### Table 3. The Transition Relation for Bisimulation.

1997

"... In PAGE 11: ... Given a sequence of labels t 2 T such that 8 2 t; = send(a; v) _ = the notation t# denotes the string representing the sequence of labels obtained from t by removing the labels and ordering alphabetically the remaining send(a; v) labels. The new transition relation =) is defined in Table3 . We denote the set of labels which appear in =) with T#.... ..."

Cited by 15

### Table 3: -laws for branching bisimulation.

1994

Cited by 14

### Table 2: Laws for strong bisimulation

### Table 2: The axiom system for bisimulation equivalence

"... In PAGE 15: ... Theorem 4.1 (Fokkink and Zantema) The axiom system in Table2 com- pletely axiomatizes bisimulation equivalence over (BPA (Act)). Thus bisimulation equivalence has a nite equational axiomatization over the language (BPA (Act)).... In PAGE 33: ...roposition 6.1 Let P; Q 2 T(BPA (Act)). If P $ Q, then Loops(P ) = Loops(Q). Proof: As the equations in Table2 are complete with respect to bisimulation equi- valence, it is su cient to show that if the equation P = Q is deducible from those in Table 2, then Loops(P) = Loops(Q). This is easily veri ed because the statement holds for the equations in the aforementioned table, and is preserved by the rules of equational deduction.... In PAGE 33: ...roposition 6.1 Let P; Q 2 T(BPA (Act)). If P $ Q, then Loops(P ) = Loops(Q). Proof: As the equations in Table 2 are complete with respect to bisimulation equi- valence, it is su cient to show that if the equation P = Q is deducible from those in Table2 , then Loops(P) = Loops(Q). This is easily veri ed because the statement holds for the equations in the aforementioned table, and is preserved by the rules of equational deduction.... ..."

### Table 3: The transition system specialised for open bisimulation

"... In PAGE 20: ... Intuitively, M collects the conditions indispensable for the action to re. In other words, M de nes the \minimal quot; substitution M which would allow P to use ; Examples of transitions are [a = b] : P ([a=b]; ) P and ( [a = b] ca: P1) j (d(x): P2) ([a=b][c=d]; ) P1 j P2fa=xg The new transition system is presented in Table3 . Its composite actions (M; ) are ranged over by .... In PAGE 20: ...quates more than , i.e. (a) = (b) implies (a) = (b). Note that, in Table3 , if P (M; ) P0, then no name bound in appears in M. The bisimulation which we de ne on the new transition system and which we shall prove to coincide with is nearly a ground bisimulation.... ..."

### Table 2: The axiom system for bisimulation equivalence

"... In PAGE 10: ... Theorem 4.1 (Fokkink and Zantema) The axiom system in Table2 completely ax- iomatizes bisimulation equivalence over (BPA (Act)). Thus bisimulation equivalence has a nite equational axiomatization over the language (BPA (Act)).... In PAGE 25: ...x + (y z) = a a TE2 x + xy = xy TE3 xy = yx Table 5: Characteristic equations for trace equivalence (Act = fag) nitely (in)equationally axiomatized over the set of closed terms over a singleton action set. Consider the axiom system E consisting of the equations A1{A5 in Table2 together with the axioms in Table 5. It is not hard to see that the equations in E are sound with respect to trace equivalence over T(BPA (Act)).... ..."

### Table 9 Axioms for IMC for lumping bisimulation

"... In PAGE 34: ...B4) (cf. Table 2), (R1) through (R3) (cf. Table 2), (RL1) and (RL3) (cf. Table 5), (I1), (RL4) (cf. Table 7) and the axioms (RL5) and (P1000) listed in Table9 . This axiom system is sound and complete for regular terms in IMC and lumping bisimulation.... ..."

### Table 2: Scheduler: performances of the tool on bisimulation minimisation

1992

Cited by 27

### Table 1. The transition system specialised for open bisimulation

1996

Cited by 5