Computing the Homology of the Lambda Algebra by Martin C. Tangora PDF

By Martin C. Tangora

ISBN-10: 0821823388

ISBN-13: 9780821823385

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Gimpel offers programs which take an applications program like ours and run it while counting the number of times each statement is executed (frequency profile) or the amount of execution time used by each statement in the program (time profile). These programs were applied to several versions of our working lambda-algebra programs. The frequency profile and the time profile gave essentially the same information, and the time profile was slower to run (about 35 times the normal execution time, as opposed to 12 times) so we dropped the time profile and worked with the frequency profile.

For short demonstration runs only the first output stream is important, and it is the only one retained in the sample program. • Choice of algorithm. 5 above). 8 below). impractical to retain full tags. ) In our preliminary report [37] we described an algorithm which is a compromise, in that it uses shortcuts as much as possible, but when a full tag or a complete cycle is needed further along, it is recalculated and then stored for possible future reference. This was successfully programmed but did not offer any important advantages over the LTO program, and was more costly in storage.

The largest degree t which we finished was t=48 with about 45,194,000 odd-ending admissible monomials. 11558E+26 <2«il« Euler characteristic check. 4), and likewise the same as the parity of the number of "stable survivors," or elements in the minimal basis for the cohomology of the Steenrod algebra. This MARTIN C. , the monomials disappear two by two. 12 can be used as a crude check on the number of survivors in each t in, say, Table 1. We can thus be confident that if we have made any mistakes, we have made an even number of them.

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Computing the Homology of the Lambda Algebra by Martin C. Tangora

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