  It is known [DemriSchnoebelen02] that both satisfiability and model-checking
problems for propositional Linear-time Temporal Logic, LTL, with only a single
propositional variable in the language are PSPACE-complete, which coincides
with the complexity of these problems for LTL with an arbitrary number of
propositional variables [SislaClarke85]. In the present paper, we show that the
same result can be obtained by modifying the original proof of SPACE-hardness
for LTL from [SislaClarke85]; i.e., we show how to modify the construction from
[SislaClarke85] to model the computations of polynomially-space bound Turing
machines using only formulas of one variable. We believe that our alternative
proof of the results from [DemriSchnoebelen02] gives additional insight into
the semantic and computational properties of LTL.
