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Coalgebraic automata theory: Basic results
 Logical Methods in Computer Science
"... Vol. 4 (4:10) 2008, pp. 1–43 www.lmcsonline.org ..."
Deriving syntax and axioms for quantitative regular behaviours
, 2009
"... We present a systematic way to generate (1) languages of (generalised) regular expressions, and (2) sound and complete axiomatizations thereof, for a wide variety of quantitative systems. Our quantitative systems include weighted versions of automata and transition systems, in which transitions ar ..."
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Cited by 7 (4 self)
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We present a systematic way to generate (1) languages of (generalised) regular expressions, and (2) sound and complete axiomatizations thereof, for a wide variety of quantitative systems. Our quantitative systems include weighted versions of automata and transition systems, in which transitions are assigned a value in a monoid that represents cost, duration, probability, etc. Such systems are represented as coalgebras and (1) and (2) above are derived in a modular fashion from the underlying (functor) type of these coalgebras. In previous work, we applied a similar approach to a class of systems (without weights) that generalizes both the results of Kleene (on rational languages and DFA’s) and Milner (on regular behaviours and finite LTS’s), and includes many other systems such as Mealy and Moore machines. In the present paper, we extend this framework to deal with quantitative systems. As a consequence, our results now include languages and axiomatizations, both existing and new ones, for many different kinds of probabilistic systems.
Generalizing the powerset construction, coalgebraically
, 2010
"... Coalgebra is an abstract framework for the uniform study of different kinds of dynamical systems. An endofunctor F determines both the type of systems (Fcoalgebras) and a notion of behavioral equivalence (∼F) amongst them. Many types of transition systems and their equivalences can be captured by a ..."
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Cited by 7 (4 self)
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Coalgebra is an abstract framework for the uniform study of different kinds of dynamical systems. An endofunctor F determines both the type of systems (Fcoalgebras) and a notion of behavioral equivalence (∼F) amongst them. Many types of transition systems and their equivalences can be captured by a functor F. For example, for deterministic automata the derived equivalence is language equivalence, while for nondeterministic automata it is ordinary bisimilarity. The powerset construction is a standard method for converting a nondeterministic automaton into an equivalent deterministic one as far as language is concerned. In this paper, we lift the powerset construction on automata to the more general framework of coalgebras with structured state spaces. Examples of applications include partial Mealy machines, (structured) Moore automata, and Rabin probabilistic automata.
TYPES AND COALGEBRAIC STRUCTURE
"... We relate weak limit preservation properties of coalgebraic type functors F to structure theoretic properties of the class of all Fcoalgebras. ..."
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Cited by 6 (4 self)
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We relate weak limit preservation properties of coalgebraic type functors F to structure theoretic properties of the class of all Fcoalgebras.
A Coalgebraic Perspective on Linear Weighted Automata
, 2011
"... Weighted automata are a generalization of nondeterministic automata where each transition, in addition to an input letter, has also a quantity expressing the weight (e.g. cost or probability) of its execution. As for nondeterministic automata, their behaviours can be expressed in terms of either ( ..."
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Cited by 4 (1 self)
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Weighted automata are a generalization of nondeterministic automata where each transition, in addition to an input letter, has also a quantity expressing the weight (e.g. cost or probability) of its execution. As for nondeterministic automata, their behaviours can be expressed in terms of either (weighted) bisimilarity or (weighted) language equivalence. Coalgebras provide a categorical framework for the uniform study of statebased systems and their behaviours. In this work, we show that coalgebras can suitably model weighted automata in two different ways: coalgebras on
GENERALIZING DETERMINIZATION FROM AUTOMATA TO COALGEBRAS
"... Abstract. 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. Coalge ..."
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Cited by 1 (0 self)
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Abstract. 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 abstract framework for the uniform study of different kinds of dynamical systems. An endofunctor F determines both the type of systems (Fcoalgebras) and a notion of behavioural equivalence (∼F) amongst them. Many types of transition systems and their equivalences can be captured by a functor F. For example, for deterministic automata the derived equivalence is language equivalence, while for nondeterministic automata it is ordinary bisimilarity. We give several examples of applications of our generalized determinization construction, including partial Mealy machines, (structured) Moore automata, Rabin probabilistic automata, and, somewhat surprisingly, even pushdown automata. To further witness the generality of the approach we show how to characterize coalgebraically several equivalences which have been object of interest in the concurrency community, such as failure or ready
Resource bisimilarity and graded bisimilarity coincide ✩
"... Resource bisimilarity has been proposed in the literature on concurrency theory as a notion of bisimilarity over labeled transition systems that takes into account the number of choices that a system has. Independently, gbisimilarity has been defined over Kripke models as a suitable notion of bisim ..."
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Resource bisimilarity has been proposed in the literature on concurrency theory as a notion of bisimilarity over labeled transition systems that takes into account the number of choices that a system has. Independently, gbisimilarity has been defined over Kripke models as a suitable notion of bisimilarity for graded modal logic. This note shows that these two notions of bisimilarity coincide over imagefinite Kripke frames. Keywords: coalgebras Concurrency, resource bisimilarity, graded bisimilarity, graded modal logic, Kripke frames, 1.
Author manuscript, published in "Information and Computation 211 (2012) 77105" A Coalgebraic Perspective on Linear Weighted Automata
, 2011
"... Weighted automata are a generalization of nondeterministic automata where each transition, in addition to an input letter, has also a quantity expressing the weight (e.g. cost or probability) of its execution. As for nondeterministic automata, their behaviours can be expressed in terms of either ( ..."
Abstract
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Weighted automata are a generalization of nondeterministic automata where each transition, in addition to an input letter, has also a quantity expressing the weight (e.g. cost or probability) of its execution. As for nondeterministic automata, their behaviours can be expressed in terms of either (weighted) bisimilarity or (weighted) language equivalence. Coalgebras provide a categorical framework for the uniform study of statebased systems and their behaviours. In this work, we show that coalgebras can suitably model weighted automata in two different ways: coalgebras on