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Applications of Algebra and Coalgebra in Scientific Modelling

Michael Hauhs, Baltasar Trancón y Widemann
2010 Electronical Notes in Theoretical Computer Science  
Only one of these has traditionally been used in ecology. The second one, which is based on a coalgebraic dualisation, offers new modelling perspectives in ecology and environmental science.  ...  In computer science, the algebra-coalgebra duality serves as a formal framework for connecting the perspectives of state-based and behavior-based models.  ...  From Interactive Modelling to Coalgebra Changing the perspective from state to behavior affects all parts of the modelling situation.  ... 
doi:10.1016/j.entcs.2010.07.016 fatcat:vaxlidqu5rhd3fwh4i2ym3uxle

Combining probabilistic and non-deterministic choice via weak distributive laws

Alexandre Goy, Daniela Petrişan
2020 Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science  
From a category theory perspective, the problem stems from the absence of a distributive law of the powerset monad over the distribution monad.  ...  As a consequence, we retrieve the well-known convex powerset monad as a weak lifting of the powerset monad to the category of convex algebras.  ...  Consider a coalgebra : → in CoAlg( ). Upon writing = T T and composing with , we obtain the composite mapping a coalgebra for the functor with carrier the free T-algebra on .  ... 
doi:10.1145/3373718.3394795 dblp:conf/lics/0003P20 fatcat:3mplbmedafg6lerggk4kssetku

Testing Semantics: Connecting Processes and Process Logics [chapter]

Dusko Pavlovic, Michael Mislove, James B. Worrell
2006 Lecture Notes in Computer Science  
Using a connection that models machines on the one hand, and the data they manipulate on the other, testing is used to capture the interactions of each with the objects on the other side: just as the data  ...  Our basic philosophy is that tests can be used as a basis for modeling interactions, as well as processes and the data on which they operate.  ...  Relating a M F P -coalgebra and a M -image of a F -algebra requires a homomorphism which is consistent with the algebra and coalgebra structures both on the covariant and on the contravariant side of the  ... 
doi:10.1007/11784180_24 fatcat:ba75kgvhsncpvdp6bcu7zijp74

Interaction and observation, categorically

Vincenzo Ciancia
2011 Electronic Proceedings in Theoretical Computer Science  
In this categorical model, from the point of view that we provide, the notions of observation and interaction are separate features.  ...  This paper proposes to use dialgebras to specify the semantics of interactive systems in a natural way. Dialgebras are a conservative extension of coalgebras.  ...  algebraically and coalgebraically at the same time.  ... 
doi:10.4204/eptcs.59.3 fatcat:zwqn23tttfa47ic2ccdlo4bzee

A Diagrammatic Approach to Quantum Dynamics

Stefano Gogioso, Michael Wagner
2019 Conference on Algebra and Coalgebra in Computer Science  
We show that the Weyl Canonical Commutation Relations between time and energy are an incarnation of the bialgebra law and we derive Schrödinger's equation from a process-theoretic perspective.  ...  We present a diagrammatic approach to quantum dynamics based on the categorical algebraic structure of strongly complementary observables.  ...  Unlike classical clocks -where a single algebraic object was needed -quantum clocks need an interacting pair of algebraic structures: one to pin down the time states (the observable ) and another one to  ... 
doi:10.4230/lipics.calco.2019.19 dblp:conf/calco/Gogioso19 fatcat:gxj7wltvsnbzngprqdyndw5uw4

Generalized Coiteration Schemata1 1Research supported by the MIUR Project COFIN 2001013518 Cometa

Daniela Cancila, Furio Honsell, Marina Lenisa
2003 Electronical Notes in Theoretical Computer Science  
In this paper, building on the notion of T -coiteration introduced by the third author and capitalizing on recent work on bialgebras by Turi-Plotkin and Bartels, we introduce and illustrate various generalized  ...  Coiterative functions can be explained categorically as final coalgebraic morphisms, once coinductive types are viewed as final coalgebras.  ...  We feel that our approach suggests a new perspective on the use of bialgebras in the context of generalized coiteration, whereby guards in coiteration schemata are construed as algebraic constructors and  ... 
doi:10.1016/s1571-0661(04)80633-9 fatcat:yt4xbcipzvbp7ht5oihvehvuo4

Towards a dual ontology: duality, a case study

Francesco Maria Ferrari
2018 Sofia  
The Aristotelian notion of potentiality diers with the usual one (employed by Platonism and/or formalism and/or conceptualism) inasmuch it does not presupposes any actuality.  ...  Actually, providing a contribution to thisvery shift is what this paper want to be focused on.  ...  ML AND COALGEBRA The duality algebra-coalgebra may serve to explain much of the interaction between ML and algebra.  ... 
doi:10.47456/sofia.v7i1.19403 fatcat:5opze73ornhs7fnwu7ajaehgh4

Steps and Traces [article]

