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Coinductive Characterisations Reveal Nice Relations Between Preorders and Equivalences

David de Frutos Escrig, Carlos Gregorio Rodríguez, Miguel Palomino
2008 Electronical Notes in Theoretical Computer Science  
By means of these new proofs and results we hope to contribute to a better knowledge of the semantics of processes and to better understand the tight relations between preorders and equivalences that define  ...  In this paper we present an shorter and simpler proof of this result, based on our coinductive characterisations of the behaviour preorders, and in particular in the existence of the canonical preorders  ...  This canonical preorder can be characterised in a simple way in terms of the corresponding equivalence and the relation I.  ... 
doi:10.1016/j.entcs.2008.04.059 fatcat:jqksu7iv45boxcdlaq54i2qthy

(Bi)simulations up-to characterise process semantics

David de Frutos Escrig, Carlos Gregorio Rodríguez
2009 Information and Computation  
The relation between bisimulations up-to and simulations up-to allows us to find some new relations between the equivalences that define the semantics and the corresponding preorders.  ...  We define (bi)simulations up-to a preorder and show how we can use them to provide a coinductive, (bi)simulation-like, characterisation of semantic (equivalences) preorders for processes.  ...  provide us with new relations between behaviour equivalences and preorders.  ... 
doi:10.1016/j.ic.2007.12.003 fatcat:jtgbwaht75cebfdh5tjy6td5yq

Modal Reasoning = Metric Reasoning, via Lawvere [article]

Ugo Dal Lago, Francesco Gavazzo
2021 arXiv   pre-print
But this is not the end of the story: we also establish a correspondence between modal program relations and program distances.  ...  This correspondence shows that modal applicative bisimilarity and (a properly extended) applicative bisimilarity distance coincide, this way revealing that modal program equivalences and program distances  ...  Notice that B-matrices are just ordinary relations, and that preorder B-matrices and equivalence B-matrices coincide with preorder and equivalence relations.  ... 
arXiv:2103.03871v1 fatcat:x6prnsruf5fdtpyrhgv5fzk4vu

Generalised Coinduction

F. Bartels
2001 Electronical Notes in Theoretical Computer Science  
By modifying Lenisa's approach we arrived at a categorical description of generalised coinductive definition and proof principles based on such a universal characterisation which specialises directly to  ...  Next, the same type of distributive law λ is used to generalise coinductive proof techniques. To this end, we introduce the notion of a λ-bisimulation relation.  ...  Acknowledgements I would like to thank my colleagues, in particular Jan Rutten, Alexandru Baltag, and Alexander Kurz, for discussions and guidance.  ... 
doi:10.1016/s1571-0661(04)80903-4 fatcat:4prfzdzeivfndhzim74ur2lvge

Generalised coinduction

FALK BARTELS
2003 Mathematical Structures in Computer Science  
By modifying Lenisa's approach we arrived at a categorical description of generalised coinductive definition and proof principles based on such a universal characterisation which specialises directly to  ...  Next, the same type of distributive law λ is used to generalise coinductive proof techniques. To this end, we introduce the notion of a λ-bisimulation relation.  ...  Acknowledgements I would like to thank my colleagues, in particular Jan Rutten, Alexandru Baltag, and Alexander Kurz, for discussions and guidance.  ... 
doi:10.1017/s0960129502003900 fatcat:f6pcvoqoffakhfmxkb5prbroru

Quantalic Behavioural Distances [article]

Sergey Goncharov, Dirk Hofmann, Pedro Nora, Lutz Schröder, Paul Wild
2022 arXiv   pre-print
covering, e.g., two-valued equivalences, metrics, and probabilistic metrics.  ...  on lax extensions of 𝖲𝖾𝗍-functors to categories of quantitative relations.  ...  The second author acknowledges support by the Center for Research and Development in Mathematics and Applications (CIDMA) through the Portuguese Foundation for Science and Technology FCT -Fundação para  ... 
arXiv:2202.07069v1 fatcat:gtkpdz3jajecllutxyntnlykqi

Sub-behaviour relations for session-based client/server systems

FRANCO BARBANERA, UGO DE'LIGUORO
2014 Mathematical Structures in Computer Science  
We show that our session behaviours and sub-behaviour relations provide sound and complete semantics for CSP-subtyping, and for Gay and Hole subtyping as a by-product.  ...  A restriction of the intersection of the first two relations characterizes the 'usual' sub-behaviour relation from the literature.  ...  We end up with a nice property of syntactical duality w.r.t. the preorders c , s and * . Let us first establish a lemma.  ... 
doi:10.1017/s096012951400005x fatcat:cahsbhhqine75bgstgzv4tp6ey

Generic Programming with Adjunctions [chapter]

