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Path category for free - Open morphisms from coalgebras with non-deterministic branching
[article]
2019
arXiv
pre-print
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The above construction provides path-categories and trace semantics for free for different flavours of transition systems: (1) non-deterministic tree automata (2) regular nondeterministic nominal automata ...
Another one is in terms of path categories and open morphisms, where a bisimulation is defined as a span of open morphisms. ...
He expresses his gratitude for having been invited to Tokyo, which initiated the present work. ...
arXiv:1811.12294v2
fatcat:gvf5r4xl65fftkmfdy43blotuy
Path Category for Free
[chapter]
2019
Green Chemistry and Sustainable Technology
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The above construction provides path-categories and trace semantics for free for different flavours of transition systems: (1) non-deterministic tree automata (2) regular nondeterministic nominal automata ...
Another one is in terms of path categories and open morphisms, where a bisimulation is defined as a span of open morphisms. ...
Conclusions and Further Work We proved that coalgebra homomorphisms for systems with non-deterministic branching can be seen as open maps for a canonical path-category, constructed from the computation ...
doi:10.1007/978-3-030-17127-8_30
dblp:conf/fossacs/WissmannDKH19
fatcat:upk6666yrrgcjnodkwvmhv3mam
A Coalgebraic View on Reachability
[article]
2020
arXiv
pre-print
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Coalgebras for an endofunctor provide a category-theoretic framework for modeling a wide range of state-based systems of various types. ...
We also study coalgebras in Kleisli categories: for a functor extending a functor on the base category, we show that the reachable part of a given pointed coalgebra can be computed in that base category ...
f ) are finitely branching non-deterministic systems. ...
arXiv:1901.10717v3
fatcat:u5jqjhexrnb7vgt4mxqu7qxoqm
On the foundations of final coalgebra semantics: non-well-founded sets, partial orders, metric spaces
1998
Mathematical Structures in Computer Science
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The properties of coalgebraic coinduction are studied both at an abstract categorical level and in some specific categories used in semantics, namely categories of non-well-founded sets, partial orders ...
The aim of the present survey is to show that the elementary categorical notion of a final coalgebra is a suitable foundation for such a coinduction principle. ...
It would be interesting to investigate whether this correspondence between open morphisms and coalgebra homomorphisms holds also for different notions of path objects and endofunctors. ...
doi:10.1017/s0960129598002588
fatcat:yszyhcmjsjeqbgzj73exutmbem
A coalgebraic view on reachability
2020
Commentationes Mathematicae Universitatis Carolinae
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This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://dml.cz ...
Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. ...
Wißmann expresses his gratitude for having been invited to Tokyo, which initiated the present work. ...
doi:10.14712/1213-7243.2019.026
fatcat:ucpljjserjd4hc6etlh2ozo3u4
A description based on languages of the final non-deterministic automaton
2014
Theoretical Computer Science
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In this paper we present a description of a final object for the category of non-deterministic automata, regarded as labelled transition systems, with the help of some structures defined in terms of languages ...
The study of the behaviour of non-deterministic automata has traditionally focused on the languages which can be associated to the different states. ...
Acknowledgements This work has been supported by the grant MTM2010-19938-C03-01 from the Ministerio de Ciencia e Innovación (Spanish Government). ...
doi:10.1016/j.tcs.2014.01.018
fatcat:4yzkmozrb5bipputmjavu6aciq
On tree coalgebras and coalgebra presentations
2004
Theoretical Computer Science
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For deterministic systems, expressed as coalgebras over polynomial functors, every tree t (an element of the ÿnal coalgebra) turns out to represent a new coalgebra At. ...
(This holds for all endofunctors of -accessible categories with colimits of !-chains.) Corollary: A set functor is bounded at in the sense of Kawahara and Mori i it is + -accessible. ...
P f -coalgebras are precisely the ÿnitely branching graphs (or non-labelled transition systems): for every coalgebra : S → P f S we consider the graph on S of all edges x → y with y ∈ (x). ...
doi:10.1016/s0304-3975(03)00378-5
fatcat:7lxymo425bf67a2aqmj4psn7pi
Graded Monads and Graded Logics for the Linear Time - Branching Time Spectrum
2019
International Conference on Concurrency Theory
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We show in the present paper that this framework of graded semantics does subsume the most important equivalences from the linear time -branching time spectrum. ...
A combination of universal coalgebra and graded monads provides a generic framework in which the semantics of concurrency can be parametrized both over the branching type of the underlying transition systems ...
