Zobrazeno 1 - 10
of 944
pro vyhledávání: '"Sobocinski, P"'
Autor:
Earnshaw, Matthew, Sobociński, Paweł
We extend the theory of formal languages in monoidal categories to the multi-sorted, symmetric case, and show how this theory permits a graphical treatment of topics in concurrency. In particular, we show that Mazurkiewicz trace languages are precise
Externí odkaz:
http://arxiv.org/abs/2306.16341
Autor:
Román, Mario, Sobociński, Paweł
Premonoidal categories are monoidal categories without the interchange law; effectful categories are premonoidal categories with a chosen monoidal subcategory of interchanging morphisms. In the same sense that string diagrams, pioneered by Joyal and
Externí odkaz:
http://arxiv.org/abs/2305.06075
Autor:
Di Lavore, Elena, Sobociński, Paweł
Publikováno v:
Logical Methods in Computer Science, Volume 19, Issue 3 (September 4, 2023) lmcs:10552
We introduce monoidal width as a measure of complexity for morphisms in monoidal categories. Inspired by well-known structural width measures for graphs, like tree width and rank width, monoidal width is based on a notion of syntactic decomposition:
Externí odkaz:
http://arxiv.org/abs/2212.13229
Autor:
Earnshaw, Matthew, Sobociński, Paweł
We introduce regular languages of morphisms in free monoidal categories, with their associated grammars and automata. These subsume the classical theory of regular languages of words and trees, but also open up a much wider class of languages over st
Externí odkaz:
http://arxiv.org/abs/2207.00526
Autor:
Di Lavore, Elena, Sobociński, Paweł
Publikováno v:
EPTCS 380, 2023, pp. 268-283
Monoidal width was recently introduced by the authors as a measure of the complexity of decomposing morphisms in monoidal categories. We have shown that in a monoidal category of cospans of graphs, monoidal width and its variants can be used to captu
Externí odkaz:
http://arxiv.org/abs/2205.08916
Autor:
Di Lavore, Elena, Sobociński, Paweł
We introduce monoidal width as a measure of the difficulty of decomposing morphisms in monoidal categories. For graphs, we show that monoidal width and two variations capture existing notions, namely branch width, tree width and path width. We propos
Externí odkaz:
http://arxiv.org/abs/2202.07582
In this paper we address the problem of proving confluence for string diagram rewriting, which was previously shown to be characterised combinatorically as double-pushout rewriting with interfaces (DPOI) on (labelled) hypergraphs. For standard DPO re
Externí odkaz:
http://arxiv.org/abs/2109.06049
Publikováno v:
9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)
We study the relationship between cartesian bicategories and a specialisation of Lawvere's hyperdoctrines, namely elementary existential doctrines. Both provide different ways of abstracting the structural properties of logical systems: the former in
Externí odkaz:
http://arxiv.org/abs/2106.08142
Autor:
Boisseau, Guillaume, Sobociński, Paweł
Publikováno v:
EPTCS 372, 2022, pp. 178-191
We develop a comprehensive string diagrammatic treatment of electrical circuits. Building on previous, limited case studies, we introduce controlled sources and meters as elements, and the impedance calculus, a powerful toolbox for diagrammatic reaso
Externí odkaz:
http://arxiv.org/abs/2106.07763
We extend the theory of Interacting Hopf algebras with an order primitive, and give a sound and complete axiomatisation of the prop of polyhedral cones. Next, we axiomatise an affine extension and prove soundness and completeness for the prop of poly
Externí odkaz:
http://arxiv.org/abs/2105.10946