Ralf Hinze
2012 Lecture Notes in Computer Science  
We discuss a multitude of basic adjunctions and show that they are directly relevant to programming and to reasoning about programs.  ...  Second, adjunctions are instrumental in unifying and generalising recursion schemes.  ...  They spotted numerous errors and suggested many improvements regarding style and presentation.  ... 
doi:10.1007/978-3-642-32202-0_2 fatcat:l7dkreiqsnbxvpy7lpsn3hi23m

Coinductive Equivalences and Metrics for Higher-order Languages with Algebraic Effects

Francesco Gavazzo
2019
In order to design the aforementioned notions of equivalence and re nement, an abstract relational framework is developed, which is based on the notions of a monad and of a relator, the latter being an  ...  At this point of the story it is then natural to ask whether there is a link between the above 'treelike' equivalences, and the interactive approach to program equivalence of previous section.  ...  We call a re exive and transitive V-relation a preorder V-relation (V-preorder, for short), and a re exive, symmetric, and transitive V-relation an equivalence V-relation (V-equivalence, for short).  ... 
doi:10.6092/unibo/amsdottorato/9075 fatcat:w3krkurbubdvxmaxlhxyhjwypy

Size matters in the modal μ-calculus [article]

Clemens Kupke and Johannes Marti and Yde Venema
2020 arXiv   pre-print
We start in a setting without alpha-equivalence.  ...  We discuss and compare complexity measures for the modal μ-calculus, focusing on size and alternation depth.  ...  not v ⊑ u) and ≡ for the equivalence relation induced by ⊑ (given by u ≡ v iff u ⊑ v and v ⊑ u).  ... 
arXiv:2010.14430v1 fatcat:fvndfh2gkvcm3fe7dfbtk6wo34

Pure bigraphs: Structure and dynamics

Robin Milner
2006 Information and Computation  
The paper also mentions briefly the use of bigraphs to model pervasive computing and biological systems.  ...  As a running example, the theory is applied to finite pure CCS, whose resulting transition system and bisimilarity are analysed in detail.  ...  If S is a binary relation and ≡ an equivalence, then we define S ≡ to be the closure of S under ≡ , i.e., the relational composition ≡S≡ .  ... 
doi:10.1016/j.ic.2005.07.003 fatcat:moxo45ttgbe4fexzlnhbxrqdhe

Streams are Forever

Jörg Endrullis, Dimitri Hendriks, Jan Willem Klop
2013 Bulletin of the European Association for Theoretical Computer Science  
(NWO) under grant numbers 639.021.020 and 612.000.934.  ...  They are also ubiquitous, arising in theoretical computer science (formal languages and functional programming), mathematics (number theory), and engineering (signal processing).  ...  It is easily checked that forms an equivalence relation, and we refer to the equivalence classes of as degrees. The reducibility relation induces a partial order on the degrees.  ... 
dblp:journals/eatcs/EndrullisHK13 fatcat:dpfouwrtwvejfa4ugtivffsgt4

Fixpoint logic, games, and relations of consequence [article]

MW Maciej Gazda, JF Jan Friso Groote, JC Jaco Van De Pol, TAC Tim Willemse
2016
Fixpoint logic, games, and relations of consequence. Eindhoven: Technische Universiteit Eindhoven.  ...  Concluding Remarks We defined and studied an elegant form of abstraction within the framework of equation systems, recasting abstraction as a form of coinductive consequence.  ...  Notable exceptions are [29] , which uses homomorphisms and which relies on an action-based model that is closely related to Kripke Modal Transition Systems; the work in [71] , in which abstraction techniques  ... 
doi:10.6100/ir841355 fatcat:f3xkk2iuhjerpogif3vvzhhplm

On the Semantics of Intensionality and Intensional Recursion [article]

G. A. Kavvos
2017 arXiv   pre-print
Intensionality is a phenomenon that occurs in logic and computation. In the most general sense, a function is intensional if it operates at a level finer than (extensional) equality.  ...  Our main contribution is a framework in which mathematical and computational constructions can be considered either extensionally, i.e. as abstract values, or intensionally, i.e. as fine-grained descriptions  ...  A partial equivalence relation (PER) is a symmetric and transitive relation.  ... 
arXiv:1712.09302v1 fatcat:5jfwgc2yujglraaxsuqr7jvmqi

Advanced reduction techniques for model checking [article]

JJA Jeroen Keiren, JF Jan Friso Groote, TAC Tim Willemse
2013
In this chapter we have shown the relations between all equivalences that we have defined, as well as the relation between our equivalences and direct simulation and Fritz and Wilke's delayed simulation  ...  Fritz and Wilke [FW06] studied preorders and equivalences that are able to relate vertices with different priorities that are incomparable to our equivalences.  ...  The comparison with the other equivalences is similar. We have used a timeout of an hour for reducing + solving, and Remark 6.41.  ... 
doi:10.6100/ir757862 fatcat:g33hz23cizcbba7k3kuyk375cu
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