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SUMMARY:Paweł Sobociński (Tallinn University of Technology)
DTSTART:20210419T133000Z
DTEND:20210419T143000Z
DTSTAMP:20260423T035729Z
UID:itaca/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/itaca/2/">Re
 writing Modulo Symmetric Monoidal Structure</a>\nby Paweł Sobociński (Ta
 llinn University of Technology) as part of ItaCa Fest 2021\n\n\nAbstract\n
 String diagrams are an elegant\, convenient and powerful syntax for arrows
  of symmetric monoidal categories. In recent years\, they have been used a
 s compositional descriptions of computational systems from various fields\
 , including quantum foundations\, linear algebra\, control theory\, automa
 ta theory\, concurrency theory\, and even linguistics. All of these applic
 ations rely on diagrammatic reasoning\, which is to string diagrams as equ
 ational reasoning is to ordinary terms.\n\nIf we are to take string diagra
 ms out of research papers and into more practical applications\, we need t
 o ask ourselves about how to implement diagrammatic reasoning. This is the
  focus of my talk.\n\nIt turns out that there is a tight correspondence be
 tween symmetric monoidal categories where every object has a coherent spec
 ial Frobenius algebra structure and categories of cospans of hypergraphs. 
 The correspondence\, therefore\, takes us from a topological understanding
  of string diagrams to a combinatorial data-structure-like description. Mo
 reover\, diagrammatic reasoning translates via this correspondence exactly
  to DPO rewriting with interfaces.\n\nGiven the above\, a natural question
  is how much of this correspondence survives if we drop the assumption abo
 ut Frobenius structure: i.e. can we use this correspondence to implement d
 iagrammatic reasoning on vanilla symmetric monoidal categories. The answer
  is yes\, but we need to restrict the kinds of cospans we consider: the un
 derlying hypergraph has to be acyclic and satisfy an additional technical 
 condition called monogamy. Moreover\, we must restrict the DPO rewriting m
 echanism to a variant that we call convex DPO rewriting. The good news is 
 that none of these modifications come with a significant algorithmic cost.
 \n\nThe material in this talk is with Filippo Bonchi\, Fabio Gadducci\, Al
 eks Kissinger and Fabio Zanasi\, and has been published in a series of pap
 ers:\n\n- “Rewriting modulo symmetric monoidal structure”\, Proceeding
 s of LiCS 2016\n\n- “Confluence of Graph Rewriting with Interfaces”\, 
 Proceedings of ESOP 2017\n\n- “Rewriting with Frobenius”\, Proceedings
  of LiCS 2018\n
LOCATION:https://researchseminars.org/talk/itaca/2/
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