This motivates the search for unifying principles that allow for a generic treatment of process equivalences of varying degrees of granularity and for systems of different branching types (non-deterministic ...
doi:10.4230/lipics.concur.2019.36
dblp:conf/concur/DorschMS19
fatcat:eld6nrsmnrhqnluzpr6cxklmlm
CIA Structures and the Semantics of Recursion
[chapter]
2010
Lecture Notes in Computer Science
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Final coalgebras for a functor serve as semantic domains for state based systems of various types. ...
For example, formal languages, streams, nonwell-founded sets and behaviors of CCS processes form final coalgebras. ...
A coalgebra x : X → X A × 2 for H is precisely a deterministic automaton with the (possibly infinite) state set X. ...
doi:10.1007/978-3-642-12032-9_22
fatcat:bdk4hktn3jgqlnzqwbsd3af2g4
On the Behaviour of Coalgebras with Side Effects and Algebras with Effectful Iteration
[article]
2021
arXiv
pre-print
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To this end, we investigate the locally ffg fixed point φ F, i.e. the colimit of all F-coalgebras with free finitely generated carrier, which is shown to be the initial ffg-Elgot algebra. ...
This is the technical foundation for our main result: the category of ffg-Elgot algebras is monadic over the category of T-algebras. ...
× X Σ on Set is the well-known subset construction turning a non-deterministic automaton into a deterministic one. . ...
arXiv:1911.06346v2
fatcat:ep3zvifouvctzolyexhbt3bcva
Endofunctors modelling higher-order behaviours
[article]
2016
arXiv
pre-print
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These functors have the challenging peculiarity to be circularly defined with their own final coalgebra. ...
From this perspective, the former can be seen as syntactic higher-order whereas the later as semantic higher-order. ...
As a direct application of the theory of coalgebras, we are now able to define a canonical higher-order coalgebraic bisimulation and show it to coincide with coalgebraic bisimulation for value-passing ...
arXiv:1602.06221v2
fatcat:fudx2s3ckrbvpmupf22wsc4fke
Abstract Congruence Criteria for Weak Bisimilarity
[article]
2021
arXiv
pre-print
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We demonstrate each criterion with various examples of success and failure and establish a formal connection with the simply WB cool rule format of Bloom and van Glabbeek. ...
Our work is founded upon Turi and Plotkin's mathematical operational semantics and the coalgebraic approach to weak bisimulation by Brengos. ...
A bialgebra morphism from ΣX X BX g h to ΣY Y BY j k is a map f : X → Y that is both a Σ-algebra and a B-coalgebra morphism. ...
arXiv:2010.07899v2
fatcat:gwuhp2gwsrfflavz734v6h7zcm
μ-Bicomplete Categories and Parity Games
[article]
2016
arXiv
pre-print
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Finally, the interpretation of a parity game in the category of sets is shown to be the set of deterministic winning strategies for a chosen player. ...
We provide concrete ex- amples of such categories and explicitly characterize this class of functors for the category of sets and functions. ...
A morphism of graphs Φ : S 1 ✲ S 2 induces a functor between the respective free categories, which we will denote by the same letter Φ. ...
arXiv:1610.06393v1
fatcat:bqz7biswezemfiqmtddch3cn7i
Towards categorical models for fairness: fully abstract presheaf semantics of SCCS with finite delay
2003
Theoretical Computer Science
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We give a denotational semantics of Milner's SCCS with ÿnite delay in the presheaf model, which di ers from previous semantics by giving the meanings of recursion by ÿnal coalgebras and meanings of ÿnite ...
The open map bisimulation is shown to coincide with extended bisimulation of Hennessy and Stirling, which is essentially fair CTL * -bisimulation. ...
Here one starts with a path category P (of non-empty path shapes) and then takes the categoryP of presheaves over P as model. ...
doi:10.1016/s0304-3975(01)00247-x
fatcat:6xf54tqzyjbqnfkdtkafyn32yu
μ-Bicomplete Categories and Parity Games
2002
RAIRO - Theoretical Informatics and Applications
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Finally, the interpretation of a parity game in the category of sets is shown to be the set of deterministic winning strategies for a chosen player. ...
We provide concrete examples of such categories and explicitly characterize this class of functors for the category of sets and functions. ...
F -coalgebras and their morphisms are defined dually and form a category C F . ...
doi:10.1051/ita:2002010
fatcat:rjxjwsdihveznjpthvm3aklagq
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