### Table 9: Translating equivalences

in Abstract

"... In PAGE 11: ... call these signatures unitary, except they sur- prisingly exclude singletons. Table9 in the appendix translates notions of equivalence. Remarkably, 26 proof rules in the Dreyer-Crary-Harper lan- guage are handled by just 3 translation rules.... ..."

### Table 1: Translating Equivalences into Rewrite Rules

"... In PAGE 11: ... We can compute APB4CPB5 directly for all CP BE BT using finite-state model checking; however, the time and space required to calculate APB4CPB5 explicitly grows polynomially at best and exponentially in general with the length of CP, which motivates our use of this indirect approach. In our previous paper we proposed a set of rewrite rules (called reductions in that context); Table1 presents these roughly as they were there presented, and then translated into rewrite rules as we have defined them in Section... ..."

### Table 1: Translating Equivalences into Rewrite Rules

"... In PAGE 11: ... We can compute APB4CPB5 directly for all CP BEBTusing finite-state model checking; however, the time and space required to calculate APB4CPB5 explicitly grows polynomially at best and exponentially in general with the length of CP, which motivates our use of this indirect approach. In our previous paper we proposed a set of rewrite rules (called reductions in that context); Table1 presents these roughly as they were there presented, and then translated into rewrite rules as we have defined them in Section... ..."

### Table 1. The translation equivalents matrix (EQ matrix)

### Table 1. Categories of relation words and typical elements.

"... In PAGE 3: ... We define an other cate- gory for relation words that cannot be classified in the above 18 categories. Table1 shows the 18 categories and typical elements. 3.... ..."

### Table 5. System Performance according to Number of Translation Equivalents

2002

"... In PAGE 6: ... Hence, the performance of system need to be eval- uated according to the number of translation equiva- lents. Table5 shows the results. Table 5.... In PAGE 6: ...In Table5 , best one denotes selecting only one translation equivalent per English query term, best two two translation equivalents, and all all possible translation equivalents. We can observe that choos- ing the best one translation equivalent for each English query term is desirable.... ..."

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