A Localic Approach to Dependency, Conflict, and Concurrency
Azimuth 2020-04-27
In the fifth talk of the ACT@UCR seminar, Gershom Bazerman will tell us about a localic approach to the semantics of dependency, conflict, and concurrency.
He’ll give his talk on Wednesday April 29th at 5 pm UTC, which is 10 am in California, or 1 pm on the east coast of the United States, or 6 pm in England. It will be held online via Zoom, here:
https://ucr.zoom.us/j/607160601
Afterwards we’ll discuss his talk at the Category Theory Community Server. You can see those discussions here if you become a member:
You can see his talk slides here.
• Gershom Bazerman, A localic approach to the semantics of dependency, conflict, and concurrency.
Abstract. Petri nets have been of interest to applied category theory for some time. Back in the 1980s, one approach to their semantics was given by algebraic gadgets called “event structures.” We use classical techniques from order theory to study event structures without conflict restrictions (which we term “dependency structures with choice”) by their associated “traces”, which let us establish a one-to-one correspondence between DSCs and a certain class of locales. These locales have an internal logic of reachability, which can be equipped with “versioning” modalities that let us abstract away certain unnecessary detail from an underlying DSC. With this in hand we can give a general notion of what it means to “solve a dependency problem” and combinatorial results bounding the complexity of this. Time permitting, I will sketch work-in-progress which hopes to equip these locales with a notion of conflict, letting us capture the full semantics of general event structures in the form of homological data, thus providing one avenue to the topological semantics of concurrent systems. This is joint work with Raymond Puzio.
