6 citations · 14 across the 9 of their papers we have counts for
12 papers
Boolean TQFTs with accumulating defects, sofic systems, and automata for infinite words
Paul Gustafson, Mee Seong Im, Mikhail Khovanov
Any finite state automaton gives rise to a Boolean one-dimensional TQFT with defects and inner endpoints of cobordisms. This paper extends the correspondence to Boolean TQFTs where…
Automata and one-dimensional TQFTs with defects
Paul Gustafson, Mee Seong Im, Remy Kaldawy +2
This paper explains how any nondeterministic automaton for a regular language gives rise to a one-dimensional oriented Topological Quantum Field Theory (TQFT) with inner endpoi…
A pasting lemma for Lipschitz functions
Matthew D. Kvalheim, Paul Gustafson, Samuel A. Burden
We give a necessary and sufficient condition ensuring that any function which is separately Lipschitz on two fixed compact sets is Lipschitz on their union.
Hybrid dynamical type theories for navigation
Paul Gustafson, Jared Culbertson, Daniel E. Koditschek
We present a hybrid dynamical type theory equipped with useful primitives for organizing and proving safety of navigational control algorithms. This type theory combines the framew…
From Torus Bundles to Particle-Hole Equivariantization
Shawn X. Cui, Paul Gustafson, Yang Qiu +1
We continue the program of constructing (pre)modular tensor categories from 3-manifolds first initiated by Cho-Gang-Kim using theory in physics and then mathematically studied…
Conley's fundamental theorem for a class of hybrid systems
Matthew D. Kvalheim, Paul Gustafson, Daniel E. Koditschek
We establish versions of Conley's (i) fundamental theorem and (ii) decomposition theorem for a broad class of hybrid dynamical systems. The hybrid version of (i) asserts that a glo…