### Table 1. Average execution time in ms of the algorithm for derivations defined by dense polynomials (100 derivations for each degree)

"... In PAGE 10: ...entium 4 HT processor of 2.8 GHz, with 512 MB of primary memory. The first test we performed calculated the average time taken by the algorithm to show that a generic derivation of a given degree, defined by a pair of randomly chosen dense polynomials does not have an algebraic solution. Table1 summarizes the output of a program that randomly generates 100 pairs of dense polynomials for each degree and computes the average CPU time taken to check that the deriva- tion defined by each of the pairs does not have an algebraic solution. In this first test, none of the derivations tested caused the algorithm to fail.... ..."

### Table 1. Axioms for the algebraic theory of the language

"... In PAGE 14: ...1. The axioms for the algebraic theory of the language are given in Table1 . In the de nition we assume ADSeq(d), ADSeq(di), ASeq(w) and ASeq(wi) for i = 1; 2.... In PAGE 14: ... Note that we do not have an axiom x+y = y +x. This equality is derivable using the axioms in Table1 , in particular, Axiom 1. The axioms in the above de nition are not su cient to prove equality of programs like ha; b; ci and ha; hb; cii.... ..."

### Table 1. Additional algebraic operators Operator Description

2000

"... In PAGE 3: ... Our extended relational algebra includes the basic relational algebra operators select ( ), project ( ), cross-product ( ), natural join (1), union ([), and di erence (?), which we do not elaborate on here; see [Ullman 1989]. The rst two lines of Table1 present useful operators derived from the basic operators, while the next three lines present additional operators that we use. In the table, X and A denote attributes, B, A1, and A2 denote attribute lists, a is an aggregate function, and expr... In PAGE 4: ...The A operator, which computes aggregate functions (e.g., max, min, avg, sum, count) over partitions of E E is a unary operator applied to a relational expression E producing a result with schema schema(E)[fXg. Recall from Table1 that the E operator is expressed as: E[X = expr]E expr is an expression evaluated over each tuple t of E (a conventional expression involving attributes of t and constants) yielding one value for each tuple; this value is entered into the new attribute X for each tuple of E. For details of similar operators see [Ceri et al.... In PAGE 4: ...perators see [Ceri et al. 1990]; examples are given in later sections. A is also a unary operator applied to a relational expression E producing a result with schema schema(E) [ fXg. Recall from Table1 that the A operator is expressed as: A[X = a(A); B]E B de nes a set of attributes on which the result of E is partitioned; each group in the... ..."

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### Table 1. LTS for Fusion

"... In PAGE 12: ... The proof relies on the de nition of three intermediate transition systems and their notions of bisimulation, which aim at modelling that fusion hyperequivalence is closed with respect to substitution. The rules of the rst transition system lts1 are similar to those given in Table1 for the fusion calculus. The only di erences derive from the fact that here the restricted name is assumed to be always x0.... ..."

### Table 6--Determinants of community-level variation in indices of variety diversity within crops in rainy season Pearl Millet Sorghum Minor millets Shannon Margalef Shannon Margalef Shannon Margalef Marginal effects

"... In PAGE 53: ... 48 Table6 --Mode of seed transactions for varieties grown in rainy season, by millet crop Pearl Millet Sorghum Finger Millet Little Foxtail Historical transactions Total Hybrid IOPV FV Total Hybrid IOPV FV Total IPLS FV Millet Millet Number of seed lots for varieties planted 165 95 46 24 381 201 38 142 192 131 59 77 25 Source (%) Gift 21 0 41 67 27 9 45 48 40 26 69 39 52 Aid 24 36 11 0 19 34 16 0 20 29 0 0 0 Purchase 55 64 48 33 54 57 39 52 40 45 31 61 48 Number of past seed replacements for varieties planted 165 95 46 24 339 201 28 110 183 123 60 24 25 Replacement (%) Gift 18 13 26 21 21 14 25 33 23 14 42 29 60 Aid 22 31 15 0 10 14 14 3 12 18 0 0 0 Purchase 61 57 59 79 69 72 61 65 65 68 58 71 40 Number of past seed transfers for varieties planted 18 0 0 18 189 59 18 113 125 67 57 36 25 Farmer Supply (%) Gift 78 0 0 78 75 76 61 77 78 94 60 64 56 Aid 0 0 0 0 4 0 28 3 0 0 0 0 0 Sales 22 22 21 24 11 20 22 6 40 36 44 See glossary for definition of terms. Gift denotes that seeds are exchanged among family and friends for money, but at less than the market price (termed token money quot;).... ..."