We compare the asymptotic time complexity of left-to-right and bidirectional parsing techniques for bilexical context-free grammars, a grammar formalis an abstraction of language models used in several state-of-the-art real-world parsers. We provide evidence that left-to-right parsing cannot be realised within acceptable time-bounds if the so called correct-prefix property is to be ensured. Our evidence is based on complexity results for the representation of regular languages.