T. Basten, Branching bisimulation is an equivalence indeed! Unpublished manuscript. Home/Search Document Not in Database Summary Related Articles Check |
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Axiomatizing Prefix Iteration with Silent Steps - Wan Fokkink Rob (1996) (1 citation) (Correct)
....a bisimulation and the symmetric closure of the composition of two bisimulations are all bisimulations. Hence is an equivalence relation. This argument does not apply for = b because the symmetric closure of the composition of two b bisimulations need not be a b bisimulation, but in [7] it is shown that also b is an equivalence relation. is the largest bisimulation (for 2 fb; j; d; wg) follows immediately from the observation that the set of bisimulations is closed under arbitrary unions. The implications hold by definition. 2 The reader familiar with the literature ....
T. Basten, Branching bisimulation is an equivalence indeed! Unpublished manuscript.
Axiomatizing Prefix Iteration with Silent Steps - Aceto, Fokkink, van.. (1995) (1 citation) (Correct)
....a bisimulation and the symmetric closure of the composition of two bisimulations are all bisimulations. Hence is an equivalence relation. This argument does not apply for = b because the symmetric closure of the composition of two b bisimulations need not be a b bisimulation, but in [7] it is shown that also b is an equivalence relation. That is the largest bisimulation (for 2 fb; j; d; wg) follows immediately from the observation that the set of bisimulations is closed under arbitrary unions. The implications hold by definition. 2 The reader familiar with the ....
T. Basten, Branching bisimulation is an equivalence indeed! Unpublished manuscript.
Branching Bisimulation as a Tool in the Analysis of Weak.. - van Glabbeek (1995) (2 citations) (Correct)
....1 (Congruence) For x 2 fb; w; dg, rx is an equivalence relation such that if p rx q then ff:p rx ff:q; p r rx q r; r p rx r q and ff p rx ff q: Moreover rx is the coarsest relation with these properties contained in x . Proof: Equivalence is straightforward; see [5] or [17] However, as observed in Basten [5] the transitivity proof for rb in [16] is wrong. He also shows that stating Definition 2 in terms of semi branching bisimulations prevents the error. That rx is a congruence for BCCS follows easily from the definitions, using that the relation ....
....an equivalence relation such that if p rx q then ff:p rx ff:q; p r rx q r; r p rx r q and ff p rx ff q: Moreover rx is the coarsest relation with these properties contained in x . Proof: Equivalence is straightforward; see [5] or [17] However, as observed in Basten [5], the transitivity proof for rb in [16] is wrong. He also shows that stating Definition 2 in terms of semi branching bisimulations prevents the error. That rx is a congruence for BCCS follows easily from the definitions, using that the relation f(ff P; ff Q) j ff 2 A ; P rx Qg [ ....
T. Basten (1995): Branching bisimulation is an equivalence indeed! Unpublished manuscript.
An Algebraic Semantics for Hierarchical P/T Nets - Basten, Voorhoeve (1995) (1 citation) Self-citation (Basten) (Correct)
....give an operational semantics for PTNA extended with silent actions. Note that the definition given here differs from the original definition given by Van Glabbeek and Weijland in [17] In fact, it is the definition of semi branching bisimulation, which was first defined in [18] as it appears in [5]. It can be shown that the two notions are equivalent [18, 5] The reason for using the alternative definition is that it is more concise and more intuitive than the original definition. It also yields shorter proofs. A comparison of the two definitions can be found in [5] Property 5.5. Rooted ....
....actions. Note that the definition given here differs from the original definition given by Van Glabbeek and Weijland in [17] In fact, it is the definition of semi branching bisimulation, which was first defined in [18] as it appears in [5] It can be shown that the two notions are equivalent [18, 5]. The reason for using the alternative definition is that it is more concise and more intuitive than the original definition. It also yields shorter proofs. A comparison of the two definitions can be found in [5] Property 5.5. Rooted branching bisimulation, # rb , is an equivalence on ....
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T. Basten. Branching Bisimulation is an Equivalence indeed! To appear.
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