### Table 4: Data structure for non-deterministic pairs of transition

1996

"... In PAGE 18: ... A pairwise comparison of all parallel transitions can assure determinism: If no two tran- sitions con ict, then the model is deterministic. Table4 and 5 outline the data structures and algorithm used for this analysis. The pairwise comparison of all transitions existing in parallel and triggered by simulta- neous events is potential costly; in the worst case (all transitions are parallel), the algorithm requires O(n2) comparisons (where n is the number of transitions in the model).... ..."

Cited by 95

### Table 1. Execution of the non-deterministic automaton in Figure 7

2006

"... In PAGE 19: ...ig. 8. Execution of a non-deterministic automaton. Table1 shows the execution of the automaton shown in Figure 7 (b). At the beginning, the set of possible states contains all initial states, which is in this case fp1g.... ..."

Cited by 16

### Table 1.1: Nondeterministic to deterministic automaton conversion by the tabular method.

1995

Cited by 12

### Table 3. Time (in sec) for Invariant Checking on the Industrial Circuits using the non-deterministic and the deterministic program

"... In PAGE 10: ...e. Table3 (b). However, the performance of the deterministic program is better than the non-deterministic version in the hard circuits in Table 3 (a).... In PAGE 10: ...he deterministic program in the simple circuits, i.e. Table 3 (b). However, the performance of the deterministic program is better than the non-deterministic version in the hard circuits in Table3 (a). Therefore, we strongly prefer the deterministic version to the non-deterministic version.... ..."

### Table 5.2: SmartState Semantics Model Rose RT Optimizied Deterministic Deterministic Nondeterministic

### Table 4: Comparison of non-deterministic Algorithm 1 with the deterministic social law presented in [4]:

### Table 2. The inference rules for PC. y0 are xed and all di erent. 3.3 Power to Simulate 2-Counter Machines The rst (and weakest) form of universality that we consider is that a process calculus has the expressive power of 2-counter machines (or, equivalently, Turing machines) in the sense that, for each n, we can exhibit a term U2CM n whose process graph simulates in lock step a universal 2-counter machine on input n. Calculi like CCS, CSP, ACP, and Meije are all universally expressive in this sense. Actu- ally, trying to code a 2-counter or Turing machine in each of these languages is a nice way to get familiar with them. Via a rather tricky encoding, we prove below that also PC has the power of 2-counter machines.1 Theorem 3.8 PC has the expressive power of 2-counter machines. Proof Suppose that a universal 2-counter machine has code of the form l1:

1993

"... In PAGE 11: ... It is also possible to view this operator as a special case of the action re nement operator as studied by Goltz and Van Glabbeek [17]: r re nes an action a into the nondeterministic sum of the actions in fb j r(a; b)g. The inference rules of PC are presented in Table2 . In the table a and b range over A,... ..."

Cited by 19

### Table 1: Summary of complexities of planning with multi- ple initial states, deterministic or non-deterministic opera- tors, and different degrees of observability.

"... In PAGE 9: ... Sets Lprime this small suffice because all operators are deterministic, and after any number of actions, independently of how the plan has branched, the sum of the cardinalities of the possible belief states is not higher than the number of initial states. square Summary The complexities of the problems discussed in this paper are summarized in Table1 and the corresponding theorems showing hardness and membership are listed in Table 2. Restriction to only one initial state affects the determinis- tic unobservable and partially observable planning problems only: they both come down to PSPACE from EXPSPACE.... ..."