Abstract
In general, a nondeterministic automaton or machine (for example a finite automaton, pushdown automaton or Turing machine) is called unambiguous if each input is accepted by at most one run or computation. Each deterministic automaton is obviously unambiguous. However, in many settings, unambiguous automata are more expressive or admit more succinct automata than deterministic models, while preserving some good algorithmic properties. The aim of this talk is to survey some classical and some more recent results on unambiguous finite automata over different kind of input structures, namely finite words, infinite words, finite trees, and infinite trees.
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References
Aho, A.V., Hopcroft, J.E., Ullman, J.D.: The Design and Analysis of Computer Algorithms. Addison-Wesley, New York (1974)
Bilkowski, M.: Ambiguity property for complements of deterministic tree languages. Presentation at the Annual Workshop of the ESF Networking Programme on Games for Design and Verification, Oxford (2010)
Bousquet, N., Löding, C.: Equivalence and inclusion problem for strongly unambiguous BĂĽchi automata. In: Dediu, A.-H., Fernau, H., MartĂn-Vide, C. (eds.) LATA 2010. LNCS, vol. 6031, pp. 118–129. Springer, Heidelberg (2010)
Carayol, A., Löding, C., Niwiński, D., Walukiewicz, I.: Choice functions and well-orderings over the infinite binary tree. Central European Journal of Mathematics 8(4), 662–682 (2010)
Carton, O., Michel, M.: Unambiguous Büchi automata. Theor. Comput. Sci. 297(1–3), 37–81 (2003)
Isaak, D., Löding, C.: Efficient inclusion testing for simple classes of unambiguous ω-automata. Information Processing Letters 112(14-15), 578–582 (2012)
Martens, W., Niehren, J.: On the minimization of xml schemas and tree automata for unranked trees. J. Comput. Syst. Sci. 73(4), 550–583 (2007)
Seidl, H.: Deciding equivalence of finite tree automata. SIAM J. Comput. 19(3), 424–437 (1990)
Stearns, R.E., Hunt III, H.B.: On the equivalence and containment problems for unambiguous regular expressions, regular grammars and finite automata. SIAM Journal on Computing 14(3), 598–611 (1985)
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Löding, C. (2013). Unambiguous Finite Automata. In: Béal, MP., Carton, O. (eds) Developments in Language Theory. DLT 2013. Lecture Notes in Computer Science, vol 7907. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38771-5_4
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DOI: https://doi.org/10.1007/978-3-642-38771-5_4
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