Minimizing LR(1) State Machines is NP-Hard
Abstract
LR(1) parsing was a focus of extensive research in the past 50 years. Though most fundamental mysteries have been resolved, a few remain hidden in the dark corners. The one we bumped into is the minimization of the LR(1) state machines, which we prove is NP-hard. It is the node-coloring problem that is reduced to the minimization puzzle. The reduction makes use of two technique: indirect reduction and incremental construction. Indirect reduction means the graph to be colored is not reduced to an LR(1) state machine directly. Instead, it is reduced to a context-free grammar from which an LR(1) state machine is derived. Furthermore, by considering the nodes in the graph to be colored one at a time, the context-free grammar is incrementally extended from a template context-free grammar that is for a two-node graph. The extension is done by adding new grammar symbols and rules. A minimized LR(1) machine can be used to recover a minimum coloring of the original graph.
Cite
@article{arxiv.2110.00776,
title = {Minimizing LR(1) State Machines is NP-Hard},
author = {Wuu Yang},
journal= {arXiv preprint arXiv:2110.00776},
year = {2021}
}
Comments
15 pages, 4 appendices, 14 figures. A preliminary version of this paper appeared in Proc. 14th International Conf. Autonomic and Autonomous Systems (ICAS 2018) May 20-24, 2018, Nice, France