Related papers: Dynamics and Coherence for the Free Cornering with…
The formalism of anchor words has enabled the development of fast topic modeling algorithms with provable guarantees. In this paper, we introduce a protocol that allows users to interact with anchor words to build customized and…
Dynamic topic modeling is widely used to analyze evolving trends in scientific literature, medical records, and social media. Traditional topic models represent each topic through a single probability vector on the multinomial simplex and…
We present categories of open dynamical systems with general time evolution as categories of coalgebras opindexed by polynomial interfaces, and show how this extends the coalgebraic framework to capture common scientific applications such…
We universally characterize the produoidal category of monoidal lenses over a monoidal category. In the same way that each category induces a cofree promonoidal category of spliced arrows, each monoidal category induces a cofree produoidal…
This paper gives a simple presentation of the free star-autonomous category over a category, based on Eilenberg-Kelly-MacLane graphs and Trimble rewiring, yielding a full coherence theorem: the commutativity of diagrams of canonical maps is…
Rewriting is a formalism widely used in computer science and mathematical logic. The classical formalism has been extended, in the context of functional languages, with an order over the rules and, in the context of rewrite based languages,…
In this note we give a simple unifying proof of the undecidability of several diagrammatic properties of term rewriting systems that include: local confluence, strong confluence, diamond property, subcommutative property, and the existence…
The aim of the paper is to provide solid foundations for a programming paradigm natively supporting the creation and manipulation of cyclic data structures. To this end, we describe coFJ, a Java-like calculus where objects can be infinite…
The deformation cohomology of a tensor category controls deformations of its monoidal structure. Here we describe the deformation cohomology of tensor categories generated by one object (the so-called Schur-Weyl categories). Using this…
The concept of_refinement_ in type theory is a way of reconciling the "intrinsic" and the "extrinsic" meanings of types. We begin with a rigorous analysis of this concept, settling on the simple conclusion that the type-theoretic notion of…
Critical pair analysis provides a convenient and computable criterion of confluence, which is a fundamental property in rewriting theory, for a wide variety of rewriting systems. Bonchi et al. showed validity of critical pair analysis for…
Term rewriting has a significant presence in various areas, not least in automated theorem proving where it is used as a proof technique. Many theorem provers employ specialised proof tactics for rewriting. This results in an interleaving…
Adding rewriting to a proof assistant based on the Curry-Howard isomorphism, such as Coq, may greatly improve usability of the tool. Unfortunately adding an arbitrary set of rewrite rules may render the underlying formal system undecidable…
In this paper, we prove that (first-order) cons-free term rewriting with a call-by-value reduction strategy exactly characterises the class of PTIME-computable functions. We use this to give an alternative proof of the result by Carvalho…
Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical…
We model collapsible and ordered pushdown systems with term rewriting, by encoding higher-order stacks and multiple stacks into trees. We show a uniform inverse preservation of recognizability result for the resulting class of term…
Consider the problem of interference mitigation in the identification of the dynamics of multidimensional control systems in the class of linear stationary models for single realizations of the observed signals. A concepts uncorrelated…
We prove a coherence theorem for actions of groups on monoidal categories. As an application we prove coherence for arbitrary braided $G$-crossed categories.
In this work, we present the integrated structure-control design of a 2-DOF underactuated mechanical system, aiming to achieve a periodic motion of the end-effector. The desired behavior is generated via input-output linearization, followed…
Natural organized systems adapt to internal and external pressures and this happens at all levels of the abstraction hierarchy. Wanting to think clearly about this idea motivates our paper, and so the idea is elaborated extensively in the…