### Table 1. Integer variables used in the probabilistic timed automata

2003

"... In PAGE 9: ... We suppose that the concrete host can send a packet to all the abstract hosts at the same time and only one of the abstract hosts can send a packet to the concrete host at a time. The set of variables of our probabilistic timed automata includes both clocks (x, y and z) and integer variables which are described in Table1 . Note that the range of the integer variable probes is changed for different verification instances, and since the abstract IP address 2 corresponds to a fresh address chosen by the concrete host we need only two buffers for the abstract hosts (corresponding to addresses of type 0 and 1).... ..."

Cited by 19

### Table 1: Stochastic automata for L (X = p 2 E)

1997

"... In PAGE 9: ... To associate a stochastic automaton to a given term in the language, we need to de ne the di erent parts of the stochastic automaton. We start by de ning predicates and - as the least relations satisfying rules in Table1 . However, not all the processes can have a straightforward stochastic automaton as a semantic interpretation.... In PAGE 9: ...The second occurrence of xG is intended to be bound to the outermost clock setting as shown by the grey arrow. Using the rules in Table1 , the following stochastic automaton would be obtained b; fxG; yHg a; ; xG xG yH... In PAGE 13: ... We use the notion of adversaries or schedulers [29, 24] to resolve non-deterministic choices. Since parallel composition of stochastic automata can be easily de ned (actually, it is de ned just like for the process algebra, see Table1 ), the simulation algorithm can compose the complete stochastic automaton on the y, which reduces the state space explosion problem. Although (probabilistic) adversaries allow to obtain a complete probabilistic nal model, the inclusion of them as a new ingredient is not that appealing since it would require an additional e ort when modelling systems.... ..."

Cited by 13

### Table 1: Stochastic automata for L (X = p 2 E)

1997

"... In PAGE 8: ... To associate a stochastic automaton to a given term in the language, we need to de ne the di erent parts of the stochastic automaton. We start by de ning predicates and - as the least relations satisfying rules in Table1 . However, not all the processes can have a straightforward stochastic automaton as a semantic interpretation, as we see as follows.... In PAGE 8: ... Consider the process p1 fjxGjg (a; fxGg7!(fjxG; yHjg fyHg7!b; stop)) (2) The second occurrence of xG is intended to be bound to the outermost clock setting as shown by the grey arrow. Using the rules in Table1 , the following stochastic automaton would be obtained b; fxG; yHg a; ; xG xG yH In this sense, xG would be captured by the innermost clock setting as shown by the black arrow in formula (2). Therefore, we consider that clocks are di erent if they are set in di erent places, although they may have the same name.... In PAGE 12: ... We use the notion of adversaries or schedulers [29, 24] to resolve non-deterministic choices. Since parallel composition of stochastic automata can be easily de ned (actually, it is de ned just like for the process algebra, see Table1 ), the simulation algorithm can compose the complete stochastic automaton on the y, which reduces the state space explosion problem. Although (probabilistic) adversaries allow to obtain a complete probabilistic nal model, the inclusion of them as a new ingredient is not that appealing since it would require an additional e ort when modelling systems.... ..."

Cited by 13

### Table Automata

2002

### lable sequence ~.6 The automata

1997

Cited by 54

### Table 1. Stochastic automata for

1999

"... In PAGE 3: ...The set of edges ?! between locations is defined as the smallest relation satisfying the rules in Table1 . The func- tion F is defined by F(xG) = G for each clock x in p.... In PAGE 6: ... Since in our semantics (cf. Table1 ) a location corre- sponds to a term, simulation can be carried out on the ba- sis of expressions rather than using their semantic repre- sentation. This means that the stochastic automaton is not entirely generated a priori but only the parts that are re- quired to choose the next step.... In PAGE 6: ...erm pi (i.e. location) and the input specification E. From term pi the set of clocks (pi) to be set is determined (by module (A) in Figure 1) and the set of possible next edges is computed according to the inference rules of Table1 (by module (B)). To compute the next valuation we only need to keep track off the last valuation vi.... ..."

Cited by 9

### Table 2. Automata details.

2005

Cited by 8

### Table 1: Stochastic automata for

"... In PAGE 5: ...smallest relation satisfying the rules in Table1 . The function F is de ned by F(xG) = G for each clock x in p.... ..."

### Table 1: Stochastic automata for

"... In PAGE 5: ...smallest relation satisfying the rules in Table1 . The function F is de ned by F(xG) = G for each clock x in p.... ..."