Jurriaan Rot, Bart Jacobs, Paul Levy
2020 arXiv   pre-print
This paper elaborates two new unifying ideas: 1) coalgebraic trace semantics is naturally presented in terms of corecursive algebras, and 2) all three approaches arise as instances of the same abstract  ...  Our perspective puts the different approaches under a common roof, and allows to derive conditions under which some of them coincide.  ...  We are grateful to the anonymous referees of both the conference version and this extended paper for various comments and suggestions.  ... 
arXiv:2004.05400v1 fatcat:dvgfts7mnnafbjep6iybl5p2ni

How to Kill Epsilons with a Dagger [chapter]

Filippo Bonchi, Stefan Milius, Alexandra Silva, Fabio Zanasi
2014 Lecture Notes in Computer Science  
More broadly, our approach extends the standard coalgebraic framework for state-based systems by taking into account the algebraic structure of the labels of their transitions.  ...  Our approach employs monads with a parametrized fixpoint operator † to give a semantics to those systems and implement a sound procedure of abstraction of the internal transitions, whose labels are seen  ...  FCOMP-01-0124-FEDER-020537 and SFRH/BPD/71956/2010. The first and the fourth author acknowledge support by project ANR 12IS0 2001 PACE.  ... 
doi:10.1007/978-3-662-44124-4_4 fatcat:twjinll36zek3g4cxple7oh4x4

Generic Trace Logics [article]

Christian Kissig, Alexander Kurz
2011 arXiv   pre-print
We combine previous work on coalgebraic logic with the coalgebraic traces semantics of Hasuo, Jacobs, and Sokolova.  ...  See Semadeni [20] for more on this perspective.  ...  Given a distributive law π : T B → BT we can define T on objects T X := T X and on morphisms T (f : X → Y ) := πY • T f There is a full and faithful functor K : KlB → B-Alg mapping X to the free algebra  ... 
arXiv:1103.3239v1 fatcat:d4kestffxja5rmc7gtjy6awupi

Generalizing the powerset construction, coalgebraically

Alexandra Silva, Filippo Bonchi, Marcello M. Bonsangue, Jan J. M. M. Rutten, Marc Herbstritt
2010 Foundations of Software Technology and Theoretical Computer Science  
In this paper, we lift the powerset construction on automata to the more general framework of coalgebras with structured state spaces.  ...  An endofunctor F determines both the type of systems (F -coalgebras) and a notion of behavioral equivalence (∼ F ) amongst them.  ...  Background In this section we introduce the preliminaries on coalgebras and algebras. First, we fix some notation on sets.  ... 
doi:10.4230/lipics.fsttcs.2010.272 dblp:conf/fsttcs/SilvaBBR10 fatcat:u55so4yysndizoyb3mhm5rroxq

Typed Linear Algebra for Weigthed (Probabilistic) Automata [chapter]

José N. Oliveira
2012 Lecture Notes in Computer Science  
This paper puts forward typed linear algebra (LA) as a candidate notation for such a role.  ...  Typed LA emerges from regarding matrices as morphisms of suitable categories whereby traditional linear algebra is equipped with at y p es y s t e m .  ...  This research was carried out in the context of the QAIS (Quantitative analysis of interacting systems: foundations and algorithms) project funded by the ERDF through the Programme COMPETE and by the Portuguese  ... 
doi:10.1007/978-3-642-31606-7_5 fatcat:yk3qmwjnljbxfdvfuz6evmhaiu


2013 International Journal of Foundations of Computer Science  
Some attention is paid to the interface between the index-free (categorial) language of matrix algebra and the corresponding index-wise, set-theoretic notation.  ...  This paper puts forward typed linear algebra as a candidate notation for such a unifying role.  ...  This research was carried out in the QAIS (Quantitative analysis of interacting systems) project funded by the ERDF through the Programme COMPETE and by the Portuguese Government through FCT (Foundation  ... 
doi:10.1142/s0129054113400145 fatcat:kp7umy6ynzcsbb4bl6b47j4fmm

The Coinductive Resumption Monad

Maciej Piróg, Jeremy Gibbons
2014 Electronical Notes in Theoretical Computer Science  
In this paper we introduce generalised resumptions in a category-theoretic, coalgebraic context and show their basic properties: they form a monad, they come equipped with a corecursion scheme in the sense  ...  Resumptions appear in many forms as a convenient abstraction, such as in semantics of concurrency and as a programming pattern.  ...  Acknowledgement We would like to thank Stefan Milius for his remarks on an early draft of this paper, and the anonymous reviewers for their detailed comments and helpful suggestions.  ... 
doi:10.1016/j.entcs.2014.10.015 fatcat:4duducsswbgkvmcy7sxamh7whu

A perspective on service orchestration

Marco A. Barbosa, Luis S. Barbosa
2009 Science of Computer Programming  
is parametric on the interaction discipline.  ...  Service-oriented computing is an emerging paradigm with increasing impact on the way modern software systems are designed and developed.  ...  ., process algebras in which parallel composition is parametric on an interaction discipline suitably encoded in the 'gene' of some process combinators.  ... 
doi:10.1016/j.scico.2008.09.019 fatcat:3syvntgicjf7rpweuvseebe55i
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