Optimal Hyper-Minimization

TL;DR

This paper introduces an improved hyper-minimization algorithm for deterministic finite automata that minimizes the number of errors with a trade-off in increased runtime, and provides experimental analysis on random automata.

Contribution

It presents a new hyper-minimization algorithm that reduces errors more effectively at the cost of quadratic runtime, solving an open problem in the field.

Findings

The new algorithm commits fewer errors than previous methods.

Experimental results show the trade-off between error minimization and runtime.

The algorithm performs well on random automata datasets.

Abstract

Minimal deterministic finite automata (DFAs) can be reduced further at the expense of a finite number of errors. Recently, such minimization algorithms have been improved to run in time O(n log n), where n is the number of states of the input DFA, by [Gawrychowski and Je\.z: Hyper-minimisation made efficient. Proc. MFCS, LNCS 5734, 2009] and [Holzer and Maletti: An n log n algorithm for hyper-minimizing a (minimized) deterministic automaton. Theor. Comput. Sci. 411, 2010]. Both algorithms return a DFA that is as small as possible, while only committing a finite number of errors. These algorithms are further improved to return a DFA that commits the least number of errors at the expense of an increased (quadratic) run-time. This solves an open problem of [Badr, Geffert, and Shipman: Hyper-minimizing minimized deterministic finite state automata. RAIRO Theor. Inf. Appl. 43, 2009]. In addition, an experimental study on random automata is performed and the effects of the existing algorithms and the new algorithm are reported.