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Hybrid Automata as Coalgebras [chapter]

Renato Neves, Luis S. Barbosa
2016 Lecture Notes in Computer Science  
The current paper revisits hybrid automata from a coalgebraic point of view.  ...  Able to simultaneously encode discrete transitions and continuous behaviour, hybrid automata are the de facto framework for the formal specification and analysis of hybrid systems.  ...  In particular, it shows how to encode hybrid automata as coalgebras, explores the associated observational semantics, and reframes the classic notion of bisimulation (for hybrid automata) as a coalgebraic  ... 
doi:10.1007/978-3-319-46750-4_22 fatcat:v3japt7bz5av7knhymgksjmvui

Coalgebraic semantics of modal logics: An overview

Clemens Kupke, Dirk Pattinson
2011 Theoretical Computer Science  
, expressiveness and complexity in these settings, both for basic languages as well as a number of extensions, such as hybrid languages and fixpoints.  ...  Coalgebras can be seen as a natural abstraction of Kripke frames. In the same sense, coalgebraic logics are generalised modal logics.  ...  As mentioned earlier on, the importance of coalgebra automata from a logical perspective lies in the fact that these automata are expressively equivalent to Venema's coalgebraic fixpoint logic [102] .  ... 
doi:10.1016/j.tcs.2011.04.023 fatcat:ffi53okdkzeqtbyqt5phjdrfaa

Fuzzy Automata as Coalgebras

Ai Liu, Shun Wang, Luis Soares Barbosa, Meng Sun
2021 Mathematics  
This paper models different types of fuzzy automata as coalgebras with a monad structure capturing fuzzy behavior.  ...  It is then an interesting topic to analyze the behavior of fuzzy automata from a coalgebraic point of view.  ...  Hybrid automata specifying both discrete and continuous behavior can also be modeled as coalgebras [24] .  ... 
doi:10.3390/math9030272 fatcat:vj3s44nm45ckbcbi5jksgbpjay

Metamathematics for Systems Design

Ichiro Hasuo
2017 New generation computing  
They typically combine one individual technique with one specific concern, such as hybrid automata that extend automata with continuous dynamics.  ...  such as probability, time, and cost make problems fundamentally different from those about software.  ...  As an example of such individual extended techniques T e , hybrid automata take finite automata as their basis T and add the additional concern e of continuous dynamics.  ... 
doi:10.1007/s00354-017-0023-1 fatcat:pw6byl77njf2boltl4qbjdh3ba

Hybrid systems and quantum automata: Preliminary announcement [chapter]

R. L. Grossman, M. Sweedler
1995 Lecture Notes in Computer Science  
These types of systems have become known as hybrid systems and are examples of formal systems with commutative R.  ...  In this paper, we present a number of examples of hybrid systems and quantum automata and point out some relationships between them.  ...  Of special interest are those systems consisting of interacting networks of classical systems and automata. These types of systems have become known as hybrid systems [5] .  ... 
doi:10.1007/3-540-60472-3_10 fatcat:lx3z7zidwjfvddiknyw7khpvtu

Automata in the Category of Glued Vector Spaces [article]

Thomas Colcombet, Daniela Petrişan
2017 arXiv   pre-print
The main instantiation of our construction is a new class of automata that are hybrid between deterministic automata and automata weighted over a field.  ...  In this paper we adopt a category-theoretic approach to the conception of automata classes enjoying minimization by design.  ...  In the coalgebraic setting one needs to consider the so-called pointed coalgebras, see for example [1] , where minimal automata are modelled as well-pointed coalgebras.  ... 
arXiv:1711.06065v1 fatcat:giecpkz3uneuxeeknggkfjgy2q

Modal Logics are Coalgebraic

C. Cirstea, A. Kurz, D. Pattinson, L. Schroder, Y. Venema
2009 Computer journal  
in a number of areas within computer science, such as knowledge representation and concurrency/mobility.  ...  Coalgebraic semantics, on the other hand, provides a uniform and encompassing view on the large variety of specific logics used in particular domains.  ...  class of automata as given by the first criterion.  ... 
doi:10.1093/comjnl/bxp004 fatcat:gpm47rtxanb5xaei7nq3z4pnea

Foundations of Software Science and Computational Structures: Selected papers from FOSSACS 2005

Vladimiro Sassone
2008 Theoretical Computer Science  
Typical topics include: algebraic models; automata and language theory; behavioural equivalences; categorical models; computation processes over discrete and continuous data; computation structures; logics  ...  EXPRESSIVITY OF COALGEBRAIC MODAL LOGIC: THE LIMITS AND BEYOND Lutz Schröder Modal logic is increasingly presented as the natural logic for coalgebras, as while the latter are a unifying semantic framework  ...  OPTIMAL REACHABILITY FOR MULTI-PRICED TIMED AUTOMATA Kim Guldstrand Larsen and Jacob Illum Rasmussen The paper is concerned with priced timed automata, which are hybrid automata with time and cost parameters  ... 
doi:10.1016/j.tcs.2007.09.019 fatcat:sknvkrnpozfl7d365rws52wwke

