Studies of Euler diagrams

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This resource shows the Euler diagrams for many Boolean functions, and aims to find a systematic way to draw them.
This is part of the documentation of a software, that is not yet published.

See the criteria for good Euler diagrams and the list of example functions.     See also sequences of numbers.

examples[edit | edit source]

Euler diagram, graph and formula tree

blightless   (examples by EC)[edit | edit source]


blighted   (reducible arity)[edit | edit source]

NP and transformations[edit | edit source]

gapspots[edit | edit source]

filtrates[edit | edit source]

splits[edit | edit source]

3 possible relationships between 2 different splits

A split is a generalization of a set without the notion of inside and outside. It just splits the universe in two sides.

decompose[edit | edit source]

decomposition into three bundles

decomposition into bundles, i.e. parts of the Euler diagram that are connected by crossing circles

ternary labels[edit | edit source]

labels with 3 and 4 digits

While the cells can be labeled with binary numbers, all segments (including edges and vertices) can be labeled with balanced ternary numbers.

grids[edit | edit source]

formula trees[edit | edit source]

algebraic normal form and Zhegalkin index[edit | edit source]

ANF to truth table
Zhegalkin matrix