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Net refinement by pullback rewriting [chapter]

Renate Klempien-Hinrichs
1998 Lecture Notes in Computer Science  
This paper aims at applying a recently developed technique for graph rewriting, the so-called pullback approach, to describe net refinement.  ...  The translation of this technique, which is based on (hyper)graph morphisms, into terms of net morphisms yields a well-defined mechanism closely related to pullback rewriting in hypergraphs.  ...  by pullbacks In this section, pullback rewriting is defined directly in the category Af of net structures.  ... 
doi:10.1007/bfb0053550 fatcat:pmw2zjgiafa25hqm3u6jsuxlha

Unfolding Grammars in Adhesive Categories [chapter]

Paolo Baldan, Andrea Corradini, Tobias Heindel, Barbara König, Paweł Sobociński
2009 Lecture Notes in Computer Science  
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  ...  Compared to previous work on the unfolding of Petri nets and graph grammars, our results apply to a wider class of systems, which is due to the use of a refined notion of grammar morphism.  ...  More precisely, as described in detail in [4] , the token game of a Petri net with place set P can be modelled by spo rewriting in the slice category S↓ P , where S is the category of (finite) sets and  ... 
doi:10.1007/978-3-642-03741-2_24 fatcat:ly7g2r4jrncdddmmbq2owwqgsm

Processes and unfoldings: concurrent computations in adhesive categories

PAOLO BALDAN, ANDREA CORRADINI, TOBIAS HEINDEL, BARBARA KÖNIG, PAWEŁ SOBOCIŃSKI
2014 Mathematical Structures in Computer Science  
Compared to previous work on the unfolding of Petri nets and graph grammars, our results apply to a wider class of systems, which is due to the use of a refined notion of grammar morphism. 2 concurrent  ...  pushout) rewriting of objects in adhesive categories.  ...  Pullback stability of rpcs will play a crucial role in the proof that that spo rewriting is preserved by grammar morphisms (Lemma 4.6).  ... 
doi:10.1017/s096012951200031x fatcat:umx7pscecfep7aozlehi72dsny

Contents and abstracts of the electronic notes in Theoretical Computer Science vol. 2

Andrea Corradini, Ugo Montanari
1998 Theoretical Computer Science  
Michel Bauderon Parallel rewriting of graphs through the pullback approach http://www.elaevier.nl/locate/entes/volume2.html In this paper, we continue the development of our description of the pullback  ...  Eike Best and Maciej Koutny Using net refinement to compute the frrpoint of a recursive expression http://www.elsevier.nl/locate/entos/volume2.html The talk illustrates the general Petri net semantics  ... 
doi:10.1016/s0304-3975(97)83719-x fatcat:r47zmpkxhfehtaenl2crpu6sk4

Compositionality of Rewriting Rules with Conditions [article]

Nicolas Behr, Jean Krivine
2019 arXiv   pre-print
We extend the notion of compositional associative rewriting as recently studied in the rule algebra framework literature to the setting of rewriting rules with conditions.  ...  category-theoretical in nature, where the definition of rule composition operations is encoding the non-deterministic sequential concurrent application of rules in Double-Pushout (DPO) and Sesqui-Pushout (SqPO) rewriting  ...  The work of NB was supported by a Marie Skłodowska-Curie Individual fellowship (Grant Agreement No. 753750 -RaSiR). We would like to thank P.A.M. Melliès, P. Sobocinski and N.  ... 
arXiv:1904.09322v1 fatcat:4wlnfl2qtvc2jksffiuqsoznqq

Towards a Notion of Transaction in Graph Rewriting

P. Baldan, A. Corradini, F.L. Dotti, L. Foss, F. Gadducci, L. Ribeiro
2008 Electronical Notes in Theoretical Computer Science  
Generalising the work on zero-safe nets, the new graphical formalism is based on a typing discipline which induces a distinction between stable and unstable items.  ...  Inspired by the approach for Petri nets proposed in [3] and extended to nets with read arcs in [4] , we introduce stable steps, stable transactions and abstract stable transactions.  ...  Formally, S(G) can be defined as the graph typed over T s obtained by considering the pullback |S(G)| ι / / |G| T s / / T Without loss of generality, we will assume a concrete choice for S(G), by imposing  ... 
doi:10.1016/j.entcs.2008.04.028 fatcat:uvap737wa5fczeurw676klcy3m

Integrated Structure and Semantics for Reo Connectors and Petri Nets

Christian Krause
2009 Electronic Proceedings in Theoretical Computer Science  
Specifically, we formalize structural gluings of connectors as pushouts, and joins of port automata as pullbacks.  ...  In this paper, we present an integrated structural and behavioral model of Reo connectors and Petri nets, allowing a direct comparison of the two concurrency models.  ...  Modeling Reconfigurations Graph rewriting techniques, such as the double pushout (DPO) approach [8] , are a powerful tool for modeling rule-based reconfigurations.  ... 
doi:10.4204/eptcs.12.4 fatcat:apnqxovsirgyxmgaztianytk2u

