  We consider the quantifier alternation hierarchy within two-variable
first-order logic FO^2[<,suc] over finite words with linear order and binary
successor predicate. We give a single identity of omega-terms for each level of
this hierarchy. This shows that it is decidable for a given regular language
and a non-negative integer m, whether the language is definable by a formula in
FO^2[<,suc] which has at most m quantifier alternations. We also consider the
alternation hierarchy of unary temporal logic TL[X,F,Y,P] defined by the
maximal number of nested negations. This hierarchy coincides with the
FO^2[<,suc] alternation hierarchy.

Logic in Computer Science;Formal Languages and Automata Theory