### Table 1. Symbolic Interpretation of Reachability Logic

1995

"... In PAGE 11: ...Table 1. Symbolic Interpretation of Reachability Logic To read the rules of Table1 some notation needs to be explained. For D aconstraintsystemandra set of variables (to be reset) r(D) denotes the set of variable assignments fr(v) j v 2 Dg.... In PAGE 12: ...directed graphs (with clock and data variables as nodes), these operations as well as testing for inclusion between constraint systems may be e ectively im- plemented in O(n2)andO(n3) using shortest path algorithms [11, 12, 6]. Now, by applying the proof rules of Table1 in a goal directed manner we obtain an algorithm (see also [13]) for deciding whether a given symbolic network con guration [l;D] satis es a property 93 . To ensure termination (and e ciency), we maintain a (past{) list L of the symbolic network con gurations encountered.... ..."

Cited by 117

### Table 2. CHR program with function terms after constraint symbol specialization

2007

"... In PAGE 8: ... Example 6. Table2 shows the program from Table 1(a) attened using con- straint symbol specialization: lines 2-4 and 5-7 encode, resp., the attening and un attening functions; line 8 implements attening corrspondence ; whereas lines 9-16 show the attened rules of the original program (the rules in lines 9-11 (resp.... ..."

### Table 1. Symbolic Interpretation of Reachability Logic

1995

"... In PAGE 9: ...Table 1. Symbolic Interpretation of Reachability Logic To read the rules of Table1 some notation needs to be explained. For D a constraint system and r a set of variables #28to be reset#29 r#28D#29 denotes the set of variable assignments fr#28v#29 j v 2 Dg.... In PAGE 10: ...directed graphs #28with clock and data variables as nodes#29, these operations as well as testing for inclusion between constraint systems may be e#0Bectively im- plemented in O#28n 2 #29andO#28n 3 #29 using shortest path algorithms #5B11, 12, 6#5D. Now, by applying the proof rules of Table1 in a goal directed manner we obtain an algorithm #28see also #5B13#5D#29 for deciding whether a given symbolic network con#0Cguration #5B l; D#5D satis#0Ces a property 93#0C.To ensure termination #28and e#0Eciency#29, we maintain a #28past#7B#29 list L of the symbolic network con#0Cgurations encountered.... ..."

Cited by 9

### Table 2: BAT Results with Manually Optimized Ordering

2002

"... In PAGE 9: ... After enough effort, we were able to find a good ordering that allows symbolic simulation to run. Table2 shows the results. In this sequence of experiments, we were able to complete the assertion check without using any constant logic values to simplify the assertion.... In PAGE 9: ... In this sequence of experiments, we were able to complete the assertion check without using any constant logic values to simplify the assertion. By comparing the results in Table 1 and in Table2 , we observe that variable ordering sig- nificantly impacts the performance of symbolic simulation. For the OBDD sizes, we show two types of data: the total number of OBDD nodes at the end of symbolic simulation (to- tal OBDD nodes), and the maximum number of OBDD nodes during the symbolic simulation (max OBDD nodes).... ..."

Cited by 1

### Table 5: Relating database and logic programming terms.

2001

"... In PAGE 16: ... The logic programming school in deduc- tive databases [32] argues that deductive databases can be effectively represented and implemented using logic and logic programming. Table5 relates the basic deductive database [53] and logic programming [32] terms. Notice that in Table 5 a definition of a predicate is introduced as a set of ground facts.... In PAGE 16: ... Table 5 relates the basic deductive database [53] and logic programming [32] terms. Notice that in Table5 a definition of a predicate is introduced as a set of ground facts. In general, of course, a predicate definition is a set of program clauses with the same predicate symbol (and arity) in their heads.... ..."

Cited by 29

### Table 2: Transformation Table for Functional Logic Programming.

"... In PAGE 11: ... fib(1,1). 2 PAGE can model this programming paradigm introducing a new transformation table ( Table2 ) which is used in conjunction with the tables used for the LP paradigm. Now we consider that functional arguments have the same notational signi cance as the previously seen ordinary variables.... In PAGE 11: ... Functional arguments are prioritized in the uni cation procedure (the uni cation procedure becomes matching procedure since we are dealing with interpreted functional terms), so that when we have to unify a variable argument which is in the argument list of a functional argument we prefer to unify the latter and discard the former. This can easily be seen in Table 3, where the equivalent AG is given after the use of transformation Table 1 in conjunction with the transformation Table2 . Fig.... In PAGE 12: ....4.1. Multi-pass execution (simple case) The method described so far ( Table2 is used) is operationally incomplete when the minimal elements in the partial ordering induced by the generated dependency graph are unbound (for instance some of the arguments in the argument list of a functional argument are unbound). In such cases, a delayed binding mechanism has to be used.... In PAGE 12: ... 6 we can see the dependency graph for the equivalent AG corresponding to Table 5 generated after the the use of Table 1 in conjunction with Table 4. Here, we do not have functional arguments and so we do not apply the transformation Table2 . Arrows corresponding to Table 1 are designed with solid lines, while arrows corresponding to Table 4 are designed with dashed lines.... In PAGE 15: ...he new inherited attribute). This is shown in Fig. 5 with the dashed lines. 2 It is noteworthy that the same behaviour is possible if we supply the FLP tranformation table ( Table2 ) with extra transformation actions, simulating this way the constraint solver. However, that actions are problem depented and they do not t in a declarative way of programming.... ..."

### Table 3: Oz and Prolog Concurrent logic programming Oz

1998

"... In PAGE 32: ... A.3 Oz and Prolog There is a strong sense in which Oz is a successor to Prolog (see Table3 ). The Oz system can be used for many of the tasks for which Prolog and constraint logic programming are used today [16, 21, 12, 24].... ..."

Cited by 1

### Table 2: Logic Symbols

"... In PAGE 13: ...resented in Sec. 4.6). 4.5 Formulas Table2 lists the built-in logic symbols for constructing formulas. Formulas in Pure Prefix Form.... ..."

### Table 2: Logic Symbols

2003

"... In PAGE 13: ...resented in Sec. 4.6). 4.5 Formulas Table2 lists the built-in logic symbols for constructing formulas. Formulas in Pure Prefix Form.... ..."

### Table 3: The transition system specialised for open bisimulation

"... In PAGE 20: ... Intuitively, M collects the conditions indispensable for the action to re. In other words, M de nes the \minimal quot; substitution M which would allow P to use ; Examples of transitions are [a = b] : P ([a=b]; ) P and ( [a = b] ca: P1) j (d(x): P2) ([a=b][c=d]; ) P1 j P2fa=xg The new transition system is presented in Table3 . Its composite actions (M; ) are ranged over by .... In PAGE 20: ...quates more than , i.e. (a) = (b) implies (a) = (b). Note that, in Table3 , if P (M; ) P0, then no name bound in appears in M. The bisimulation which we de ne on the new transition system and which we shall prove to coincide with is nearly a ground bisimulation.... ..."