### Table 1 Upper bounds for string matching without transposition invariance Distance Distance evaluation Searching

"... In PAGE 8: ... For the simpler distances, on the other hand, our only solution is to evaluate them at every text position. Table1 gives a simplified list of upper bounds that are known for these problems without transposition invariance. Table 2 gives the achieved upper bounds for the transposition invariant versions of these problems.... ..."

### Table 2 Our upper bounds for transposition invariant string matching Distance Distance evaluation Searching

"... In PAGE 8: ... Table 1 gives a simplified list of upper bounds that are known for these problems without transposition invariance. Table2 gives the achieved upper bounds for the transposition invariant versions of these problems. We start by describing our solutions to the edit distances, since they are the main empha- sis of this paper.... ..."

### Table 1. The relations among randomness, stochasticity and approximations

### Table 1. Example of the transposition cipher key and encryption process

"... In PAGE 1: ... In this case, the message is broken into blocks of ten characters, and after encryption the seventh character in the block will be moved to position 1, the tenth moved character in the block will be moved to position 2, the forth is moved to position 3, the second to position 4, the eighth to position 5, the first to position 6, the fifth to the position 7, the ninth to the position 8, the sixth to the position 9 and the third to position 10. In Table1 shows the key and the encryption process of the previously described transposition cipher. It can be noticed that the random string quot;X quot; was appended to the end of the message to enforce a message length, which is a multiple of the block size.... ..."

### Table 7: Transposition time (seconds) for (block,block) distributions aInvariant code motion and some code transformations where performed by hand for this distribution

"... In PAGE 20: ... The column heads describe the distribution of the array dimensions: for instance c5c7 stands for (cyclic(5),cyclic(7)). Table7 show the (block,block) transposition time for various array arrangements, involving up to 16 proces- sors. These raw measures are analyzed in the next section.... ..."

### Table 7: Transposition time (seconds) for (block,block) distributions aInvariant code motion and some code transformations where performed by hand for this distribution

"... In PAGE 16: ... The column heads describe the distribution of the array dimensions: for instance c5c7 stands for (cyclic(5),cyclic(7)). Table7 show the (block,block) transposition time for various array arrangements, involving up to 16 proces- sors. These raw measures are analyzed in the next section.... ..."

### Table 2. IOInboxQCtl Invariants Inv Exact Approximate

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### Table 3. ReqDecode Invariants Inv Exact Approximate

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### Table 4. ReqService Invariants Inv Exact Approximate

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### Table 5. IOMiscBusCtl Invariants Inv Exact Approximate

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