On the complexity and performance of parsing with derivatives
Abstract
Current algorithms for context-free parsing inflict a trade-off between ease of understanding, ease of implementation, theoretical complexity, and practical performance. No algorithm achieves all of these properties simultaneously. Might et al. introduced parsing with derivatives, which handles arbitrary context-free grammars while being both easy to understand and simple to implement. Despite much initial enthusiasm and a multitude of independent implementations, its worst-case complexity has never been proven to be better than exponential. In fact, high-level arguments claiming it is fundamentally exponential have been advanced and even accepted as part of the folklore. Performance ended up being sluggish in practice, and this sluggishness was taken as informal evidence of exponentiality. In this paper, we reexamine the performance of parsing with derivatives. We have discovered that it is not exponential but, in fact, cubic. Moreover, simple (though perhaps not obvious) modifications to the implementation by Might et al. lead to an implementation that is not only easy to understand but also highly performant in practice.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jun 02, 2016
- Source ID
- 10.1145/2980983.2908128
Entities
People
- Celeste Hollenbeck
- Matthew Might
- Michael D. Adams
Organizations
- Defense Advanced Research Projects Agency
- National Science Foundation
- University of Utah