Caron, Pascal; Flouret, Marianne Glushkov construction for series: The non commutative case. (English) Zbl 1033.68058 Int. J. Comput. Math. 80, No. 4, 457-472 (2003). Summary: We present an extension to multiplicities of a classical algorithm for computing a boolean automaton from a regular expression. The Glushkov construction computes an automaton with \(n+ 1\) states from a regular expression with \(n\) occurences of letters. We give an extension of the Glushkov algorithm for the multiplicity case in a non-commutative semiring. Next, we give four equivalent extended step by step algorithms. Cited in 2 ReviewsCited in 6 Documents MSC: 68Q45 Formal languages and automata Keywords:automata with multiplicities; rational series PDFBibTeX XMLCite \textit{P. Caron} and \textit{M. Flouret}, Int. J. Comput. Math. 80, No. 4, 457--472 (2003; Zbl 1033.68058) Full Text: DOI References: [1] Andary, P., Caron, P., Champamaud, J.M., Duchamp, G., Flouret, M. and Laugerotte, E. Sea: A symbolic environment for automata theory. Automata Implementation: Fourth International Workshop on Implementing Automata, WIA’99. volume 2214, pp.13–26. Lecture Notes in Computer Science · Zbl 1050.68587 [2] DOI: 10.1016/0304-3975(86)90088-5 · Zbl 0626.68043 [3] Berstel J., Rational series and their languages. EATCS Monographs on Theoretical Computer Science (1988) · Zbl 0668.68005 [4] DOI: 10.1016/0304-3975(93)90287-4 · Zbl 0811.68096 [5] Caron, P. and Flouret, M. Glushkov construction for multiplicities. Fifth International Conference on Implementation and Application of Automata, CIAA ’00. London, Ontario. volume 2088, Berlin: Springer-Verlag. Lecture Notes in Computer Science · Zbl 0989.68075 [6] DOI: 10.1016/S0747-7171(08)80125-3 · Zbl 0804.68096 [7] DOI: 10.1080/00207169908804865 · Zbl 0949.68090 [8] CulikII K., Lecture Notes in Computer Science 944, in: Proceedings of ICALP 95 (1995) [9] DOI: 10.1016/S0304-3975(00)00298-X · Zbl 0984.68098 [10] Eilenberg S., Automata, Languages and Machines (1974) [11] DOI: 10.1070/RM1961v016n05ABEH004112 · Zbl 0104.35404 [12] Hopcroft J. E., Introduction to Automata Theory, Languages and Computation (1979) · Zbl 0426.68001 [13] Kleene, S. 1956.Representation of events in nerve nets and finite automata. Automata Studies, Ann. Math. Studies 34 3–41. Princeton U. Press. [14] DOI: 10.1109/TEC.1960.5221603 [15] Mirkin B. G., Engineering Cybernetics pp 110– (1966) [16] DOI: 10.1016/S0019-9958(61)80020-X · Zbl 0104.00702 [17] DOI: 10.1145/363347.363387 · Zbl 0164.46205 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.