Compositional Exploration of Combinatorial Scientific Models [article]

Kristopher Brown, Tyler Hanks, James Fairbanks
2022 arXiv   pre-print
We demonstrate our framework by generating a tool which fits experimental data, searching an epidemiology-relevant subspace of mass-action kinetic models.  ...  We implement a novel representation of model search spaces as diagrams over a category of models, where we have restricted attention to a broad class of models whose structure is presented by \C-sets.  ...  Funding The authors were supported by DARPA Award W911NF2110323.  ... 
arXiv:2206.08755v1 fatcat:h4xypm6fxnfpdcoakljekqh2la

Graph Transactions as Processes [chapter]

Paolo Baldan, Andrea Corradini, Luciana Foss, Fabio Gadducci
2006 Lecture Notes in Computer Science  
Inspired by the approach for Petri nets proposed in [4] , and extended to nets with read arcs in [5] , we introduce stable steps, transactions and abstract transactions.  ...  In data-centered formalisms, like rewriting formalisms and (possibly High-Level) Petri nets, where the control structures are typically poor and the emphasis is on the structure of the state that evolves  ... 
doi:10.1007/11841883_15 fatcat:odlty7obvvbhffkokjm6rj7mlm

Modular System Development with Pullbacks [chapter]

Marek A. Bednarczyk, Luca Bernardinello, Benoît Caillaud, Wiesław Pawłowski, Lucia Pomello
2003 Lecture Notes in Computer Science  
A novel approach is presented in which they turn out to be merely special instances of pullback, a general categorical limit construction.  ...  The net in the middle can be seen as a product of the two state machines. The product is computed by putting the nets side by side, separately, and then identifying events with identical names.  ...  Yet, only in the area of action refinement one can track these ideas. The lukewarm support can be attributed to conceptual problems that come along.  ... 
doi:10.1007/3-540-44919-1_12 fatcat:bny6n67uz5flpnk5727wtewbry

Page 3339 of Mathematical Reviews Vol. , Issue 2001E [page]

2001 Mathematical Reviews  
Winter, UML packages for PROgrammed Graph REwriting Systems (396-409); Julia Padberg, Maike Gajewsky and Kathrin Hoffmann, Incremental development of safety prop- erties in Petri net transformations (410  ...  and Anca Muscholl, The power of local computations in graphs with initial knowledge (71-84); Hartmut Ehrig, Reiko Heckel, Mercé Llabrés, Fernando Orejas, Julia Padberg and Grzegorz Rozenberg, Double-pullback  ... 

Rule Algebras for Adhesive Categories

Nicolas Behr, Pawel Sobocinski
2019 Logical Methods in Computer Science  
This observation complements the classical Concurrency Theorem of DPO rewriting.  ...  We demonstrate that the most well-known approach to rewriting graphical structures, the Double-Pushout (DPO) approach, possesses a notion of sequential compositions of rules along an overlap that is associative  ...  By pullback-pullback decomposition, the square (M 21 , O 1 , N 21 , I 2 ) is a pullback.  ... 
doi:10.23638/lmcs-16(3:2)2020 fatcat:26vl6ijso5hmlpm5al2xqwng6u

Rule Algebras for Adhesive Categories [article]

Nicolas Behr, Pawel Sobocinski
2020 arXiv   pre-print
This observation complements the classical Concurrency Theorem of DPO rewriting.  ...  We demonstrate that the most well-known approach to rewriting graphical structures, the Double-Pushout (DPO) approach, possesses a notion of sequential compositions of rules along an overlap that is associative  ...  By pullback-pullback decomposition, the square (M 21 , O 1 , N 21 , I 2 ) is a pullback.  ... 
arXiv:1807.00785v4 fatcat:snozvgzcx5gwbj6g3kblxqwfxa

Open-graphs and monoidal theories

LUCAS DIXON, ALEKS KISSINGER
2013 Mathematical Structures in Computer Science  
We can do this without introducing explicitly named variables by introducing a "copy" operation. ∧ ∧ ¬  ...  A salient feature of our theory is that it ensures rewrite systems are "type-safe" in the sense that rewriting respects the inputs and outputs.  ...  This research was funded by EPSRC grant EPE/005713/1 and by a Clarendon Studentship. We would also like to thank Ross Duncan for his invaluable input to the various stages of this work.  ... 
doi:10.1017/s0960129512000138 fatcat:zy6tai2a4vctncug4gx6uvfika

Page 2039 of Mathematical Reviews Vol. , Issue 99c [page]

1991 Mathematical Reviews  
refine- ment by pullback rewriting (189-202); Oliver Matz, On piecewise testable, starfree, and recognizable picture languages (203-210); E.  ...  Gadducci, Rational term rewriting (156-171); Reinhold Heckmann, The appearance of big integers in exact real arithmetic based on linear fractional transformations (172-188); Renate Klempien-Hinrichs, Net  ... 
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