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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.
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
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