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A Coalgebraic Approach to Process Equivalence and a Coinduction Principle for Traces

Bartek Klin
2004 Electronical Notes in Theoretical Computer Science  
Preorders and equivalences on processes are modelled as coalgebras for behaviour endofunctors lifted to a category of test suites.  ...  As an immediate application, coinductive proof principles are described for these equivalences, in particular for trace equivalence.  ...  Application: coinduction principle for traces One of the most useful applications of coalgebraic semantics of processes is the coinduction proof principle, based on the fact that the bisimulation equivalence  ... 
doi:10.1016/j.entcs.2004.02.029 fatcat:g2dcfmq3yndjvemphwyvqb3rmu

A Coalgebraic Foundation for Coinductive Union Types [chapter]

Marcello Bonsangue, Jurriaan Rot, Davide Ancona, Frank de Boer, Jan Rutten
2014 Lecture Notes in Computer Science  
This paper introduces a coalgebraic foundation for coinductive types, interpreted as sets of values and extended with set theoretic union.  ...  Further, we provide a technique for reducing subtyping to inclusion between sets of finite traces, based on approximation.  ...  Types and values can be represented by coalgebras, and bisimulation provides a concrete proof principle for type equivalence.  ... 
doi:10.1007/978-3-662-43951-7_6 fatcat:dxksvgigpne67kbrfqjtjiyiim

Towards Incrementalization of Holistic Hyperproperties [chapter]

Dimiter Milushev, Dave Clarke
2012 Lecture Notes in Computer Science  
A hyperproperty is a set of sets of finite or infinite traces over some fixed alphabet and can be seen as a very generic system specification.  ...  Systems specified holistically tend to be more intuitive but difficult to reason about, whereas incremental specifications have a straightforward verification approach.  ...  We would like to thank Frank Piessens and José Proenca for valuable comments on drafts of this paper. We also thank the anonymous reviewers for their constructive feedback.  ... 
doi:10.1007/978-3-642-28641-4_18 fatcat:753w7aj2bjabffbmrpw7ja7tdi

An Exercise on Transition Systems

Paula R. Ribeiro, L.S. Barbosa, Shuling Wang
2008 Electronical Notes in Theoretical Computer Science  
In particular, it discusses how a notion of weak bisimilarity can be lifted from the relational to the coalgebraic level, to become an effective reasoning tool on coinductively defined process algebras  ...  On the other hand, the coalgebraic perspective regards processes as inhabitants of a final universe and allows for an intuitive definition of the semantics of process' combinators.  ...  We are currently working on this topic resorting to coalgebras over dependent types.  ... 
doi:10.1016/j.entcs.2008.03.087 fatcat:pk5sempy35h6hbyhf4dffzxcvy

Final Semantics for Decorated Traces

Filippo Bonchi, Marcello Bonsangue, Georgiana Caltais, Jan Rutten, Alexandra Silva
2012 Electronical Notes in Theoretical Computer Science  
As a consequence, proofs of decorated trace equivalence can be given by coinduction, using different types of (Moore-) bisimulation (up-to), which is helpful for automation.  ...  They are generally referred to as decorated traces, and examples include ready, failure, trace and complete trace equivalence.  ...  On the other hand, we would like to understand how our approach can be combined with [3] to obtain a coinductive approach to denotational (linear-time) semantics of different kinds of processes calculi  ... 
doi:10.1016/j.entcs.2012.08.006 fatcat:xi5lbwldqjbnrivzi6eawohwsa

Processes as formal power series: A coinductive approach to denotational semantics

Michele Boreale, Fabio Gadducci
2006 Theoretical Computer Science  
We characterize must testing equivalence on CSP in terms of the unique homomorphism from the Moore automaton of CSP processes to the final Moore automaton of partial formal power series over a certain  ...  The final automaton is then turned into a CSP-algebra: operators and fixpoints are defined, respectively, via behavioural differential equations and simulation relations.  ...  Trace semantics Two CSP processes P and Q are convergent-trace equivalent, written P ctr Q, if for each w ∈ A * • P ⇓ w iff Q ⇓ w, and • P w ⇒ iff Q w ⇒.  ... 
doi:10.1016/j.tcs.2006.05.030 fatcat:dnq7qy3zbraivd247ds5wgalzi

Coalgebras in functional programming and type theory

Venanzio Capretta
2011 Theoretical Computer Science  
This is a survey article on the use of coalgebras in functional programming and type theory. It presents the basic theory underlying the implementation of coinductive types, families and predicates.  ...  It also sketches some advanced topics in the study of the solutions to non-guarded corecursive equations and the design of non-standard type theory.  ...  Readers are encouraged to delve deeper into the cited literature for more technical and ample expositions of these topics and others that had to be omitted here.  ... 
doi:10.1016/j.tcs.2011.04.024 fatcat:rh7dkwzphvd3tcc5xzfe3kwquu

