Related papers: Concurrent Kleene Algebra: Free Model and Complete…
We try to clarify the relationship between interleaving concurrency and true concurrency, based on the very recent work on truly concurrent process algebra, especially, giving models of true concurrency, such as event structure, Petri net…
Canonical Correlation Analysis (CCA) is a statistical technique used to extract common information from multiple data sources or views. It has been used in various representation learning problems, such as dimensionality reduction, word…
We generalise the notion of coherent states to arbitrary Lie algebras by making an analogy with the GNS construction in $C^*$-algebras. The method is illustrated with examples of semisimple and non-semisimple finite dimensional Lie algebras…
The Automated Model Evaluation (AutoEval) framework entertains the possibility of evaluating a trained machine learning model without resorting to a labeled testing set. Despite the promise and some decent results, the existing AutoEval…
In this paper, we present a systematic way of deriving (1) languages of (generalised) regular expressions, and (2) sound and complete axiomatizations thereof, for a wide variety of systems. This generalizes both the results of Kleene (on…
This paper is addressed to logicians not familiar with category theory. It gives a new proof of coherence for symmetric monoidal closed categories, proven by Kelly and Mac Lane in early 1970s. We find this result of great importance for…
A model companion is shown to exist for the theory of partial differential fields of characteristic zero equipped with free operators that commute with the derivations. The free operators here are those introduced in [R. Moosa and T.…
We reconstruct Peleg's concurrent dynamic logic in the context of modal Kleene algebras. We explore the algebraic structure of its multirelational semantics and develop an abstract axiomatisation of concurrent dynamic algebras from that…
Many areas of machine learning and science involve large linear algebra problems, such as eigendecompositions, solving linear systems, computing matrix exponentials, and trace estimation. The matrices involved often have Kronecker,…
Turing's famous `machine' model constitutes the first intuitively convincing framework for computing with real numbers. Kleene's computation schemes S1-S9 extend Turing's approach to computing with objects of any finite type. Both…
We present simple new Hoare logics and refinement calculi for hybrid systems in the style of differential dynamic logic. (Refinement) Kleene algebra with tests is used for reasoning about the program structure and generating verification…
We propose Weighted Guarded Kleene Algebra with Tests (wGKAT), an uninterpreted weighted programming language equipped with branching, conditionals, and loops. We provide an operational semantics for wGKAT using a variant of weighted…
A partial combinatory algebra (PCA) is a set equipped with a partial binary operation that models a notion of computability. This paper studies a generalization of PCAs, introduced by W. Stekelenburg, where a PCA is not a set but an object…
We prove that any reduced amalgamated free product C*-algebra is KK-equivalent to the corresponding full amalgamated free product C*-algebra. The main ingredient of its proof is Julg--Valette's geometric construction of Fredholm modules…
First we identify the free algebras of the class of algebras of binary relations equipped with the composition and domain operations. Elements of the free algebras are pointed labelled finite rooted trees. Then we extend to the analogous…
Augmenting algorithms with learned predictions is a promising approach for going beyond worst-case bounds. Dinitz, Im, Lavastida, Moseley, and Vassilvitskii~(2021) have demonstrated that a warm start with learned dual solutions can improve…
A framework named Copula Component Analysis (CCA) for blind source separation is proposed as a generalization of Independent Component Analysis (ICA). It differs from ICA which assumes independence of sources that the underlying components…
The present paper constructs three new systems of clarithmetic (arithmetic based on computability logic --- see http://www.cis.upenn.edu/~giorgi/cl.html): CLA8, CLA9 and CLA10. System CLA8 is shown to be sound and extensionally complete…
We introduce a version of probabilistic Kleene algebra with angelic nondeterminism and a corresponding class of automata. Our approach implements semantics via distributions over multisets in order to overcome theoretical barriers arising…
Higher-dimensional automata (HDA) are a model of concurrency that models simultaneous execution of events using higher dimensional cells. HDA recognize languages of pomsets, a generalization of finite words whose letters are partially…