?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=Rewriting+with+Frobenius.&rft.creator=Bonchi%2C+F&rft.creator=Gadducci%2C+F&rft.creator=Kissinger%2C+A&rft.creator=Sobocinski%2C+P&rft.creator=Zanasi%2C+F&rft.description=Symmetric+monoidal+categories+have+become+ubiquitous+as+a+formal+environment+for+the+analysis+of+compound+systems+in+a+compositional%2C+resource-sensitive+manner+using+the+graphical+syntax+of+string+diagrams.+Recently%2C+reasoning+with+string+diagrams+has+been+implemented+concretely+via+double-pushout+(DPO)+hypergraph+rewriting.+The+hypergraph+representation+has+the+twin+advantages+of+being+convenient+for+mechanisation+and+of+completely+absorbing+the+structural+laws+of+symmetric+monoidal+categories%2C+leaving+just+the+domain-specific+equations+explicit+in+the+rewriting+system.%0D%0AIn+many+applications+across+different+disciplines+(linguistics%2C+concurrency%2C+quantum+computation%2C+control+theory%2C...)+the+structural+component+appears+to+be+richer+than+just+the+symmetric+monoidal+structure%2C+as+it+includes+one+or+more+Frobenius+algebras.+In+this+work+we+develop+a+DPO+rewriting+formalism+which+is+able+to+absorb+multiple+Frobenius+structures%2C+thus+sensibly+simplifying+diagrammatic+reasoning+in+the+aforementioned+applications.+As+a+proof+of+concept%2C+we+use+our+formalism+to+describe+an+algorithm+which+computes+the+reduced+form+of+a+diagram+of+the+theory+of+interacting+bialgebras+using+a+simple+rewrite+strategy.&rft.publisher=ACM&rft.contributor=Dawar%2C+A&rft.contributor=Gr%C3%A4del%2C+E&rft.date=2018-07-12&rft.type=Proceedings+paper&rft.language=eng&rft.source=+++++In%3A+Dawar%2C+A+and+Gr%C3%A4del%2C+E%2C+(eds.)+Proceedings+of+the+33rd+Annual+ACM%2FIEEE+Symposium+on+Logic+in+Computer+Science.++(pp.+pp.+165-174).++ACM%3A+Oxford%2C+United+Kingdom.+(2018)+++++&rft.format=text&rft.identifier=https%3A%2F%2Fdiscovery.ucl.ac.uk%2Fid%2Feprint%2F10053250%2F1%2FpaperLICS18.pdf&rft.identifier=https%3A%2F%2Fdiscovery.ucl.ac.uk%2Fid%2Feprint%2F10053250%2F&rft.rights=open