Leaf languages and string compression

Tight connections between leafs languages and strings compressed via straight-line programs (SLPs) are established. It is shown that the compressed membership problem for a language L is complete for the leaf language class defined by L via logspace machines. A more difficult variant of the compressed membership problem for L is shown to be complete for the leaf language class defined by L via polynomial time machines. As a corollary, it is shown that there exists a fixed linear visibly pushdown language for which the compressed membership problem is PSPACE-complete. For XML languages, it is shown that the compressed membership problem is coNP-complete. Furthermore it is shown that the embedding problem for SLP-compressed strings is hard for PP (probabilistic polynomial time).

• Type: Conference
• Year: 2008
• Where: FSTTCS
• Authors: Markus Lohrey
• Keywords: FSTTCS 2008, Leaf Language Class, Membership Problem, Polynomial Time, Software Engineering