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Towards Trace Metrics via Functor Lifting
2015
Conference on Algebra and Coalgebra in Computer Science
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We investigate the possibility of deriving metric trace semantics in a coalgebraic framework. ...
By exploiting some recent work on an abstract determinization, these results enable the derivation of trace metrics starting from coalgebras in Set. ...
This is then applied to derive trace metrics for nondeterministic automata and probabilistic automata, by relying on suitable liftings of the machine functor. ...
doi:10.4230/lipics.calco.2015.35
dblp:conf/calco/BaldanBK015
fatcat:q737653gurd3lnw7go6u5uuzie
Towards Trace Metrics via Functor Lifting
[article]
2015
arXiv
pre-print
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We investigate the possibility of deriving metric trace semantics in a coalgebraic framework. ...
By exploiting some recent work on an abstract determinization, these results enable the derivation of trace metrics starting from coalgebras in Set. ...
Trace semantics via deter-
minization. ...
arXiv:1505.08105v1
fatcat:eov2ypm3mfai3jvudvoused2ee
Towards Trace Metrics via Functor Lifting *
licensed under Creative Commons License CC-BY 6th International Conference on Algebra and Coalgebra in Computer Science (CALCO'15)
unpublished
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We investigate the possibility of deriving metric trace semantics in a coalgebraic framework. ...
By exploiting some recent work on an abstract determinization, these results enable the derivation of trace metrics starting from coalge-bras in Set. ...
This is then applied to derive trace metrics for nondeterministic automata and probabilistic automata, by relying on suitable liftings of the machine functor. ...
fatcat:deqplo3jmbconagu5hyikssrki
Coalgebraic Behavioral Metrics
[article]
2018
arXiv
pre-print
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In order to model linear-time metrics (generalizing trace equivalences), we show sufficient conditions for lifting distributive laws and monads. ...
A crucial step is the lifting of the functor H on Set to a functor H on the category PMet of pseudometric spaces. ...
Via the lifted distributive law we can transfer a functor F : P M et → P M et to an endofunctor F on EM(T ). ...
arXiv:1712.07511v3
fatcat:sfmjhfcbjrbl7khxoihvfcpduy
Up-To Techniques for Behavioural Metrics via Fibrations
2018
International Conference on Concurrency Theory
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In order to obtain a general framework, we need a systematic way to lift functors: we show that the Wasserstein lifting of a functor, introduced in a previous work, corresponds to a change of base in a ...
We focus on the fibrations of predicates and relations valued in a quantale, for which pseudo-metric spaces are an example. ...
Nevertheless, the up-to convex closure technique can find meaningful applications in linear, trace-based behavioural metrics (see [4] ). ...
doi:10.4230/lipics.concur.2018.17
dblp:conf/concur/Bonchi0P18
fatcat:n6dyzhli2zgatgwndph4nnmyxi
Up-To Techniques for Behavioural Metrics via Fibrations
[article]
2018
arXiv
pre-print
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In order to obtain a general framework, we need a systematic way to lift functors: we show that the Wasserstein lifting of a functor, introduced in a previous work, corresponds to a change of base in a ...
We focus on the fibrations of predicates and relations valued in a quantale, for which pseudo-metric spaces are an example. ...
Behavioral metrics via functor lifting. In FSTTCS, volume 29 of LIPIcs, 2014. 5 P. Baldan, F. Bonchi, H. Kerstan, and B. König. Towards trace metrics via functor lifting. ...
arXiv:1806.11064v1
fatcat:lfvzqseo3bdjvhlesq64gnyl4m
Probabilistic systems coalgebraically: A survey
2011
Theoretical Computer Science
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Behavioral distances via finality: metric vs. measurable spaces The work on behavioral pseudometrics for probabilistic systems by van Breugel and Worrell; cf. e.g. ...
Via the probability distribution functor on Sets and the Giry functor on Meas (and related categories) probabilistic systems enter coalgebra. ...
doi:10.1016/j.tcs.2011.05.008
pmid:21998490
pmcid:PMC3185909
fatcat:z4iljxlfofc5jbzyg3bwxk4g5y
Expressive Logics for Coinductive Predicates
2020
Annual Conference for Computer Science Logic
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The approach is illustrated with logics characterising similarity, divergence and a behavioural metric on automata. ...
Coinductive predicates are expressed abstractly via fibrations and functor lifting, and logic via a contravariant adjunction. Therefore, we make the following assumptions. ...
