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# Logic System Free Formula Analyzer

IP.com Disclosure Number: IPCOM000087503D
Original Publication Date: 1977-Feb-01
Included in the Prior Art Database: 2005-Mar-03
Document File: 2 page(s) / 60K

IBM

## Related People

Larson, LE: AUTHOR

## Abstract

This analyzer uses a combination of tables and heuristic algorithms to provide a means of substituting, simplifying, and reconstituting formulas.

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Logic System Free Formula Analyzer

This analyzer uses a combination of tables and heuristic algorithms to provide a means of substituting, simplifying, and reconstituting formulas.

The process consists of examining the formula, and decomposing the formula into simple formula having only one operator. Note that the simple formula may contain the results of other simple formula. Each simple formula is then compared to a table of substitutions. If the simple formula contains the results of a second simple formula, then the second simple formula becomes a part of the comparison as well. If the substitution applies, then its substituted formula replaces the original simple formula. The processing required is outlined in the high level flowchart of Fig. 1. An example of the table manipulations is presented in Fig. 2.

Since many of the logic systems to be processed are indeterminant (cannot be handled by truth tables), and since many of the substitutions are identities (can be applied both ways), a set of heuristic algorithms are constructed which guide the processor toward productive conclusions. The algorithms provided are:
1) Substitution Examination - Simplification processes applied uniformly to each simple statement eliminate the possibility that later substitutions can be applied and achieve the goal more quickly. This algorithm chooses which simple statements will be examined for potential substitutions. 2) Parenthetical Expression - Some substitutions apply irr...