### Table 7. Conditions on the synchronization function.

"... In PAGE 7: ... Axioms for synchronous cooperation with blocking. Atomic actions and concurrent actions Like [7], we assume a xed but arbitrary set AA of atomic actions (tau 2 AA), a xed but arbitrary set CA AA of concurrent actions, and a xed but arbitrary synchronization function j : CA CA ! CA satisfying that: { tau 2 AA; { for an action 2 CA if and only if 2 AA or there exist 0; 00 such that = 0j 00; { for an action 2 CA there is a boolean value ? stating that is independent or blocked; { the equations in Table7 are also satis ed with ; 0; 00 2 CA. Hence, each concurrent action can be reduced to one of the following form: { a with a 2 AA; { a1j : : : jan with a1; : : : an 2 AA for n gt; 1; The set BA of basic actions is extended with this set CA of concurrent actions.... In PAGE 7: ... Hence, each concurrent action can be reduced to one of the following form: { a with a 2 AA; { a1j : : : jan with a1; : : : an 2 AA for n gt; 1; The set BA of basic actions is extended with this set CA of concurrent actions. We note that the last two axioms of Table7 on independence and reply condi- tions state that the execution of the act of simultaneously performing is always accepted and it produces a positive reply. The synchronous cooperation with blocking strategy The synchronous cooperation of threads in SVP is dynamic.... ..."

### Table 2 Sensitivity to Initial Conditions: Synchronous

### Table 1 Synchronization condition.

"... In PAGE 11: ... We calculate the set as follows. For each Rend(E; g) 2 RI; E = fE1; ; Emg : (1) extract all transitions on gate g, for each Ei 2 E (let sync ev(Ei; g) be the extracted transitions for Ei); (2) calculate the set of tuples f(e1; ; em)jei 2 sync ev(Ei; g)g where each tuple can satisfy the synchronization condition in Table1 (let Tuples(E; g) denote the set). Next, we convert the synchronous tuples to rendezvous indications as follows, so that they satisfy the criteria in Sect.... In PAGE 11: ...hat they satisfy the criteria in Sect. 2.2. For each Tuples(E; g) : (i) calculate the set of output values OV where each value is assigned to undefined variables by the synchronization. (ii) for each Ei 2 E and each v 2 OV, calculate the set of transitions Ai where each transition satisfies the synchronization conditions in Table1 with v; and compose a rendezvous indication of the tuple hE; (A1; ; Am)i. (iii) If Ai includes both input (g?) and output (g!) transitions, we divide such a ren- dezvous indication hE; (A1; ; Am)i to hE; (A1; ; Ain i ; ; Am)i and hE; (A1; ; Aout i ; ; Am)i so that each Ain i (Aout i ) includes only input (output) transitions.... ..."

### Table 7. Conditions on the synchronization function. Here ; 0; 00 2 CA.

"... In PAGE 9: ...able 8. Axioms for synchronous cooperation with blocking. Atomic actions and concurrent actions Like [8], we assume a xed but arbitrary set AA of atomic actions (tau 2 AA), a xed but arbitrary set CA AA of concurrent actions, and a xed but arbitrary synchronization function j : CA CA ! CA satisfying that: { tau 2 AA; { for an action 2 CA if and only if 2 AA or there exist 0; 00 such that = 0j 00; { for an action 2 CA there is a boolean value ? stating that is independent or blocked. Hence, each concurrent action can be reduced to one of the following form: { a with a 2 AA; { a1j : : : jan with a1; : : : an 2 AA for n gt; 1; The axioms for concurrent actions are given in Table7 . We assume that the independence of a concurrent action and its reply depend only on its last atomic action.... ..."

### Table 4: Number of test sections classi ed as reference condition using the FFT of the synchronous avaerage

"... In PAGE 11: ... When extra noise is introduced, the system also fails to discriminate between the normal condition and the outer race fault. In Table4 , the number of test sections classi ed as belonging to each condition using the FFT of the synchronous average as a feature vector, is shown. Here the classi cation is 100% successful, indicating that there is enough information in the average, even with the second-order features such as the periodic random impulses removed, to discriminate between the four conditions.... ..."

### Table 2: Conditions for synchronization obtained using di erent methods. the condition obtained using the last technique is too restrictive. What we gain is the robustness of synchronization. If local transversal Lyapunov exponents are everywhere negative then we are sure that in the neighborhood of the synchronization subspace the trajectory is attracted to this subspace. 5 SYNCHRONIZATION OF HYPERCHAOTIC CIRCUITS IN THE PRESENCE OF NOISE As a second example let us consider a four{dimensional electronic circuit [13] de ned by the following state equation:

"... In PAGE 7: ... In this case noise of a small amplitude will not in uence the synchronization behavior (synchronization is robust). In Table2 we collect conditions for synchronization obtained using three di erent techniques. It is evident that the method based on local transversal Lyapunov exponents gives the condition stronger than two other methods.... ..."

### Table 7. Blocks and synchronization

1999

"... In PAGE 21: ...Statements Table 6 contains the rules for expression statements, skip and conditional state- ments. Table7 contains the rules for blocks and synchronization. The statements for control manipulation (return and exception try) are treated in Section 3.... ..."

Cited by 25

### Table 8. Blocks and synchronization

1999

"... In PAGE 21: ...Statements Table 7 contains the rules for expression statements, skip and conditional state- ments. Table8 contains the rules for blocks and synchronization. The statements for control manipulation (return and exception try) are treated in Section 3.... ..."

Cited by 25

### Table 1: Degree of Scattering for DPI(Dynamic Programming Interface), Portable Interceptor(PI), Error Handling, Pre/Post Condition Checking, Logging, Synchronization, and all the aspects combined

2003

"... In PAGE 4: ... The degree of scattering is measured for both Vendor Code Space (VCS)6 and Complete Code Space (CCS). All results are reported in Table1 . Result Analysis provides a brief analysis of the mining data.... In PAGE 5: ... We use AMTEX to combine the individual results, which yields some statistical information that illustrates the scattering in CORBA platforms from a slightly different an- gle. The Table1 shows, in all of the three CORBA imple- mentations, more than 50% of the classes are crosscut by at least one aspect. 10% to 15% of the classes contain three or more aspects.... ..."

Cited by 46

### Table 4: Behavior expression with some exclusive synchronizations

2001

"... In PAGE 14: ... Therefore, we have adopted a policy making multiple groups of threads to evaluate the synchronization conditions in parallel and to select the synchronization of the group which finished the negotiation earlier than the other groups. Below, we explain our algorithm using an example in Table4 . In our technique, the processes F1, F2, F3 and F4 are mapped to different threads and invoked in parallel.... ..."

Cited by 3