Related papers: A Compositional Account of Generalized Reversible …
Conventional coded computing frameworks are predominantly tailored for structured computations, such as matrix multiplication and polynomial evaluation. Such tasks allow the reuse of tools and techniques from algebraic coding theory to…
We generalise clones, which are sets of functions $f:A^n \rightarrow A$, to sets of mappings $f:A^n \rightarrow A^m$. We formalise this and develop language that we can use to speak about it. We then look at bijective mappings, which have…
We extend categorical semantics of monadic programming to reversible computing, by considering monoidal closed dagger categories: the dagger gives reversibility, whereas closure gives higher-order expressivity. We demonstrate that Frobenius…
Compositional data are commonly known as multivariate observations carrying relative information. Even though the case of vector or even two-factorial compositional data (compositional tables) is already well described in the literature,…
We give a general categorical construction that yields several monads of measures and distributions as special cases, alongside several monads of filters. The construction takes place within a categorical setting for generalized functional…
Reversible computing models settings in which all processes can be reversed. Applications include low-power computing, quantum computing, and robotics. It is unclear how to represent side-effects in this setting, because conventional…
This article is an attempt to generalize the classical theory of reversible computing, principally developed by Bennet [IBM J. Res. Develop., 17(1973)] and by Fredkin and Toffoli [Internat. J. Theoret. Phys., 21(1982)], to the quantum case.…
A physical neural network (PNN) has both the strong potential to solve machine learning tasks and intrinsic physical properties, such as high-speed computation and energy efficiency. Reservoir computing (RC) is an excellent framework for…
Recently there has been significant interest in using causal modelling techniques to understand the structure of physical theories. However, the notion of `causation' is limiting - insisting that a physical theory must involve causal…
Quantum computation can be formulated through various models, each highlighting distinct structural and resource-theoretic aspects of quantum computational power. This paper develops a unified categorical framework that encompasses these…
This paper uncovers the fundamental relationship between total and partial computation in the form of an equivalence of certain categories. This equivalence involves on the one hand effectuses, which are categories for total computation,…
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…
We study a composition operation on monads, equivalently presented as large equational theories. Specifically, we discuss the existence of tensors, which are combinations of theories that impose mutual commutation of the operations from the…
This paper presents an abstraction of Hoare logic to traced symmetric monoidal categories, a very general framework for the theory of systems. Our abstraction is based on a traced monoidal functor from an arbitrary traced monoidal category…
To enable the study of open sets in computational approaches to mathematics, lots of extra data and structure on these sets is assumed. For both foundational and mathematical reasons, it is then a natural question, and the subject of this…
In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored.…
Continuous-variable bosonic systems stand as prominent candidates for implementing quantum computational tasks. While various necessary criteria have been established to assess their resourcefulness, sufficient conditions have remained…
Computation, if treated as a set of physical processes that act on information represented by states of matter, encompasses biological systems, digital systems, and other constructs, and may be a fundamental measure of living systems. The…
Reversible algorithms play a crucial role both in classical and quantum computation. While for a classical bit the only nontrivial reversible operation is the bit-flip, nature is far more versatile in what it allows to do to a quantum bit.…
Residuation theory concerns the study of partially ordered algebraic structures, most often monoids, equipped with a weak inverse for the monoidal operator. One of its area of application has been constraint programming, whose key…