Abstract
The hierarchical algebraic decomposition of finite state automata (Krohn-Rhodes Theory) has been a mathematical theory without any computational implementations until the present paper, although several possible and promising practical applications, such as automated object-oriented programming in software development [5], formal methods for understanding in artificial intelligence [6], and a widely applicable integer-valued complexity measure [8,7], have been described. As a remedy for the situation, our new implementation, described here, is freely available [2] as open-source software. We also present two different computer algebraic implementations of the Krohn-Rhodes decomposition, the V ∪ T and holonomy decompositions [4,3], and compare their efficiency in terms of the number of hierarchical levels in the resulting cascade decompositions.
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Egri-Nagy, A., Nehaniv, C.L. (2005). Algebraic Hierarchical Decomposition of Finite State Automata: Comparison of Implementations for Krohn-Rhodes Theory. In: Domaratzki, M., Okhotin, A., Salomaa, K., Yu, S. (eds) Implementation and Application of Automata. CIAA 2004. Lecture Notes in Computer Science, vol 3317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30500-2_32
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DOI: https://doi.org/10.1007/978-3-540-30500-2_32
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