD is a representation of a Boolean function, whereas a ZDD
is a representation of a set of sets. However, there is a one-to-one
correspondence between Boolean functions and sets of sets, and therefore we
could also regard a BDD as a representation of a set of sets, and similarly for
a ZDD and a Boolean function. The aim of this paper is to give an explanation
why the distinction between BDDs and ZDDs mentioned above is made despite the
existence of the one-to-one correspondence. To achieve this, we first observe
that Boolean functions and sets of sets are equipped with non-isomorphic
functor structures, and show that these functor structures are reflected in the
definitions of BDDs and ZDDs. This result can be stated formally as naturality
of certain maps. To the author's knowledge, this is the first formally stated
theorem that justifies the commonly accepted distinction between BDDs and ZDDs.
In addition, we show that this result extends to sentential decision diagrams
and their zero-suppressed variant.

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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: dg-ga