Studies of Euler diagrams

dummy

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

medusa

Euler diagram, graph and formula tree

blightless   (examples by EC)

multi-bundle

4-ary bundles

blighted   (reducible arity)

bloated

blotted

NP and transformations

dukeli NP

gapspots

gap variants

hard and soft

filtrates

splits

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

decomposition into three bundles

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

ternary labels

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

formula trees

algebraic normal form and Zhegalkin index

ANF to truth table

Zhegalkin matrix