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Applications of Algebra and Coalgebra in Scientific Modelling
2010
Electronical Notes in Theoretical Computer Science
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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
2020
Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science
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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]
2006
Lecture Notes in Computer Science
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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
2011
Electronic Proceedings in Theoretical Computer Science
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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
2019
Conference on Algebra and Coalgebra in Computer Science
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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
2003
Electronical Notes in Theoretical Computer Science
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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
2018
Sofia
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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]
2020
arXiv
pre-print
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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]
2014
Lecture Notes in Computer Science
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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]
2011
arXiv
pre-print
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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
2010
Foundations of Software Technology and Theoretical Computer Science
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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]
2012
Lecture Notes in Computer Science
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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
WEIGHTED AUTOMATA AS COALGEBRAS IN CATEGORIES OF MATRICES
2013
International Journal of Foundations of Computer Science
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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
2014
Electronical Notes in Theoretical Computer Science
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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
2009
Science of Computer Programming
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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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