### Table 1 Synchronization constraints and the boolean signal evaluation

"... In PAGE 10: ... Therefore, any signal A can be associated its clock a2, and two synchronous signals A and B satisfy a2 = b2. Table1 shows how the programs are transformed into polynomial equations (we refer to [LBBLG91] for more details), leading to an ILTS models semantics. Nevertheless, the delay operator $ deserves some additional explanations.... In PAGE 11: ...Table 1 Synchronization constraints and the boolean signal evaluation The translation of Table1 is automatically performed by the Signal compiler. The automata semantics can then be used as a basis for the veri cation of Signal programs.... ..."

### Table 1 Synchronization constraints and the boolean signal evaluation

"... In PAGE 10: ... Therefore, any signal A can be associated its clock a2, and two synchronous signals A and B satisfy a2 = b2. Table1 shows how the programs are transformed into polynomial equations (we refer to [LBBLG91] for more details), leading to an ILTS models semantics. Nevertheless, the delay operator $ deserves some additional explanations.... In PAGE 11: ...Table 1 Synchronization constraints and the boolean signal evaluation The translation of Table1 is automatically performed by the Signal compiler. The automata semantics can then be used as a basis for the veri cation of Signal programs.... ..."

### Table 1 shows how all the primitive operators are translated into polynomial equations. Remark that for the non boolean expressions, we just translate the synchronization between the signals. Boolean expressions

1999

"... In PAGE 10: ... Table1 . Translation of the primitive operators.... ..."

Cited by 8

### Table 1: From Signal operators to boolean equations Free conditions: Due to some distributivity properties of the operators when, default, and (on boolean-valued signals) and or, the expressions when C and when(not C) can be rewritten as intersection and union of clocks. If a clock when C cannot be rewritten, the boolean C is said to be a free condition. The rewriting rules are not enumerated here; they can be found in [5]. Example: If A and B are two synchronous boolean signals, the boolean signal C = A and B is not a free condition for, the clocks when C and when (not C) can be rewritten as:

1994

Cited by 12

### 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 table = (Table) list[0]; // External Object try f // Rotate to the left to the loading angle. table.left(); table.angle().waitValue(POS FEEDBELT); table.stop h(); // Move table down to the loading high. table.downward(); table.down().waitValue(Boolean.TRUE); table.stop v(); // Inform feed belt that table is ready. waitTable.synchronize();

1999

### 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.... ..."

### lable: boolean);

in Simple and Integrated Heuristic Algorithms for Scheduling Tasks with Time and Resource Constraints

1987

Cited by 21