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TZID:Europe/Paris
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UID:8980@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20260122T110000
DTEND;TZID=Europe/Paris:20260122T123000
DTSTAMP:20260121T165722Z
URL:https://www.i2m.univ-amu.fr/evenements/the-spectral-space-of-a-round-b
 ased-protocol/
SUMMARY:Cameron Calk (LIS): The spectral space of a round-based protocol
DESCRIPTION:Cameron Calk: An important question in the domain of distribute
 d computing is that of task solvability : given a distributed task\, the a
 nalog of a program specification for distributed systems\, under which con
 ditions can it be solved by some distributed protocol ? The topological ap
 proach to distributed computing represents tasks and protocols as relation
 s between simplicial complexes\, combinatorial objects which encode possib
 le global states of the system. These have a spatial interpretation\, whic
 h led to the Asynchronous Computability Theorem (ACT)\, which relates\, fo
 r certain computational models\, the existence of a continuous map to task
  solvability\, using subdivisions of the input space.\n\nIn this talk\, I 
 will present a generalisation of the ACT for colourless protocols based on
  categorical and duality theoretic constructions. This is achieved by view
 ing an iterated protocol as an endofunctor on the category of simplicial c
 omplexes\, along with a natural transformation encoding the relation betwe
 en inputs and computational outputs. From this data we produce\, for each 
 possible set of inputs\, a limit object in the form of a spectral space wh
 ich encodes all possible computational outputs\, and characterises the tas
 k solvability of the protocol. Indeed\, a protocol can solve a task if\, a
 nd only if\, there exists a continuous map from the associated spectral sp
 ace to the space of outputs. This construction works for any iterated prot
 ocol\, but we additionally show that it is compatible with the original ap
 proach using subdivision protocols\, since in this case the geometric real
 isation\, the space used in the original ACT\, is a canonical subspace of 
 the associated spectral space.\n\nThis is a joint work with Emmanuel Godar
 d\, and a pre-print can be found on arXiv.
CATEGORIES:Séminaire,Logique et Interactions,LSC
LOCATION:Luminy - LIS\, salle 04.05\, Campus de Luminy\, Marseille\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Campus de Luminy\, Marseill
 e\, France;X-APPLE-RADIUS=100;X-TITLE=Luminy - LIS\, salle 04.05:geo:0,0
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DTSTART:20251026T020000
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