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14
Weighted bisimulations in linear algebraic form
, 2009
"... We study bisimulation and minimization for weighted automata, relying on a geometrical representation of the model, linear weighted automata (lwa). In a lwa, the statespace of the automaton is represented by a vector space, and the transitions and weighting maps by linear morphisms over this vect ..."
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We study bisimulation and minimization for weighted automata, relying on a geometrical representation of the model, linear weighted automata (lwa). In a lwa, the statespace of the automaton is represented by a vector space, and the transitions and weighting maps by linear morphisms over this vector space. Weighted bisimulations are represented by subspaces that are invariant under the transition morphisms. We show that the largest bisimulation coincides with weighted language equivalence, can be computed by a geometrical version of partition refinement and that the corresponding quotient gives rise to the minimal weightedlanguage equivalence automaton. Relations to Larsen and Skou’s probabilistic bisimulation and to classical results in Automata Theory are also discussed.
On coalgebras over algebras
 In ”Proceedings of the Tenth Workshop on Coalgebraic Methods in Computer Science (CMCS 2010)”, Electr. Notes
"... We extend Barr’s wellknown characterization of the final coalgebra of a Setendofunctor H as the completion of its initial algebra to the EilenbergMoore category Alg(M) of algebras associated to a Setmonad M, if H can be lifted to Alg(M). As further analysis, we introduce the notion of commuting ..."
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We extend Barr’s wellknown characterization of the final coalgebra of a Setendofunctor H as the completion of its initial algebra to the EilenbergMoore category Alg(M) of algebras associated to a Setmonad M, if H can be lifted to Alg(M). As further analysis, we introduce the notion of commuting pair of endofunctors (T,H) with respect to a monad M and show that under reasonable assumptions, the final Hcoalgebra can be obtained as the completion of the free Malgebra on the initial Talgebra.
Stream Differential Equations: Specification Formats and Solution Methods
, 2014
"... Streams, or infinite sequences, are infinite objects of a very simple type, yet they have a rich theory partly due to their ubiquity in mathematics and computer science. Stream differential equations are a coinductive method for specifying streams and stream operations, and their theory has been dev ..."
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Streams, or infinite sequences, are infinite objects of a very simple type, yet they have a rich theory partly due to their ubiquity in mathematics and computer science. Stream differential equations are a coinductive method for specifying streams and stream operations, and their theory has been developed in many papers over the past two decades. In this paper we present a survey of the many results in this area. Our focus is on the classification of different formats of stream differential equations, their solution methods, and the classes of streams they can define. Moreover, we describe in detail the connection between the socalled syntactic solution method and abstract GSOS.
Coalgebras, Stone Duality, Modal Logic
, 2006
"... A brief outline of the topics of the course could be as follows. Coalgebras generalise transition systems. Modal logics are the natural logics for coalgebras. Stone duality provides the relationship between coalgebras and modal logic. Furthermore, some basic category theory is needed to understand c ..."
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A brief outline of the topics of the course could be as follows. Coalgebras generalise transition systems. Modal logics are the natural logics for coalgebras. Stone duality provides the relationship between coalgebras and modal logic. Furthermore, some basic category theory is needed to understand coalgebras as well as Stone duality. So we
Coalgebras and Their Logics 1
, 2006
"... Some comments about the last Logic Column, on nominal logic. Pierre Lescanne points out ..."
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Some comments about the last Logic Column, on nominal logic. Pierre Lescanne points out
Acknowledgment
, 1973
"... During the course of the Datacomputer Project, many people have contributed to the development of datalanguage. The suggestions and criticisms of Dr. Gordon Everest (University of ..."
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During the course of the Datacomputer Project, many people have contributed to the development of datalanguage. The suggestions and criticisms of Dr. Gordon Everest (University of
Newton series, coinductively
"... Abstract. We present a comparative study of four product operators on weighted languages: (i) the convolution, (ii) the shuffle, (iii) the infiltration, and (iv) the Hadamard product. Exploiting the fact that the set of weighted languages is a final coalgebra, we use coinduction to prove that a cla ..."
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Abstract. We present a comparative study of four product operators on weighted languages: (i) the convolution, (ii) the shuffle, (iii) the infiltration, and (iv) the Hadamard product. Exploiting the fact that the set of weighted languages is a final coalgebra, we use coinduction to prove that a classical operator from difference calculus in mathematics: the Newton transform, generalises (from infinite sequences) to weighted languages. We show that the Newton transform is an isomorphism of rings that transforms the Hadamard product of two weighted languages into an infiltration product, and we develop various representations for the Newton transform of a language, together with concrete calculation rules for computing them. 1