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4.2 The Word Game

The Norwegian logician and mathematician Axel Thue [12] devised "The Word Problem" as an exercise in logic. Consider a set of rules used to determine equality between two words formed  from a finite alphabet. Following is a set of such rules:

EAT    =       AT

ATE    =       A

LATER =       LOW

PAN    =       PILLOW

CARP   =   ME

With these rules we can deduce equality between the words LAP and LEAP through the following derivations: LAP = LATEP = LEATEP = LEAP

Consider the words CARPET and MEAT. These words are unequal. How can we say that? It's simple. Sum of the numbers of A's, M's and W's in any member of the equality list remains the  same. It is 1 for CARPET, whereas 2 for MEAT. This method for deciding inequality may not work for some other pair of words. In general, there is no obvious algorithm to decide when two  words are unequal. To determine if another word pair is unequal we would invent another method using our intelligence.