### Table 14: Run{Time Error

"... In PAGE 31: ...ule (7) By standard inductive arguments and by Proposition 6.1. 2 We now introduce the notion of run{time error and prove type safety. Run{time errors are de ned in Table14 in terms of the predicate N s ??! error that holds true when within the net N a process P at site s attempts to perform an action that is not allowed by its capabilities. Let us recall that the type of a site codi es the policy of access rights and that #p s0 denotes the access rights of s over s0, for s and s0 sites and type of s.... In PAGE 32: ...By induction on length of the derivation of N s ??! error , we prove that N s ??! error implies that N is not well{typed. The base step is when rule (act) of Table14 is the only rule used. In this case we have that N = s :: a:P and s :: a:P s ??! error because #p (loc(a)) 6 v fcap(a)g.... ..."

### Table 9. Run-Time Error

2003

"... In PAGE 17: ...ow, we introduce the notion of run-time error and state type safety, i.e. that executable nets do not give rise to run-time errors. Run-time errors are defined by the rules in Table9 in terms of predicate N quot; l that holds true when, within the net N, a process P located at a node with address l attempts to perform an action that is not allowed by the access policy of the node or to invoke a process not valid for the node. The rules are straightforward.... ..."

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### Table 14 Run-time error

"... In PAGE 29: ...ule (7). By standard inductive arguments and by Proposition 6.1. We now introduce the notion of run-time error and prove type safety. Run-time errors are de ned in Table14 in terms of the predicate N s ! error that holds true when within the net N a process P at site s attempts to perform an action that is not allowed by its capabilities. Let us recall that the type of a site codi es the policy of access rights and that #p s0 denotes the access rights of s over s0, for s and s0 sites and type of s.... In PAGE 30: ... By induction on length of the derivation of N s ! error, we prove that N s ! error implies that N is not well-typed. The base step is when rule (act) of Table14 is the only rule used. In this case we have that N = s :: a:P and s :: a:P s ! error because #p (loc(a)) 6v fcap(a)g.... ..."

### Table 2: Running times and error rate for the password application.

1994

"... In PAGE 8: ...5) 1 (1 ( 1 e kn/M )k )d. Table2... ..."

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### Table 1: Numerical results for 1D Example Run Times Errors

### Table 2: Numerical results for 2D Example Run Times Errors

### TABLE 1. The running time of some PTASs with 20% error.

2006

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