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algorithm array binary operation Boolean algebra Boolean expression Boolean matrices called code word complement compute congruence relation Consider construct corresponding coset cycle decoding defined denoted determine digraph encoding function equivalence relation Example 1 Let Example 11 EXERCISE SET Figure finite set finite-state machine graph group G Hasse diagram homomorphism input integer isomorphic labeled language lattice Let G loop lower bound mathematical induction matrix monoid Moore machine normal subgroup number of l's offspring ordered pairs partial order partition path of length permutation poset positive integer Proof prove pseudocode quotient real numbers recursive reflexive regular expression result Section semigroup sequence shown in Fig Solution steps string subgroup of G SUBROUTINE subset subtree Suppose symbol symmetric relation syntax diagram Theorem topological sorting transitive true truth table upper bound variables vertex vertices