Generic Forward and Backward Simulations [chapter]

Ichiro Hasuo
2006 Lecture Notes in Computer Science  
We do so by identifying forward/backward simulations as lax/oplax morphisms of coalgebras. Starting from this observation, we present a systematic study of this generic notion of simulations.  ...  Instead, a completeness result is proved for a certain combination of forward and backward simulations (hybrid simulations), as is done in [LV95] .  ...  Trace inclusion implies existence of a certain kind of hybrid simulation, namely a backward-forward simulation.  ... 
doi:10.1007/11817949_27 fatcat:5xzokv4wbzgupngnqni2uzl36m

Page 3441 of Mathematical Reviews Vol. , Issue 99e [page]

1999 Mathematical Reviews  
Kopke, Anuj Puri and Pravin Varaiya, What’s decidable about hybrid automata? (94-124).  ...  (electronic)); Andrea Corradini, Martin GroBe-Rhode and Reiko Heckel, Struc- tured transition systems as lax coalgebras (20 pp. (electronic)); H.  ... 

Testing Semantics: Connecting Processes and Process Logics [chapter]

Dusko Pavlovic, Michael Mislove, James B. Worrell
2006 Lecture Notes in Computer Science  
Our basic philosophy is that tests can be used as a basis for modeling interactions, as well as processes and the data on which they operate.  ...  that are input into a machine can be viewed as tests that the machine can be subjected to, the machine can be viewed as a test that can be used to distinguish data.  ...  In addition, we have illustrated our approach with standard examples: finite automata, pushdown automata and Turing machines, as well as results that show how our approach captures simulation and strong  ... 
doi:10.1007/11784180_24 fatcat:ba75kgvhsncpvdp6bcu7zijp74

Realization Theory of Nonlinear Hybrid Systems [chapter]

Mihály Petreczky, Jean-Baptiste Pomet
2013 Taming Heterogeneity and Complexity of Embedded Control  
Thus, finiteness of the strong Lie-rank can be seen as an "almost" sufficient condition.  ...  We will use theory of Sweedler-type coalgebras for studying the formal realization problem. RÉSUMÉ.  ...  A hybrid coalgebra system is a tuple HC = (A, Σ, q 0 ), where -A = (Q, Γ, O, δ, λ) is a Moore-automata, q 0 ∈ Q, -Σ = (C, H, ψ, φ, µ) is a coalgebra system, such that -C = L q∈Q C q , where C q is a subcoalgebra  ... 
doi:10.1002/9780470612217.ch31 fatcat:afc4myymmncnzpmqudrnu4ulru

Optimal Satisfiability Checking for Arithmetic $$\mu $$ -Calculi [chapter]

Daniel Hausmann, Lutz Schröder
2019 Green Chemistry and Sustainable Technology  
well as an extension of the (two-valued) probabilistic µ-calculus with polynomial inequalities.  ...  The coalgebraic µ-calculus provides a generic semantic framework for fixpoint logics with branching types beyond the standard relational setup, e.g. probabilistic, weighted, or game-based.  ...  We have applied this principle to satisfiability checking in coalgebraic (next-step) modal logics [35] , coalgebraic hybrid logics [26] , and reasoning with global assumptions in coalgebraic modal logics  ... 
doi:10.1007/978-3-030-17127-8_16 dblp:conf/fossacs/HausmannS19 fatcat:a532tjzygzez5ctwmsohietthu

Behaviour-refinement of coalgebraic specifications with coinductive correctness proofs [chapter]

Bart Jacobs
1997 Lecture Notes in Computer Science  
A notion of re nement is de ned in the context of coalgebraic speci cation of classes in object-oriented languages.  ...  The coalgebraic approach allows us to use coinductive proof methods in establishing re nements (via (bi)simulations). This is illustrated in several examples.  ...  Our (coalgebraic) notion of re nement scales up to a \hybrid" setting 12], combining discrete and continuous behaviour.  ... 
doi:10.1007/bfb0030641 fatcat:4qszl64icngajisapdbjm6jqgu

Page 7068 of Mathematical Reviews Vol. , Issue 2003i [page]

2003 Mathematical Reviews  
Janicki and Koutny’s proposition is the most liberal, since it allows steps for which no valid linearization exists; Montanari and Rossi's, as well as Busi and Pinna’s, is more conservative since they  ...  Existence of a terminal coalgebra is also proven under the con- dition that F is bounded.  ... 
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