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Convolution Products on Double Categories and Categorification of Rule Algebras
Motivated by compositional categorical rewriting theory, we introduce a convolution product over presheaves of double categories which …
Nicolas Behr, Paul-André Melliès, Noam Zeilberger
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Tracelet Hopf algebras and decomposition spaces
Tracelets are the intrinsic carriers of causal information in categorical rewriting systems. In this work, we assemble tracelets into a …
Nicolas Behr, Joachim Kock
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Concurrency Theorems for Non-linear Rewriting Theories
Sesqui-pushout (SqPO) rewriting along non-linear rules and for monic matches is well-known to permit the modeling of fusing and cloning …
Nicolas Behr, Russ Harmer, Jean Krivine
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On Stochastic Rewriting and Combinatorics via Rule-Algebraic Methods
Building upon the rule-algebraic stochastic mechanics framework, we present new results on the relationship of stochastic rewriting …
Nicolas Behr
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Stochastic Graph Transformation For Social Network Modeling
Adaptive networks model social, physical, technical, or biological systems as attributed graphs evolving at the level of both their …
Nicolas Behr, Bello Shehu Bello, Sebastian Ehmes, Reiko Heckel
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Efficient Computation of Graph Overlaps for Rule Composition: Theory and Z3 Prototyping
Graph transformation theory relies upon the composition of rules to express the effects of sequences of rules. In practice, graphs are …
Nicolas Behr, Maryam Ghaffari Saadat, Reiko Heckel
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Tracelets and Tracelet Analysis Of Compositional Rewriting Systems
Taking advantage of a recently discovered associativity property of rule compositions, we extend the classical concurrency theory for …
Nicolas Behr
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Rewriting Theory for the Life Sciences: A Unifying Theory of CTMC Semantics
The Kappa biochemistry and the MØD organo-chemistry frameworks are amongst the most intensely developed applications of rewriting …
Nicolas Behr, Jean Krivine
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Sesqui-Pushout Rewriting: Concurrency, Associativity and Rule Algebra Framework
Sesqui-pushout (SqPO) rewriting provides a variant of transformations of graph-like and other types of structures that fit into the …
Nicolas Behr
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Rule Algebras for Adhesive Categories
We show that every adhesive category gives rise to an associative algebra of rewriting rules induced by the notion of double-pushout …
Nicolas Behr, Pawel Sobocinski
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