### Table 1. Timed automata for L

"... In PAGE 6: ... But it can be straightforwardly proven by induction on the depth of the proof tree taking into account that if ; 0 2 (C) then ^ 0; _ 0 2 (C). Rules in Table1 capture the behaviour above described in terms of timed automata. In particular, it deserves to notice that a process p + q can idle as long as one of them can.... In PAGE 6: ... For instance, consider the term p (x 2) (fjxjg (x = 1)7!a; stop). Clearly, x is free in the invariant (x 2), however, using rules in Table1... In PAGE 8: ...-; @; ) where -, @ and are de ned as the least set satisfying rules in Table1 and rules in Table 2. u t Table 2.... ..."

### Table 1: Timed automata for L

1996

"... In PAGE 8: ...3 (Associated timed automaton) Let p 2 L. ncv, the predicate of non-con ict of variables is de ned inductively according to rules in Table1 . For all process p such that ncv(p) the timed automaton associated to p is de ned by [[p]]T = (L; A; C; p; - ; @; ) where -, @ and are de ned as the least sets satisfying the rules of Table 1.... In PAGE 10: ... But it can be straightforwardly proven by induction on the depth of the proof tree taking into account that if ; 0 2 (C) then ^ 0; _ 0 2 (C). 2 Rules in Table1 capture the behaviour described in Section 3.1 in terms of timed automata.... In PAGE 10: ... For instance, consider the term p (x 2) (fjxjg (x = 1)7!a; stop). Clearly, x is free in the invariant (x 2), however, using rules in Table1 , we derive @(p) = (x 2) and (p) = fxg. Thus, according to De nition 2.... In PAGE 11: ... De nition 3.6 (Associated timed automaton) Let E be a recursive speci cation such that ncv(E) holds according to rules in Table1 and Table 2, i.... In PAGE 11: ...able 1 and Table 2, i.e., E does not have con ict of variables. The timed automaton associated to p 2 Lv is de ned by [[p]]T = (L; A; C; p; -; @; ) where -, @ and are de ned as the least set satisfying rules in Table1 and rules in Table 2. 2 Table 2: Timed automata for recursion The following rules are de ned for all X = p 2 E ncv(X) ncv(p) ncv(X = p) 8X = p 2 E: ncv(X = p) ncv(E) (p[p=X]) = C (X) = C @(p[p=X]) = @(X) = p[p=X] a; - p0 X a; - p0 De nition 3.... ..."

Cited by 48

### Table 3. XPath Queries

2004

"... In PAGE 9: ...3. Queries The XPath queries listed in Table3 were tested in our ex- periments. These queries have different characteristics in terms of selectivity, presence of values and twig structure.... In PAGE 10: ...4. Performance Analysis In Figure 6 we summarize the performance results in total time elapsed for the queries listed in Table3 . We first discuss the benefits of PRIX over ViST.... In PAGE 11: ... TwigStackXB uses XB-Trees to skip nodes in the sorted input stream. Note that for all the queries in Table3 that we tested, TwigStack performed worse than TwigStackXB. Table 7 shows the performance results for TwigStack and TwigStackXB for the DBLP dataset.... ..."

Cited by 26

### Table 3: XPath Queries

2004

"... In PAGE 20: ... 7.3 Queries The XPath Queries listed in Table3 were tested in our experiments. These queries have different character- istics in terms of selectivity, presence of values and twig structure.... In PAGE 20: ... These queries have different character- istics in terms of selectivity, presence of values and twig structure. Table3 also shows the number of twig... In PAGE 21: ... 7.4 Performance Analysis In Figure 9 we summarize the performance results in total time elapsed for the queries listed in Table3 . We first discuss the benefits of PRIX over ViST.... In PAGE 23: ... TwigStackXB uses XB-Trees to skip nodes in the sorted input stream. Note that for all the queries in Table3 that we tested, TwigStack performed worse than TwigStackXB. As an example, Table 7 shows the performance results for TwigStack and TwigStackXB for the DBLP dataset.... ..."

Cited by 26

### Table 1: Stochastic automata for

"... In PAGE 5: ...smallest relation satisfying the rules in Table1 . The function F is de ned by F(xG) = G for each clock x in p.... ..."

### Table 1: Stochastic automata for

"... In PAGE 5: ...smallest relation satisfying the rules in Table1 . The function F is de ned by F(xG) = G for each clock x in p.... ..."

### Table 3 Configuration of XPath Generator

"... In PAGE 22: ...Table 3 Configuration of XPath Generator Having set the values of the parameters as shown in Table3 , we generated sets of 100, 300, 1,000, 3,000, and 10,000 queries (the ratio of increase is approximately 3) to test the scalability of the Query Evaluators of XTREAM and its enhancement. In addition, to evaluate the performance of XTREAM with those of other existing streaming XML data processors, XMLTK and XSQ, we chose several types of queries from synthetically generated XPath queries.... ..."

### Table 1. The tree automata A, B, and C.

"... In PAGE 7: ...utomata share no other states. Hence L(Gnv) = !k Rnv. The recognizability of !k Rs is obtained by replacing B by the tree automaton C that accepts in state i all terms. ut Table1 shows the tree automata A, B, and C used in the proof of the above lemma for the following TRS R: 1: f(g(x); a) ! f(h(h(x)); x) 2: h(a) ! h(b) 3: h(f(x; b)) ! x The underlinings are to ensure that only states 1, 2, and 3 are shared between A and B (C). Consider the tree automaton A.... ..."

### Table 1. Stochastic automata for

1999

"... In PAGE 3: ...The set of edges ?! between locations is defined as the smallest relation satisfying the rules in Table1 . The func- tion F is defined by F(xG) = G for each clock x in p.... In PAGE 6: ... Since in our semantics (cf. Table1 ) a location corre- sponds to a term, simulation can be carried out on the ba- sis of expressions rather than using their semantic repre- sentation. This means that the stochastic automaton is not entirely generated a priori but only the parts that are re- quired to choose the next step.... In PAGE 6: ...erm pi (i.e. location) and the input specification E. From term pi the set of clocks (pi) to be set is determined (by module (A) in Figure 1) and the set of possible next edges is computed according to the inference rules of Table1 (by module (B)). To compute the next valuation we only need to keep track off the last valuation vi.... ..."

Cited by 9