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 (φcCFL), 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 φcCFL 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. & copy; W. Czerwinski & S. Lasota.
CITATION STYLE
Czerwiñski, W., & Lasota, S. (2012). Partiallycommutative contextfree languages. In Electronic Proceedings in Theoretical Computer Science, EPTCS (Vol. 89, pp. 35–48). Open Publishing Association. https://doi.org/10.4204/EPTCS.89.4
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