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Avraham Trahtman
Avraham Naumovich Trahtman (Trakhtman) ((ロシア語:Абрам Наумович Трахтман); b. 1944, USSR) is a mathematician at Bar-Ilan University (Israel). In 2007, Trahtman solved a problem in combinatorics that had been open for 37 years, the Road Coloring Conjecture posed in 1970.〔J.E. Pin. On two combinatorial problems arising from automata theory. Annals of Discrete Math., 17, 535-548, 1983.〕
==Road coloring problem posed and solved==
Trahtman's solution to the road coloring problem was accepted in 2007 and published in 2009 by the ''Israel Journal of Mathematics''.〔Avraham N. Trahtman: The Road Coloring Problem. ''Israel Journal of Mathematics'', Vol. 172, 51–60, 2009〕 The problem arose in the subfield of symbolic dynamics, an abstract part of the field of dynamical systems. The road coloring problem was raised by R. L. Adler and L. W. Goodwyn from the United States, and the Israeli mathematician B. Weiss.〔R.L. Adler, B. Weiss. Similarity of automorphisms of the torus, Memoirs of the Amer. Math. Soc. 98, Providence, RI, 1970〕〔R.L. Adler, L.W. Goodwyn, B. Weiss. Equivalence of topological Markov shifts, Israel J. of Math. 27, 49-63, 1977〕 The proof used results from earlier work.〔K. Culik II, J. Karhumaki, J. Kari. A note on synchronized automata and Road Coloring Problem. Developments in Language Theory (5th Int. Conf., Vienna, 2001), Lecture Notes in Computer Science, 2295, 175-185, 2002〕〔J. Friedman. On the road coloring problem. Proc. of the Amer. Math. Soc. 110, 1133-1135, 1990〕〔A.N. Trahtman. An Algorithm for Road Coloring. Lect. Notes in Comp. Sci, 7056 (2011), Springer, 349--360〕
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