MIT 6 871 - Lecture notes (5 pages)

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Lecture notes



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Lecture notes

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Lecture Notes


Pages:
5
School:
Massachusetts Institute of Technology
Course:
6 871 - Knowledge-Based Applications Systems

Unformatted text preview:

MACSYMA Symbolic Mathematics The Spirit Of The Undertaking Origins In Macsyma And Dendral Goals of the Project System Description Lessons 6 871 Lecture 3 6 871 Lecture 3 Goals of Project Symbolic Mathematics AI Approaches To help applied mathematicians in solving problems x4 1 x 5 2 2 6 871 Lecture 3 4 SAINT Symbolic Automatic Integrator x 6 871 Lecture 3 2 5 2 sin 4 y dy cos 4 y three possible ways to deal with this z4 dz 1 z2 1 1 z 2 dz 1 z2 sin 4 y dy cos 4 y 5 dx Try y arcsin x yielding Slagle SAINT Moses SIN Moses and Martin MACSYMA Reduce II Mathematica Matlab tan 4 ydy 4 1 x 2 z cot 4 ydy z4 32 1 z 1 z 2 2 4 dz from z tan y z dz z 4 1 z 2 z3 dz 3 1 z2 try w arctan z 1 arcsin x tan arcsin x tan 3 arcsin x 3 6 871 Lecture 3 6 6 871 Lecture 3 13 1 SAINT SAINT Steps 26 standard forms 1 step solutions tables 8 Algorithmic transforms eg sum of integrals 10 Heuristic transforms of which derivative divides is the most successful Goals evaluated on depth of integrand Ex xe x 2 is of depth 3 6 871 Lecture 3 Worked like the average engineer i e lots of search and backtracking Conceived of in terms of search worked because of that The power comes from 14 Problem decomposition Methodical exploration of alternatives Looking far wide and deep Speedy tree construction search backtracking Success is just a matter of trying enough alternatives 6 871 Lecture 3 SAINT The Mindset Shift SAINT will frequently need to explore several paths to a solution because it lacks the powerful machinery that SIN possesses One of the striking features of these programs is how little knowledge they require in order to obtain a solution Persson in his recent thesis dealing with sequence prediction seems to feel that placing a great deal of context dependent information in a program would be cheating This emphasis seems to be useful when one desires to study certain problem solving mechanisms in as pure a manner as possible We on the other hand intended no such study of specific problem solving



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