Related papers: Situated Transition Systems
Open dynamical systems are mathematical models of machines that take input, change their internal state, and produce output. For example, one may model anything from neurons to robots in this way. Several open dynamical systems can be…
A (closed) dynamical system is a notion of how things can be, together with a notion of how they may change given how they are. The idea and mathematics of closed dynamical systems has proven incredibly useful in those sciences that can…
A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This…
For a fixed object X in a monoidal category, an X-commutation structure on an object A is just a map from XA to AX. We study aspects of such structure in case A has a dual.
We present a unified framework for categorical systems theory which packages a collection of open systems, their interactions, and their maps into a symmetric monoidal loose right module of systems over a symmetric monoidal double category…
We propose a formal model of concurrent systems in which the history of a computation is explicitly represented as a collection of events that provide a view of a sequence of configurations. In our model events generated by transitions…
Fong developed `decorated cospans' to model various kinds of open systems: that is, systems with inputs and outputs. In this framework, open systems are seen as the morphisms of a category and can be composed as such, allowing larger open…
In this paper, we introduce the notions of stable future, past and total component systems on a directed space with no loops. Then, we associate the stable component category to a stable (future, past or total) component system. Stable…
We build a model structure from the simple point of departure of a structured interval in a monoidal category - more generally, a structured cylinder and a structured co-cylinder in a category.
We consider the computational power of silent transitions in one-way automata with storage. Specifically, we ask which storage mechanisms admit a transformation of a given automaton into one that accepts the same language and reads at least…
Reversible computing is a new paradigm that has emerged recently and extends the traditional forwards-only computing mode with the ability to execute in backwards, so that computation can run in reverse as easily as in forward. Two…
We study combinatorial structures arising from finite-time transition probabilities of the Totally Asymmetric Simple Exclusion Process with open boundary conditions. While much of the existing combinatorial theory regarding the TASEP…
Containers represent a wide class of type constructions relevant for functional programming and (co)inductive reasoning. Indexed containers generalize this notion to better fit the scope of dependently typed programming. When interpreting…
We construct a compact closed category out of any symmetric monoidal category by freely adding adjoints to its objects. The morphisms of the completion are defined as string diagrams annotated by objects and morphisms from the original…
We identify the algebraic structure of the material histories generated by concurrent processes. Specifically, we extend existing categorical theories of resource convertibility to capture concurrent interaction. Our formalism admits an…
Changing time of simple continuous-time Markov counting processes by independent unit-rate Poisson processes results in Markov counting processes for which we provide closed-form transition rates via composition of trajectories and with…
The concept of process is ubiquitous in science, engineering and everyday life. Category theory, and monoidal categories in particular, provide an abstract framework for modelling processes of many kinds. In this paper, we concentrate on…
The concept of typed topological space is introduced, for which open sets in a topology on a finite set will be assigned types (from lattice). The neighborhood system of a point, the closure and the connectedness can be defined according to…
Applied category theory often studies symmetric monoidal categories (SMCs) whose morphisms represent open systems. These structures naturally accommodate complex wiring patterns, leveraging (co)monoidal structures for splitting and merging…
We introduce a variant of transition systems, where activation of transitions depends on conditions of the environment and upgrades during runtime potentially create additional transitions. Using a cornerstone result in lattice theory, we…