### Table 1 : Grace Abstract Operations

"... In PAGE 16: ... These objects are structured in a hierarchy under the object hierarchy for the conceptual model. The mapping process involves identifying which of the Grace primitives (as seen in Table1 ) are needed to perform the activity specific operations. A full description of the Help Desk specification and mapping can be found in (Benford et al 1991).... ..."

### Table 2 Grace Note Number Grace Note IOI (SD) Proportional Grace Note IOI (% of

"... In PAGE 16: ... For example, a proportional grace note IOI of 50% means that the grace note IOI is half as long as the local 8th note IOI. Table2 shows the mean inter-onset intervals and proportional equivalents for each grace note position across tempo blocks and repetitions. Insert Table 2 about here To determine the effects of local tempo and grace note position on the length of the grace notes an ANCOVA was calculated with proportional grace note IOI as a dependent variable, local 8th note IOI as a covariate (rather than taking tempo as a... In PAGE 16: ... Table 2 shows the mean inter-onset intervals and proportional equivalents for each grace note position across tempo blocks and repetitions. Insert Table2 about here To determine the effects of local tempo and grace note position on the length of the grace notes an ANCOVA was calculated with proportional grace note IOI as a dependent variable, local 8th note IOI as a covariate (rather than taking tempo as a... ..."

### TABLE 1 Average # of Graceful Transitions

### Table 1. Computing all solutions for graceful graphs.

### TABLE 2 Coefficients ri forExample2,whereA Must Be a Root of the Polynomial p.A/ in (5) n p2r0.n/ p2r1.n/ p2r2.n/

2000

### Table 2. Complexity of non-disjunctive QDLP Fragments for p 2 R

1999

"... In PAGE 11: ...and disjunctive quantitative programs are summarized in Table2 and 3, respectively. A box in the tables contains the complexity of the decisional problem given by the corresponding column header for the fragment of QDLP given by the corresponding... In PAGE 11: ...Table 2. Complexity of non-disjunctive QDLP Fragments for p 2 R The results in Table2 for the non-disjunctive fragments are valid for p 2 R. For both positive and stratified classes, all decisional QDLP problems, apart from p- Consistency which is O(1), are polynomial.... ..."

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### Table 5: De nition of conditional operator on RTTS (p 2 R 0, s 2 R, : R 0 ! B )

"... In PAGE 11: ... On the basis of these rules the conditional operator can also be directly de ned on real time transition systems in a straightforward way. In Table5 , the conditional operator is de ned on RTTS (A) in terms of this operator. Additionally, the operators introduced for conditions are de ned on B .... ..."

### Table 13: De nition of discretization (a 2 A , p 2 R 0, s 2 R)

"... In PAGE 20: ... Discrete time processes can be viewed as real time processes that are discretized. We de ne the notion of a discretized real time process in terms of the auxiliary discretization operators D : P ! P and D : B ! B of which the de ning axioms are given in Table13 . In [6], discretization is also de ned... ..."