ass2_monoids

# ass2_monoids - M 1 3 Let M 2 = h a,b | aa = ε,bb = ε,bab...

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MATH 335 001 Computational Algebra Winter 2006 Assignment 2.1. Monoids. 1) Let A = { a 1 ,...,a n } be a ﬁnite alphabet and A * the free monoid with basis A . For a given word u A * ﬁnd all solutions in A * of the equation xu = ux. 2) Let M 1 = h a,b | abab = ε,baba = ε i . Find a complete rewriting systems for the monoid M 1 . Is M 1 ﬁnite or inﬁnite? Are the words b 2 abab 3 aba and ababab 2 equal in
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Unformatted text preview: M 1 ? 3) Let M 2 = h a,b | aa = ε,bb = ε,bab = aba i . • Show that M 2 is ﬁnite. • Write down the multiplication table for M 2 . 4) Let M 3 = h a,b | aa = ε,bb = ε,babab = ε i . • Find a complete rewriting systems for the monoid M 3 . • What is the order (number of elements) of M 3 ?...
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