Papers by Pawel Sobocinski
The exactness properties of coproducts in extensive categories and pushouts along monos in adhesi... more The exactness properties of coproducts in extensive categories and pushouts along monos in adhesive categories have found various applications in theoretical computer science, e.g. in program semantics, data type theory and rewriting. We show that these properties can be understood as a single universal property in the associated bicategory of spans. To this end, we first provide a general notion of Van Kampen cocone that specialises to the above colimits. The main result states that Van Kampen cocones can be characterised as exactly those diagrams in ℂ that induce bicolimit diagrams in the bicategory of spans \(\mathcal{S}pan_{\mathbb{C}}\) , provided that ℂ has pullbacks and enough colimits.
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Rewriting systems over adhesive categories have been recently introduced as a general framework w... more Rewriting systems over adhesive categories have been recently introduced as a general framework which encompasses several rewriting-based computational formalisms, including various modelling frameworks for concurrent and distributed systems. Here we begin the development of a truly concurrent semantics for adhesive rewriting systems by defining the fundamental notion of process, well-known from Petri nets and graph grammars. The main result of the paper shows that processes capture the notion of true concurrency—there is a one-to-one correspondence between concurrent derivations, where the sequential order of independent steps is immaterial, and (isomorphism classes of) processes. We see this contribution as a step towards a general theory of true concurrency which specialises to the various concrete constructions found in the literature.
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Abstract. We generalize the unfolding semantics, previously developed for concrete formalisms suc... more Abstract. We generalize the unfolding semantics, previously developed for concrete formalisms such as Petri nets and graph grammars, to the abstract setting of (single pushout) rewriting over adhesive categories. The unfolding construction is characterized as a coreflection, ie the unfolding functor arises as the right adjoint to the embedding of the category of occurrence grammars into the category of grammars.
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… of Software Science and Computation Structures, Jan 1, 2004
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Logic in Computer Science, 2005. …, Jan 1, 2005
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Nordic Journal of Computing, Jan 1, 2003
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Foundations of Software Science …, Jan 1, 2007
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Electronic Notes in Theoretical Computer …, Jan 1, 2002
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Electronic Notes in Theoretical Computer …, Jan 1, 2005
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… of Software Science …, Jan 1, 2006
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CONCUR 2008-Concurrency Theory, Jan 1, 2008
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Theoretical Computer Science, Jan 1, 2005
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Algebra and Coalgebra in Computer …, Jan 1, 2005
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Fifth Ifip International Conference On Theoretical …, Jan 1, 2008
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Applied Categorical Structures, Jan 1, 2008
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CONCUR 2003-Concurrency Theory, Jan 1, 2003
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Papers by Pawel Sobocinski