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Towards Trace Metrics via Functor Lifting

Paolo Baldan, Filippo Bonchi, Henning Kerstan, Barbara König, Marc Herbstritt
2015 Conference on Algebra and Coalgebra in Computer Science  
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]

Paolo Baldan, Filippo Bonchi, Henning Kerstan, Barbara König
2015 arXiv   pre-print
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 *

Paolo Baldan, Filippo Bonchi, Henning Kerstan, Barbara König, Paolo Baldan, Filippo Bonchi, Henning Kerstan, Barbara König
licensed under Creative Commons License CC-BY 6th International Conference on Algebra and Coalgebra in Computer Science (CALCO'15)   unpublished
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]

Paolo Baldan, Filippo Bonchi, Henning Kerstan, Barbara König
2018 arXiv   pre-print
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

Filippo Bonchi, Barbara König, Daniela Petrisan, Michael Wagner
2018 International Conference on Concurrency Theory  
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]

Filippo Bonchi, Barbara König, Daniela Petrisan
2018 arXiv   pre-print
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

Ana Sokolova
2011 Theoretical Computer Science  
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

Clemens Kupke, Jurriaan Rot, Michael Wagner
2020 Annual Conference for Computer Science Logic  
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]

Frank M. V. Feys, Helle Hvid Hansen, Lawrence S. Moss
2018 Lecture Notes in Computer Science  
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

Stefan Milius, Tadeusz Litak
2013 Electronic Proceedings in Theoretical Computer Science  
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]

Adriana Balan, Alexander Kurz, Jiří Velebil
2018 arXiv   pre-print
) 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

Corina Cîrstea
2011 Theoretical Computer Science  
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]

Clemens Kupke, Jurriaan Rot
2021 arXiv   pre-print
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]

David Ayala, John Francis
2021 arXiv   pre-print
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]

Jim de Groot, Helle Hvid Hansen, Alexander Kurz
2020 arXiv   pre-print
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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