### Table 1: Verification Issues in Business Process Specifications

2002

"... In PAGE 3: ...Analysis Issues in Business Process Modeling The ease and flexibility of graphical modeling languages brings with it a possibility for introducing control flow anomalies in process specifications. Table1 illustrates a few of the major control flow verification issues, i.... ..."

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### Table 2. The processes abstracting the SBML species of the Tyson model.

in Design and Implementation of a Tool for Translating SBML into the Biochemical Stochastic π-calculus

"... In PAGE 4: ...tion rules to the set of reactions of the cell cycle SBML model reported in Table 1. The species processes, defined according to equation 1, are given in Table2 . Applying the rules to each reaction in turn we obtain the following specifications of the components in Table 2: PMR1 = (chR1;rR1):(PC2jPY P) using (5) PC2R2 = (chR2;rR2):PCP using (5) PCPR3 = (chR3;rR3):PC2 using (5) PCPR4 = (chR4;rR4):PpM using (9) PYR4 = (chR4;rR4):0 using (11) PMR5 = (chR5;rR5):PpM using (5) PESR6 = (chR6;rR6):(PESjPY ) using (3) PYR7 = (chR7;rR7):0 using (6) PY PR8 = (chR8;rR8):0 using (6) PpMR9 = (chR9;rR9):M using (5) Since there are eight first order reactions in the model, using equation (7) we define a clock process CLK as: CLK = (chR1;rR1):CLK + (chR2;rR2):CLK+ (chR3;rR3):CLK + (chR5;rR5):CLK+ (chR6;rR6):CLK + (chR7;rR7):CLK+ (chR8;rR8):CLK + (chR9;rR9):CLK The set of processes so defined are concurrently composed in the whole system by using parallel composition.... ..."

### Table 5. Abstract ow descriptions for the composition of processes

"... In PAGE 9: ... In fact, we not only check a safe process com- position but we also individuate possibly more restrictive constraints that have to be imposed to processes in order to obtain a safe composition. Let us consider the case represented in Table5 . In our framework the ow P1-into-P2 is satis able if and only if the intersection of input domain of P2 has a non-empty intersection with the output domain of P1.... ..."

### Table 3 Typical example showing the performance of the initial model and the model obtained by task-dependent domain abstraction during a time frame of 9.75 seconds Quantitative (no abstraction) Initial abstraction Qualitative abstraction

2001

"... In PAGE 18: ... Both models were then confronted with actual measurements taken from the car. Table3 shows the results for a continuously run- ning measurement that involved a leakage fault in the pipe between the turbine and the engine inlet. The duration of the shown time frame is approximately 10 seconds, and 1053... ..."

### Table 1 : Grace Abstract Operations

"... In PAGE 16: ... These objects are structured in a hierarchy under the object hierarchy for the conceptual model. The mapping process involves identifying which of the Grace primitives (as seen in Table1 ) are needed to perform the activity specific operations. A full description of the Help Desk specification and mapping can be found in (Benford et al 1991).... ..."

### Table 1. Verification results

2004

"... In PAGE 11: ... Note that spin carries out a step- by-step execution, allowing the inspection of code and variables in every step. The size of the state space produced by this model is shown in Table1 (row safety in concrete model). Note that the state space increases exponentially with the number of floors in the lift.... In PAGE 16: ... 15, with this transformation the error NoMove is not present in either the abstract model or, using Theorem 1, the concrete model. The benefits of using the abstract formula to discard this error are sum- marized in Table1 and Fig. 19.... In PAGE 16: ... Now the verification result for the abstract formula is valid , which ensures (using Theorem 1) that the con- crete model satisfies the property. Again, the benefits of verifying with this method are shown in Table1 and Fig. 19.... ..."

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### Table 4. Time performances for model building and verification of the abstract model Ip 1

"... In PAGE 10: ...ig. 7. Number of lines of the MDP for the abstract model Ip 1 fact that this model is built through the parallel com- position of subcomponents which may explain why the compaction methods are not as efficient in this case. The experimental results concerning the verification with Prism for the full protocol Implp 1 and abstract model Ip 1 are shown in Table 3 and Table4 respectively. The left-most column shows the deadline used in the property, and the right-most column shows the minimal probability with which the system has reached a state where a leader is elected before the deadline.... ..."

### Table 2: parallel composition, alternation, composition and abstraction

"... In PAGE 6: ...Table2 the equation for parallel composition makes use of two subsidiary equations for combining pairs of traces and pairs of refusals. The trace combinator sP j[ A ]j sQ is de ned recursively as (assuming a 2 A; b; c 62 A and sP A = sQ A) hi j[ A ]j hi = fhig sP j[ A ]j hi = fsPg hi j[ A ]j sQ = fsQg (t; a) a sP j[ A ]j (t; a) a sQ = f(t; a) a (sP j[ A ]j sQ)g (t1; b) a sP j[ A ]j (t2; c) a sQ = 8 gt; gt; gt; gt; gt; lt; gt; gt; gt; gt; gt; gt; : f(t1; b) a (sP j[ A ]j (t2; c) a sQ)g; if t1 lt; t2 f(t2; c) a ((t1; b) a sP j[ A ]j sQ)g; if t2 lt; t1 f(t1; b) a (sP j[ A ]j (t2; c) a sQ)g [ f(t2; c) a ((t1; b) a sP j[ A ]j sQ)g; if t1 = t2 The recursive de nition is necessary because we wish to respect the order of simultaneous events.... ..."

### Table 1. Model generation statistics process gen. min. #states #trans

1998

"... In PAGE 4: ...2 Generation of a Model of CFS From the specification depicted on Figure 2, the graph for CFSSystem, modelling the management of a single CFS block, has been generated compositionally, using environ- ments to reduce the initial sizes of processes User and OutputQ. Table1 gives the sizes of the different compo- nents and the generation and minimization times (in sec- onds, on a Sun Ultra-1 workstation). Two derived models have also been generated: Abstract is CFSSystem where only gates read and write remain visible.... ..."

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### Table 1. Model generation statistics process gen. min. #states #trans

"... In PAGE 4: ...2 Generation of a Model of CFS From the specification depicted on Figure 2, the graph for CFSSystem, modelling the management of a single CFS block, has been generated compositionally, using environ- ments to reduce the initial sizes of processes User and OutputQ. Table1 gives the sizes of the different compo- nents and the generation and minimization times (in sec- onds, on a Sun Ultra-1 workstation). Two derived models have also been generated: Abstract is CFSSystem where only gates read and write remain visible.... ..."