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This work revisits operator learning from a spectral perspective by introducing Polar Linear Algebra, a structured framework based on polar geometry that combines a linear radial component with a periodic angular component. Starting from…
The semiring of discrete dynamical systems is a simple algebraic model for modularity in deterministic systems. The objects of the semiring are finite transformations (viewed as directed graphs and regarded up to isomorphism), the sum of…
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…
Minimizing finite automata, proving trace equivalence of labelled transition systems or representing sofic subshifts involve very similar arguments, which suggests the possibility of a unified formalism. We propose finite states…
A fermionic operator circuit is a product of fermionic operators of usually different and partially overlapping support. Further elements of fermionic operator circuits (FOCs) are partial traces and partial projections. The presented…
The concurrent refinement algebra has been developed to support rely/guarantee reasoning about concurrent programs. The algebra supports atomic commands and defines parallel composition as a synchronous operation, as in Milner's SCCS. In…
GP (for Graph Programs) is a rule-based, nondeterministic programming language for solving graph problems at a high level of abstraction, freeing programmers from handling low-level data structures. The core of GP consists of four…
Categorical compositional distributional semantics is an approach to modelling language that combines the success of vector-based models of meaning with the compositional power of formal semantics. However, this approach was developed…
The operational semantics of a programming language is said to be small-step if each transition step is an atomic computation step in the language. A semantics with this property faithfully corresponds to the implementation of the language.…
We introduce a novel compositional description of Feynman diagrams, with well-defined categorical semantics as morphisms in a dagger-compact category. Our chosen setting is suitable for infinite-dimensional diagrammatic reasoning,…
Since the introduction of the CDC 6600 in 1965 and its `scoreboarding' technique processors have not (necessarily) executed instructions in program order. Programmers of high-level code may sequence independent instructions in arbitrary…
Bialgebrae provide an abstract framework encompassing the semantics of different kinds of computational models. In this paper we propose a bialgebraic approach to the semantics of logic programming. Our methodology is to study logic…
Tractable Boolean and arithmetic circuits have been studied extensively in AI for over two decades now. These circuits were initially proposed as "compiled objects," meant to facilitate logical and probabilistic reasoning, as they permit…
Temporal grounding is the task of locating a specific segment from an untrimmed video according to a query sentence. This task has achieved significant momentum in the computer vision community as it enables activity grounding beyond…
In programming models with a reversible semantics, computational steps can be undone. This paper addresses the integration of reversible semantics into process languages for communication-centric systems equipped with behavioral types. In…
Deductive verification techniques for C11 programs have advanced significantly in recent years with the development of operational semantics and associated logics for increasingly large fragments of C11. However, these semantics and logics…
When approaching the semantic segmentation of overhead imagery in the decimeter spatial resolution range, successful strategies usually combine powerful methods to learn the visual appearance of the semantic classes (e.g. convolutional…
Modelling musical structure is vital yet challenging for artificial intelligence systems that generate symbolic music compositions. This literature review dissects the evolution of techniques for incorporating coherent structure, from…
The causal structure of a unitary transformation is the set of relations of possible influence between any input subsystem and any output subsystem. We study whether such causal structure can be understood in terms of compositional…
Stepwise refinement of algebraic specifications is a well known formal methodology for program development. However, traditional notions of refinement based on signature morphisms are often too rigid to capture a number of relevant…