Kosaburo Hashiguchi

Kosaburo Hashiguchi (橋口攻三郎, Hashiguchi Kōsaburō) is a Japanese mathematician and computer scientist at the Toyohashi University of Technology and Okayama University, known for his research in formal language theory.

In 1988, he found the first algorithm to determine the star height of a regular language, a problem that had been open since 1963 when Lawrence Eggan solved the related star height problem, showing that there is no finite bound on the star height. Hashiguchi's algorithm for star height is extremely complex, and impractical on all but the smallest examples.^[1]^[2]^[H88] A simpler method, showing also that the problem is PSPACE-complete, was provided in 2005 by Kirsten.^[1]^[3]

Earlier, in 1979, Hashiguchi had also solved another open problem on regular languages, of deciding whether, for a given language $A$ , there exists a finite number $n$ such that $A^{n}=A^{*}$ .^[4]^[H79]

Hashiguchi is the uncle of Japanese-born American pianist Grace Nikae.

Selected publications

H79.

Hashiguchi, Kosaburo (1979). "A decision procedure for the order of regular events". Theoretical Computer Science. 8 (1): 69–72. doi:10.1016/0304-3975(79)90057-4. MR 0523661.

H88.

Hashiguchi, Kosaburo (1988). "Algorithms for determining relative star height and star height". Information and Computation. 78 (2): 124–169. doi:10.1016/0890-5401(88)90033-8. MR 0955580.

References

1 2 Lombardy, Sylvain; Sakarovitch, Jacques (2008). "The universal automaton". In Flum, Jörg; Grädel, Erich; Wilke, Thomas (eds.). Logic and Automata: History and Perspectives. Texts Log. Games. Vol. 2. Amsterdam: Amsterdam Univ. Press. pp. 457–504. MR 2508751. See in particular p. 488.
↑ Pin, Jean-Éric (2017). "Open problems about regular languages, 35 years later". In Konstantinidis, Stavros; Moreira, Nelma; Reis, Rogério; Shallit, Jeffrey (eds.). The Role Of Theory In Computer Science: Essays Dedicated To Janusz Brzozowski. World Scientific. ISBN 9789813148215. See in particular p. 164.
↑ Kirsten, Daniel (2005). "Distance desert automata and the star height problem". RAIRO Theoretical Informatics and Applications. 39 (3): 455–509. doi:10.1051/ita:2005027. MR 2157045.
↑ Brzozowski, Janusz (2014). "Open problems about regular languages". In Book, Ronald V. (ed.). Formal Language Theory: Perspectives and Open Problems. Academic Press. pp. 23–38. ISBN 9781483267500. See in particular p. 45.

External links

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[ls-1] 1 2 Lombardy, Sylvain; Sakarovitch, Jacques (2008). "The universal automaton". In Flum, Jörg; Grädel, Erich; Wilke, Thomas (eds.). Logic and Automata: History and Perspectives. Texts Log. Games. Vol. 2. Amsterdam: Amsterdam Univ. Press. pp. 457–504. MR 2508751. See in particular p. 488.

[pin-2] Pin, Jean-Éric (2017). "Open problems about regular languages, 35 years later". In Konstantinidis, Stavros; Moreira, Nelma; Reis, Rogério; Shallit, Jeffrey (eds.). The Role Of Theory In Computer Science: Essays Dedicated To Janusz Brzozowski. World Scientific. ISBN 9789813148215. See in particular p. 164.

[kirsten-3] Kirsten, Daniel (2005). "Distance desert automata and the star height problem". RAIRO Theoretical Informatics and Applications. 39 (3): 455–509. doi:10.1051/ita:2005027. MR 2157045.

[brz-4] Brzozowski, Janusz (2014). "Open problems about regular languages". In Book, Ronald V. (ed.). Formal Language Theory: Perspectives and Open Problems. Academic Press. pp. 23–38. ISBN 9781483267500. See in particular p. 45.

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