Syntactic semigroups of avoided languages (Q1272006)

Let \(L\) and \(\Lambda\) be languages over alphabets \(A\) and \(\Sigma\), respectively. The author considers a language \(L\) of the shape ``\(L\) avoids \(\Lambda\)'', more presicely, the syntactic semigroup \(S_L\) of the language \(L\) of all binary strongly cube-free words. The main result is a solution of the word problem in \(S_L\); i.e., given an arbitrary pair of words in \(A\), decide whether they represent the same element of \(S_L\) (whether this pair belongs to the syntactic congruence of the language \(L\)).