The paper is about a class of languages that extends context-free languages
(CFL) and is stable under shuffle. Specifically, we investigate the class of
partially-commutative context-free languages (PCCFL), where non-terminal
symbols are commutative according to a binary independence relation, very much
like in trace theory. The class has been recently proposed as a robust class
subsuming CFL and commutative CFL. This paper surveys properties of PCCFL. We
identify a natural corresponding automaton model: stateless multi-pushdown
automata. We show stability of the class under natural operations, including
homomorphic images and shuffle. Finally, we relate expressiveness of PCCFL to
two other relevant classes: CFL extended with shuffle and trace-closures of
CFL. Among technical contributions of the paper are pumping lemmas, as an
elegant completion of known pumping properties of regular languages, CFL and
commutative CFL.Comment: In Proceedings EXPRESS/SOS 2012, arXiv:1208.244
