2009/06/21 by Marco Almeida, Almeida, Marco, Nelma Moreira +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · #Algorithms and Data Compression #DNA and Biological Computing #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.0906.3853
openalex publication_date 2009/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In general, the representation of combinatorial objects is decisive for the feasibility of several enumerative tasks. In this work, we show how a (unique) string representation for (complete) initially-connected deterministic automata (ICDFAs) with n states over an alphabet of k symbols can be used for counting, exact enumeration, sampling and optimal coding, not only the set of ICDFAs but, to some extent, the set of regular languages. An exact generation algorithm can be used to partition the set of ICDFAs in order to parallelize the counting of minimal automata (and thus of regular languages). We present also a uniform random generator for ICDFAs that uses a table of pre-calculated values. Based on the same table it is also possible to obtain an optimal coding for ICDFAs.