Efficient enumeration of regular languages

Authors:
Margareta Ackerman;Jeffrey Shallit
Affiliations:
University of Waterloo, Waterloo, ON, Canada;University of Waterloo, Waterloo, ON, Canada
Venue:
CIAA'07 Proceedings of the 12th international conference on Implementation and application of automata
Year:
2007

Citing 3
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Abstract

The cross-section enumeration problem is to list all words of length n in a regular language L in lexicographical order. The enumeration problem is to list the first m words in L according to radix order. We present an algorithm for the cross-section enumeration problem that is linear in n. We provide a detailed analysis of the asymptotic running time of our algorithm and that of known algorithms for both enumeration problems. We discuss some shortcomings of the enumeration algorithm found in the Grail computation package. In the practical domain, we modify Mäkinen's enumeration algorithm to get an algorithm that is usually the most efficient in practice. We performed an extensive performance analysis of the new and previously known enumeration and cross-section enumeration algorithms and found when each algorithm is preferable.