On equations including string variables

S-equations are of the form E1(x1,..., xk) ⊇ E2 (X1,...,xk) where E1 and E2 are shuffle expressions having two types of symbols; variables and constants. E1⊇E2 is said to be S-satisfiable if the language expressed by E1(α1,...,αk) includes the language expressed by E2(α1,...,αk) where α1,...,αk are some strings of constants. A wide range of problems in string manipulation, data bases, etc., can be described in terms of S-equations. Major results include the solvability and complexity of several classes of S-satisfiability problems.