Coalgebraic theories of sequences in PVS

U Hensel
1999 Journal of Logic and Computation  
The nality axiom gives rise to various reasoning principles, like bisimulation, simulation, invariance, and induction for admissible predicates.  ...  The use of sequences as a nal coalgebra is demonstrated in two (standard) applications: a re nement result for automata involving sequences of actions, and a coalgebraic de nition plus correctness proof  ...  Acknowledgements We thank Marco Devillers and David Gri oen for stimulating discussions, and for pushing us to substantiate our claims about the suitability of the coalgebraic approach.  ... 
doi:10.1093/logcom/9.4.463 fatcat:kdp6sm3dezgtdi76bckrrlauaa

Session Coalgebras: A Coalgebraic View on Regular and Context-free Session Types

Alex C. Keizer, Henning Basold, Jorge A. Pérez
2022 ACM Transactions on Programming Languages and Systems  
Furthermore, we extend our coalgebraic approach to account for context-free session types, by equipping session coalgebras with a stack.  ...  As a result, we rediscover type equivalence, duality, and subtyping relations in terms of canonical coinductive presentations.  ...  ACKNOWLEDGMENTS We are grateful to the anonymous reviewers for their useful remarks and suggestions.  ... 
doi:10.1145/3527633 fatcat:3jlornnuu5g5dhs26urcpqlclq

Homomorphism between AOMRC and Hoare Model of Deterministic Reconfiguration Processes in Reconfigurable Computing Systems

P. C. Vinh
2007 Scientific Annals of Computer Science  
Then, under the theory of coalgebras, we build a homomorphism between AOMRC and a Hoare model of deterministic reconfiguration processes.  ...  In other words, since AOMRC and the Hoare model of deterministic reconfiguration processes are seen as coalgebras, their homomorphic relationship results in the behavioral equivalence between AOMRC being  ...  Acknowledgements: Thank to the anonymous reviewers for their helpful comments and valuable suggestions which have contributed to the final preparation of the paper.  ... 
doaj:97982aff92604ccaad2e607eecd942dc fatcat:5z7rnsjubzecphazkfnzynhtbq

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  
This paper studies Markov decision processes (MDPs) from the categorical perspective of coalgebra and algebra.  ...  The main contributions of this paper are (i) to give a coinductive explanation of policy improvement using a new proof principle, based on Banach's Fixpoint Theorem, that we call contraction coinduction  ...  This principle has clear coinductive overtones, and our aim is to situate it in a body of mathematics that is also concerned with infinite behavior and coinductive proof principles, i.e., in coalgebra.  ... 
doi:10.1007/978-3-030-00389-0_6 fatcat:75sk42pkp5fzpnlbyolsu575em

Integrating Induction and Coinduction via Closure Operators and Proof Cycles [chapter]

Liron Cohen, Reuben N. S. Rowe
2020 Lecture Notes in Computer Science  
We develop a sound and complete non-well-founded proof system for the extended logic, whose cyclic subsystem provides the basis for an effective system for automated inductive and coinductive reasoning  ...  Nonetheless developing natural proof systems (especially ones amenable to automation) for reasoning about coinductive data remains a challenge.  ...  We are grateful to Alexandra Silva for valuable coinductive reasoning examples, and Juriaan Rot for helpful comments and pointers.  ... 
doi:10.1007/978-3-030-51074-9_21 fatcat:r76cypliujbwbjlhb2zj5ln43m

Coalgebraic Tools for Bisimilarity and Decorated Trace Semantics [article]

Georgiana Caltais
2015 arXiv   pre-print
In particular, we are interested in handling notions of behavioural equivalence/preorder ranging from bisimilarity for systems that can be represented as non-deterministic coalgebras, to decorated trace  ...  The aim of this thesis is to exploit the strengths of the (co)algebraic framework in modelling reactive systems and reasoning on several types of associated semantics, in a uniform fashion.  ...  years, inspired me in my work and provided me with the support I needed in order to complete this thesis.  ... 
arXiv:1502.02910v1 fatcat:dypxhnudsnfqznjeg244p2u54a

Bialgebras for structural operational semantics: An introduction

Bartek Klin
2011 Theoretical Computer Science  
Two states in a PTS are observationally equivalent if and only if they are related by a probabilistic bisimulation; see [9] for a detailed coalgebraic treatment of PTSs.  ...  Two states in an LTS are observationally equivalent if and only if they are bisimilar; see e.g. [45] for more details on the coalgebraic understanding of LTSs. Example 6.  ...  If B admits a final coalgebra, this is equivalent to saying that x and y are equated by the coinductive extension of h.  ... 
doi:10.1016/j.tcs.2011.03.023 fatcat:zct3uyknbrfyhem36ygu7z5laq

Universal coalgebra: a theory of systems

J.J.M.M. Rutten
2000 Theoretical Computer Science  
of subcoalgebras and bisimulations, simple coalgebras and coinduction, and a covariety theorem for coalgebras similar to Birkho 's variety theorem.  ...  Such a principle was missing for coalgebras until the work of Aczel (Non-Well-Founded sets, CSLI Leethre Notes, Vol. 14, center for the study of Languages and information, Stanford, 1988) on a theory of  ...  Many thanks also to the Anonymous Referee, for a very constructive report, containing many valuable comments and suggestions.  ... 
doi:10.1016/s0304-3975(00)00056-6 fatcat:cnzwwld5tjfpdjmosrwpj7ov6e
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