Wiring diagrams form a kind of graphical language that describes operations or processes with
multiple inputs and outputs and shows how such operations are wired together to form a larger
and more complex operation. This monograph presents a comprehensive study of the combinatorial
structure of the various operads of wiring diagrams their algebras and the relationships
between these operads.The book proves finite presentation theorems for operads of wiring
diagrams as well as their algebras. These theorems describe the operad in terms of just a few
operadic generators and a small number of generating relations. The author further explores
recent trends in the application of operad theory to wiring diagrams and related structures
including finite presentations for the propagator algebra the algebra of discrete systems the
algebra of open dynamical systems and the relational algebra. A partial verification of David
Spivak's conjecture regarding the quotient-freeness of the relational algebra is also provided.
In the final part the author constructs operad maps between the various operads of wiring
diagrams and identifies their images. Assuming only basic knowledge of algebra combinatorics
and set theory this book is aimed at advanced undergraduate and graduate students as well as
researchers working in operad theory and its applications. Numerous illustrations examples
and practice exercises are included making this a self-contained volume suitable for
self-study.
