Boolean differential calculus

Boolean differential calculus (BDC) (German: Boolescher Differentialkalkül (BDK)) is a subject field of

Boolean differential calculus concepts are analogous to those of classical differential calculus, notably studying the changes in functions and variables with respect to another/others.^[1]

The Boolean differential calculus allows various aspects of dynamical systems theory such as

• finite automata
• Petri net theory^[2]
• supervisory control theory (SCT)

to be discussed in a united and closed form, with their individual advantages combined.

History and applications

Originally inspired by the design and testing of

Since then, significant advances were accomplished in both, the theory and in the application of the BDC in switching circuit design and logic synthesis.

Works of André Thayse,^{[10][11][12][13][14]} Marc Davio^[11][12][13] and Jean-Pierre Deschamps^[13] in the 1970s formed the basics of BDC on which Dieter Bochmann [de],^[15] Christian Posthoff^[15] and Bernd Steinbach [de]^[16] further developed BDC into a self-contained mathematical theory later on.

A complementary theory of Boolean integral calculus (German: Boolescher Integralkalkül) has been developed as well.^[15][17]

BDC has also found uses in

The differentials ${\displaystyle dx_{i}}$ are binary. They can be used just like common binary variables.

See also

• Boolean Algebra
• Boole's expansion theorem
• Ramadge–Wonham framework

References