A first step towards generalisation beyond bisimilarity is obtained by replacing Rel(B) by an arbitrary lifting B : Rel → Rel of B. ...
doi:10.4230/lipics.csl.2020.26
dblp:conf/csl/KupkeR20
fatcat:fxdsbiiedrgshgqbeyasc7gina
Long-Term Values in Markov Decision Processes, (Co)Algebraically
[chapter]
2018
Lecture Notes in Computer Science
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We also explore boundedness features of the Kantorovich lifting of the distribution monad to metric spaces. ...
proof principle, based on Banach's Fixpoint Theorem, that we call contraction coinduction, and (ii) to show that the long-term value function of a policy with respect to discounted sums can be obtained via ...
We can view a Markow reward process u, t σ : S → R × ∆S as a coalgebra in Met for the lifted functor H∆, by equipping the state space S with a metric. ...
doi:10.1007/978-3-030-00389-0_6
fatcat:75sk42pkp5fzpnlbyolsu575em
Guard Your Daggers and Traces: On The Equational Properties of Guarded (Co-)recursion
2013
Electronic Proceedings in Theoretical Computer Science
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We also introduce the notion of guarded trace operator on a category, and we prove that guarded trace and guarded fixpoint operators are in one-to-one correspondence. ...
., cpo-based) models of iteration theories and models of guarded recursion such as complete metric spaces or the topos of trees studied by Birkedal et al. ...
Regarding the examples given in [9] , see also Proposition 2.6 below. (6) Let be the lifting functor (−) ⊥ on CPO, i.e. for any cpo X, X ⊥ is the cpo with a newly added least element. ...
doi:10.4204/eptcs.126.6
fatcat:jij5vglkhrcxrgxobnufoj6i54
Extending set functors to generalised metric spaces
[article]
2018
arXiv
pre-print
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) are related via change of base. ...
Mathematically, the heart of the matter is to show that, for any commutative quantale V, the 'discrete' functor D:Set→V-cat from sets to categories enriched over V is V-cat-dense and has a density presentation ...
Extending functors via relation lifting. ...
arXiv:1809.02229v2
fatcat:vifadi26x5d3tdt3o5fvfvkmli
Maximal traces and path-based coalgebraic temporal logics
2011
Theoretical Computer Science
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The semantics of such logics relies on the existence of execution maps similar to the trace maps introduced by Jacobs and co-authors as part of the coalgebraic theory of finite traces (Hasuo et al., 2007 ...
We consider finite execution maps derived from the theory of finite traces, and a new notion of maximal execution map that accounts for maximal, possibly infinite executions. ...
Maximal traces and executions Some initial steps towards a general coalgebraic treatment of maximal (possibly infinite) traces and executions were made in [11] , where infinite trace maps were defined ...
doi:10.1016/j.tcs.2011.04.025
fatcat:4n4fr2226fbqtgxwfi4fzfvy2y
Expressive Logics for Coinductive Predicates
[article]
2021
arXiv
pre-print
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The approach is illustrated with logics characterising similarity, divergence and a behavioural metric on automata. ...
Coinductive predicates are expressed abstractly via fibrations and functor lifting, and logic via a contravariant adjunction. Therefore, we make the following assumptions. ...
A first step towards generalisation beyond bisimilarity is obtained by replacing Rel(B) by an arbitrary lifting B : Rel → Rel of B. ...
arXiv:2006.12465v4
fatcat:idu3sha5yvbntjlc4ihq6tu5a4
Traces for factorization homology in dimension 1
[article]
2021
arXiv
pre-print
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We construct a circle-invariant trace from the factorization homology of the circle trace∫^α_𝕊^1 underline End(V) ⟶ associated to a dualizable object V∈𝔛 in a symmetric monoidal ∞-category. ...
This proves a conjecture of Toën–Vezzosi on existence of circle-invariant traces. ...
exploits that the monoidal structure on X is restricted from its sym-
metric monoidal structure (see (26)). ...
arXiv:2105.01143v2
fatcat:ezx7q4eqpfh7jieyipxocuwjea
Logic-Induced Bisimulations
[article]
2020
arXiv
pre-print
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In particular, the latter does not rely on a duality between functors 𝖳 (the type of the coalgebras) and 𝖫 (which gives the logic), nor on properties of the logical connection ρ. ...
We show that it is structural in the sense that it is defined only in terms of the coalgebra structure and the one-step modal semantics and, moreover, can be characterised by a form of relation lifting ...
Characterisation via relation lifting Another property of bisimulations for Set-coalgebras is that they can be characterised via relation lifting (see e.g. [31, Section 2.2]), and that bisimilarity on ...
arXiv:2008.09238v1
fatcat:yztwjqd5qzd4xobklxdg4w3esy
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