Terminal Coalgebras for Measure-Polynomial Functors

Schubert, Christoph

doi:10.1007/978-3-642-02017-9_35

Cited by 12 publications

(11 citation statements)

References 7 publications

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“…Our contributions are: 1) coalgebraic modeling of automata with the Büchi/parity conditions; 2) characterizing their accepted languages by diagrams with µ's and ν's (tr p in (1)); and 3) proving that the characterization indeed captures the conventional definitions. The last "sanity-check" proves to be intricate in the probabilistic case, and our proof-relying on previous [8,26]-identifies the role of final sequences [36] in probabilistic processes.…”

Section: Contributionsmentioning

confidence: 99%

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Coalgebraic Trace Semantics for Buechi and Parity Automata

Urabe

Shimizu

Hasuo

2016

Preprint

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Despite its success in producing numerous general results on state-based dynamics, the theory of coalgebra has struggled to accommodate the Büchi acceptance condition-a basic notion in the theory of automata for infinite words or trees. In this paper we present a clean answer to the question that builds on the "maximality" characterization of infinite traces (by Jacobs and Cîrstea): the accepted language of a Büchi automaton is characterized by two commuting diagrams, one for a least homomorphism and the other for a greatest, much like in a system of (least and greatest) fixed-point equations. This characterization works uniformly for the nondeterministic branching and the probabilistic one; and for words and trees alike. We present our results in terms of the parity acceptance condition that generalizes Büchi's.

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Section: Contributionsmentioning

confidence: 99%

“…The technical requirement of being standard Borel-meaning that it arises from a Polish space [11]-will be used in the probabilistic setting of §5; we follow [8,26] in its use.…”

Section: Coalgebras In a Kleisli Categorymentioning

confidence: 99%

Coalgebraic Trace Semantics for Buechi and Parity Automata

Urabe

Shimizu

Hasuo

2016

Preprint

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“….. It is known that G : Meas → Meas preserves a limit of an ω op -sequence that consists of standard Borel sets [18]. This means that ((F ‡ i ) ⊕ A, (Jπ k ) k∈ω ) is a limit over a sequence 1…”

Section: Lemma E2mentioning

confidence: 99%

Categorical Büchi and Parity Conditions via Alternating Fixed Points of Functors

Urabe

Hasuo

2018

Coalgebraic Methods in Computer Science

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Categorical studies of recursive data structures and their associated reasoning principles have mostly focused on two extremes: initial algebras and induction, and final coalgebras and coinduction. In this paper we study their in-betweens. We formalize notions of alternating fixed points of functors using constructions that are similar to that of free monads. We find their use in categorical modeling of accepting run trees under the Büchi and parity acceptance condition. This modeling abstracts away from states of an automaton; it can thus be thought of as the "behaviors" of systems with the Büchi or parity conditions, in a way that follows the tradition of coalgebraic modeling of system behaviors.

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“…We will just sketch the proof given in Schubert (2009c). We will just sketch the proof given in Schubert (2009c).…”

Section: Terminal Coalgebrasmentioning

confidence: 99%

“…Proof. We will just sketch the proof given in Schubert (2009c). The terminal sequence of a Standard Borel measure-polynomial endofunctor T defined as the following diagram:…”

Section: Terminal Coalgebrasmentioning

confidence: 99%

Coalgebraic logic over general measurable spaces – a survey

Doberkat¹,

Schubert²

2011

Math. Struct. Comp. Sci.

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Link to this article: http://journals.cambridge.org/abstract_S0960129510000526How to cite this article: ERNST-ERICH DOBERKAT and CHRISTOPH SCHUBERT (2011). Coalgebraic logic over general measurable spaces -a survey.In this survey we discuss the generalisation of stochastic Kripke models for general modal logics through predicate liftings for functors over general measurable spaces. We derive results on expressivity and show that selection arguments allow us to incorporate the discussion of bisimilarity, provided the underlying spaces are assumed to be standard Borel.

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Terminal Coalgebras for Measure-Polynomial Functors

Cited by 12 publications

References 7 publications

Coalgebraic Trace Semantics for Buechi and Parity Automata

Coalgebraic Trace Semantics for Buechi and Parity Automata

Categorical Büchi and Parity Conditions via Alternating Fixed Points of Functors

Coalgebraic logic over general measurable spaces – a survey

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