3 Search Results for "Hayman, Jonathan"


Document
Causal Unfoldings

Authors: Marc de Visme and Glynn Winskel

Published in: LIPIcs, Volume 139, 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)


Abstract
In the simplest form of event structure, a prime event structure, an event is associated with a unique causal history, its prime cause. However, it is quite common for an event to have disjunctive causes in that it can be enabled by any one of multiple sets of causes. Sometimes the sets of causes may be mutually exclusive, inconsistent one with another, and sometimes not, in which case they coexist consistently and constitute parallel causes of the event. The established model of general event structures can model parallel causes. On occasion however such a model abstracts too far away from the precise causal histories of events to be directly useful. For example, sometimes one needs to associate probabilities with different, possibly coexisting, causal histories of a common event. Ideally, the causal histories of a general event structure would correspond to the configurations of its causal unfolding to a prime event structure; and the causal unfolding would arise as a right adjoint to the embedding of prime in general event structures. But there is no such adjunction. However, a slight extension of prime event structures remedies this defect and provides a causal unfolding as a universal construction. Prime event structures are extended with an equivalence relation in order to dissociate the two roles, that of an event and its enabling; in effect, prime causes are labelled by a disjunctive event, an equivalence class of its prime causes. With this enrichment a suitable causal unfolding appears as a pseudo right adjoint. The adjunction relies critically on the central and subtle notion of extremal causal realisation as an embodiment of causal history.

Cite as

Marc de Visme and Glynn Winskel. Causal Unfoldings. In 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 139, pp. 9:1-9:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{devisme_et_al:LIPIcs.CALCO.2019.9,
  author =	{de Visme, Marc and Winskel, Glynn},
  title =	{{Causal Unfoldings}},
  booktitle =	{8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)},
  pages =	{9:1--9:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-120-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{139},
  editor =	{Roggenbach, Markus and Sokolova, Ana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2019.9},
  URN =		{urn:nbn:de:0030-drops-114376},
  doi =		{10.4230/LIPIcs.CALCO.2019.9},
  annote =	{Keywords: Event Structures, Parallel Causes, Causal Unfolding, Probability}
}
Document
Graphs, Rewriting and Pathway Reconstruction for Rule-Based Models

Authors: Vincent Danos, Jerome Feret, Walter Fontana, Russell Harmer, Jonathan Hayman, Jean Krivine, Chris Thompson-Walsh, and Glynn Winskel

Published in: LIPIcs, Volume 18, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)


Abstract
In this paper, we introduce a novel way of constructing concise causal histories (pathways) to represent how specified structures are formed during simulation of systems represented by rule-based models. This is founded on a new, clean, graph-based semantics introduced in the first part of this paper for Kappa, a rule-based modelling language that has emerged as a natural description of protein-protein interactions in molecular biology [Bachman 2011]. The semantics is capable of capturing the whole of Kappa, including subtle side-effects on deletion of structure, and its structured presentation provides the basis for the translation of techniques to other models. In particular, we give a notion of trajectory compression, which restricts a trace culminating in the production of a given structure to the actions necessary for the structure to occur. This is central to the reconstruction of biochemical pathways due to the failure of traditional techniques to provide adequately concise causal histories, and we expect it to be applicable in a range of other modelling situations.

Cite as

Vincent Danos, Jerome Feret, Walter Fontana, Russell Harmer, Jonathan Hayman, Jean Krivine, Chris Thompson-Walsh, and Glynn Winskel. Graphs, Rewriting and Pathway Reconstruction for Rule-Based Models. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 276-288, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)


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@InProceedings{danos_et_al:LIPIcs.FSTTCS.2012.276,
  author =	{Danos, Vincent and Feret, Jerome and Fontana, Walter and Harmer, Russell and Hayman, Jonathan and Krivine, Jean and Thompson-Walsh, Chris and Winskel, Glynn},
  title =	{{Graphs, Rewriting and Pathway Reconstruction for Rule-Based Models}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)},
  pages =	{276--288},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-47-7},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{18},
  editor =	{D'Souza, Deepak and Radhakrishnan, Jaikumar and Telikepalli, Kavitha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2012.276},
  URN =		{urn:nbn:de:0030-drops-38669},
  doi =		{10.4230/LIPIcs.FSTTCS.2012.276},
  annote =	{Keywords: concurrency, rule-based models, graph rewriting, pathways, causality}
}
Document
The unfolding of general Petri nets

Authors: Jonathan Hayman and Glynn Winskel

Published in: LIPIcs, Volume 2, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2008)


Abstract
The unfolding of (1-)safe Petri nets to occurrence nets is well understood. There is a universal characterization of the unfolding of a safe net which is part and parcel of a coreflection from the category of occurrence nets to the category of safe nets. The unfolding of general Petri nets, nets with multiplicities on arcs whose markings are multisets of places, does not possess a directly analogous universal characterization, essentially because there is an implicit symmetry in the multiplicities of general nets, and that symmetry is not expressed in their traditional occurrence net unfoldings. In the present paper, we show how to recover a universal characterization by representing the symmetry in the behaviour of the occurrence net unfoldings of general Petri nets. We show that this is part of a coreflection between enriched categories of general Petri nets with symmetry and occurrence nets with symmetry.

Cite as

Jonathan Hayman and Glynn Winskel. The unfolding of general Petri nets. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, pp. 223-234, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)


Copy BibTex To Clipboard

@InProceedings{hayman_et_al:LIPIcs.FSTTCS.2008.1755,
  author =	{Hayman, Jonathan and Winskel, Glynn},
  title =	{{The unfolding of general Petri nets}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{223--234},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-08-8},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{2},
  editor =	{Hariharan, Ramesh and Mukund, Madhavan and Vinay, V},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2008.1755},
  URN =		{urn:nbn:de:0030-drops-17552},
  doi =		{10.4230/LIPIcs.FSTTCS.2008.1755},
  annote =	{Keywords: Petri nets, symmetry, unfolding}
}
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