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Non-Deterministic Kleene Coalgebras

Alexandra Silva ; Marcello Bonsangue ; Jan Rutten.

In this paper, we present a systematic way of deriving (1) languages of (generalised) regular expressions, and (2) sound and complete axiomatizations thereof, for a wide variety of systems. This generalizes both the results of Kleene (on regular languages and deterministic finite automata) and&nbsp;[&hellip;]

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Generalizing determinization from automata to coalgebras

Alexandra Silva ; Filippo Bonchi ; Marcello Bonsangue ; Jan Rutten.

The powerset construction is a standard method for converting a nondeterministic automaton into a deterministic one recognizing the same language. In this paper, we lift the powerset construction from automata to the more general framework of coalgebras with structured state spaces. Coalgebra is an&nbsp;[&hellip;]

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Coinductive Foundations of Infinitary Rewriting and Infinitary Equational Logic

Jörg Endrullis ; Helle Hvid Hansen ; Dimitri Hendriks ; Andrew Polonsky ; Alexandra Silva.

We present a coinductive framework for defining and reasoning about the infinitary analogues of equational logic and term rewriting in a uniform, coinductive way. The setup captures rewrite sequences of arbitrary ordinal length, but it has neither the need for ordinals nor for metric convergence.&nbsp;[&hellip;]

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A coalgebraic treatment of conditional transition systems with upgrades

Harsh Beohar ; Barbara König ; Sebastian Küpper ; Alexandra Silva ; Thorsten Wißmann.

We consider conditional transition systems, that model software product lines with upgrades, in a coalgebraic setting. By using Birkhoff's duality for distributive lattices, we derive two equivalent Kleisli categories in which these coalgebras live: Kleisli categories based on the reader and on the&nbsp;[&hellip;]

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Distribution Bisimilarity via the Power of Convex Algebras

Filippo Bonchi ; Alexandra Silva ; Ana Sokolova.

Probabilistic automata (PA), also known as probabilistic nondeterministic labelled transition systems, combine probability and nondeterminism. They can be given different semantics, like strong bisimilarity, convex bisimilarity, or (more recently) distribution bisimilarity. The latter is based on&nbsp;[&hellip;]

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Equivalence checking for weak bi-Kleene algebra

Tobias Kappé ; Paul Brunet ; Bas Luttik ; Alexandra Silva ; Fabio Zanasi.

Pomset automata are an operational model of weak bi-Kleene algebra, which describes programs that can fork an execution into parallel threads, upon completion of which execution can join to resume as a single thread. We characterize a fragment of pomset automata that admits a decision procedure for&nbsp;[&hellip;]

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