Contained in LOGCFL.
Strictly contains DCFL [Bra77] and indeed UCFL.
Defined in [Bra77], where it was also shown that 1NAuxPDAp strictly contains CFL and is strictly contained in LOGCFL. The class corresponds to the closure of CFL under one-way log-space reductions.
The class of languages accepted by deterministic pushdown automata.
Defined in [GG66], where it was also shown that DCFL is strictly contained in CFL, contained in UCFL, and strictly contains REG. The inclusion in UCFL is also strict.
The class of decision problems recognized by quantum context-free languages, which are defined in [MC00]. The authors also showed that QCFL does not equal CFL.
The class of context-free languages which can be represented by grammars where each word in the language has exactly one leftmost derivation.
Strictly contains Deterministic CFL. Strictly contained in CFL.