A Discipline of Programming
A Taxonomy of Algorithms for Constructing Minimal Acyclic Deterministic Finite Automata
WIA '99 Revised Papers from the 4th International Workshop on Automata Implementation
Directly Constructing Minimal DFAs: Combining Two Algorithms by Brzozowski
CIAA '00 Revised Papers from the 5th International Conference on Implementation and Application of Automata
Incremental and semi-incremental construction of pseudo-minimal automata
CIAA'05 Proceedings of the 10th international conference on Implementation and Application of Automata
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We present a semi-incremental algorithm for constructing minimal acyclic deterministic finite automata. Such automata are useful for storing sets of words for spell-checking, among other applications. The algorithm is semi-incremental because it maintains the automaton in near-minimal condition and requires a final minimization step after the last word has been added (during construction). The algorithm derivation proceeds formally (with correctness arguments) from two separate algorithms, one for minimization and one for adding words to acyclic automata. The algorithms are derived in such a way as to be combinable, yielding a semi-incremental one. In practice, the algorithm is both easy to implement and displays good running time performance.