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CATEGORIES:Logic and Semantics Seminar (Computer Laboratory)
SUMMARY:Interacting Hopf monoids: the algebra of signal fl
ow diagrams - Fabio Zanasi\, Radboud University o
f Nijmegen\, Netherlands
DTSTART;TZID=Europe/London:20160129T140000
DTEND;TZID=Europe/London:20160129T150000
UID:TALK62231AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/62231
DESCRIPTION:This talk illustrates the signal flow calculus\, a
n algebraic and diagrammatic foundation of signal
processing circuits. Signal flow graphs\, a class
of circuits that play a foundational role in contr
ol theory\, are recovered via a Kleene’s theorem\,
as the rational fragment of the calculus. The hig
h-point of our developments is a sound and complet
e axiomatisation for semantic equivalence\, which
we call the theory of interacting Hopf monoids (IH
). The relevance of IH goes beyond the signal flow
calculus: its equations describe the interplay of
familiar structures\, such as Frobenius monoids a
nd Hopf monoids\, in a way that appeared independe
ntly in other research threads\, in quantum inform
ation theory and concurrency theory. Our approach
gives a formal explanation for this ubiquity\, by
showing that the equations of IH present categorie
s of linear subspaces — completeness for the signa
l flow calculus follows as a corollary. This chara
cterisation passes through a modular account of IH
: its axioms are explained in terms of compositio
n of simpler algebraic theories\, using distributi
ve laws of PROPs as in the work of Steve Lack.\n\n
This talk is based on joint work with Filippo Bonc
hi and Pawel Sobocinski.
LOCATION:SS03
CONTACT:Ohad Kammar
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