Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
On lexicographic enumeration of regular and context-free languages
Acta Cybernetica
Combinatorial Algorithms: For Computers and Hard Calculators
Combinatorial Algorithms: For Computers and Hard Calculators
Three New Algorithms for Regular Language Enumeration
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
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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+t, where t is the output size. 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 Makinen'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.