Abstract
We prove the closure under complementation of the class of languages of scattered and countable N-free posets recognized by branching automata. The proof relies entirely on effective constructions.
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References
Almeida, J.: Finite Semigroups and Universal Algebra. Series in Algebra, vol. 3. World Scientific, Singapore (1994)
Bedon, N.: Logic and bounded-width rational languages of posets over countable scattered linear orderings. In: Artemov, S., Nerode, A. (eds.) LFCS 2009. LNCS, vol. 5407, pp. 61–75. Springer, Heidelberg (2008)
Bedon, N.: Logic and branching automata. Log. Meth. Comput. Sci. 11(4:2), 1–38 (2015)
Bedon, N., Rispal, C.: Series-parallel languages on scattered and countable posets. Theor. Comput. Sci. 412(22), 2356–2369 (2011)
Bruyère, V., Carton, O.: Automata on linear orderings. J. Comput. Syst. Sci. 73(1), 1–24 (2007)
Büchi, J.R.: On a decision method in the restricted second-order arithmetic. In: Proceedings of International Congress on Logic, Methodology and Philosophy of Science, Berkeley 1960 (1962)
Büchi, J.R.: Transfinite automata recursions and weak second order theory of ordinals. In: Proceedings of International Congress on Logic, Methodology, and Philosophy of Science 1964 (1965)
Carton, O., Rispal, C.: Complementation of rational sets on countable scattered linear orderings. Int. J. Found. Comput. Sci. 16(4), 767 (2005)
Colcombet, T.: Factorisation forests for infinite words and applications to countable scattered linear orderings. Theor. Comput. Sci. 411, 751–764 (2010)
Eilenberg, S., Schützenberger, M.P.: Rational sets in commutative monoids. J. Algebra 13(2), 173–191 (1969)
Kuske, D.: Infinite series-parallel posets: logic and languages. In: Welzl, E., Montanari, U., Rolim, J.D.P. (eds.) ICALP 2000. LNCS, vol. 1853, pp. 648–662. Springer, Heidelberg (2000)
Kuske, D.: Towards a language theory for infinite N-free pomsets. Theor. Comput. Sci. 299, 347–386 (2003)
Lodaya, K., Weil, P.: A Kleene iteration for parallelism. In: Arvind, V., Sarukkai, S. (eds.) FST TCS 1998. LNCS, vol. 1530, pp. 355–367. Springer, Heidelberg (1998)
Lodaya, K., Weil, P.: Series-parallel posets: algebra, automata and languages. In: Meinel, C., Morvan, M. (eds.) STACS 1998. LNCS, vol. 1373, pp. 555–565. Springer, Heidelberg (1998)
Lodaya, K., Weil, P.: Series-parallel languages and the bounded-width property. Theor. Comput. Sci. 237(1–2), 347–380 (2000)
Lodaya, K., Weil, P.: Rationality in algebras with a series operation. Inform. Comput. 171, 269–293 (2001)
Muller, D.E.: Infinite sequences and finite machines. In: Proceedings of Fourth Annual Symposium on Switching circuit theory and logical design. IEEE (1963)
Rabin, M.O.: Decidability of second-order theories and automata on infinite trees. Trans. Am. Math. Soc. 141, 1–35 (1969)
Rival, I.: Optimal linear extension by interchanging chains. Proc. AMS 89(3), 387–394 (1983)
Rosenstein, J.G.: Linear Orderings. Academic Press, New York (1982)
Sakarovitch, J.: Elements of Automata Theory. Cambridge University Press, Cambridge (2009)
Valdes, J., Tarjan, R.E., Lawler, E.L.: The recognition of series parallel digraphs. SIAM J. Comput. 11, 298–313 (1982)
Wilke, T.: An algebraic theory for regular languages of finite and infinite words. Int. J. Algebra Comput. 3(4), 44–489 (1993)
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Bedon, N. (2016). Complementation of Branching Automata for Scattered and Countable Series-Parallel Posets. In: Brlek, S., Reutenauer, C. (eds) Developments in Language Theory. DLT 2016. Lecture Notes in Computer Science(), vol 9840. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53132-7_2
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DOI: https://doi.org/10.1007/978-3-662-53132-7_2
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