Abstract
Brüggemann-Klein and Wood have introduced a new family of regular languages, the one-unambiguous regular languages, a very important notion in XML DTDs. A regular language L is one-unambiguous if and only if there exists a regular expression E over the operators of sum, catenation and Kleene star such that L(E) = L and the position automaton of E is deterministic. It implies that for a one-unambiguous expression, there exists an equivalent linear-size deterministic recognizer. In this paper, we extend the notion of one-unambiguity to weak one-unambiguity over regular expressions using the complement operator ¬. We show that a DFA with at most (n + 2) states can be computed from a weakly one-unambiguous expression and that it is decidable whether or not a given DFA recognizes a weakly one-unambiguous language.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Blum, N.: An O(n logn) implementation of the standard method for minimizing n-state finite automata. Inform. Process. Lett. 57(2), 65–69 (1996)
Bray, T., Paoli, J., Sperberg-Mc Queen, C.M., Maler, E., Yergeau, F.: Extensible Markup Language (XML) 1.0, 4th edn. (2006), http://www.w3.org/TR/2006/REC-xml-20060816
Brüggemann-Klein, A., Wood, D.: One-unambiguous regular languages. Inform. Comput. 140, 229–253 (1998)
Gelade, W.: Succinctness of regular expressions with interleaving, intersection and counting. Theor. Comput. Sci. 411(31-33), 2987–2998 (2010)
Gelade, W., Neven, F.: Succinctness of the complement and intersection of regular expressions. In: Albers, S., Weil, P. (eds.) STACS. Dagstuhl Seminar Proceedings, vol. 08001, pp. 325–336 (2008)
Glushkov, V.M.: The abstract theory of automata. Russian Mathematical Surveys 16, 1–53 (1961)
Hopcroft, J.E.: An n log n algorithm for minimizing the states in a finite automaton. In: Kohavi, Z. (ed.) The Theory of Machines and Computations, pp. 189–196. Academic Press, New York (1971)
Kleene, S.: Representation of events in nerve nets and finite automata. In: Automata Studies, Ann. Math. Studies, vol. 34, pp. 3–41. Princeton U. Press (1956)
McNaughton, R.F., Yamada, H.: Regular expressions and state graphs for automata. IEEE Transactions on Electronic Computers 9, 39–57 (1960)
Moore, E.F.: Gedanken experiments on sequential machines. In: Automata Studies, pp. 129–153. Princeton Univ. Press, Princeton (1956)
Myhill, J.: Finite automata and the representation of events. WADD, TR-57-624, 112–137 (1957)
Nerode, A.: Linear automata transformation. In: Proceedings of AMS, vol. 9, pp. 541–544 (1958)
Rabin, M.O., Scott, D.: Finite automata and their decision problems. IBM J. Res. 3(2), 115–125 (1959)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Caron, P., Han, YS., Mignot, L. (2011). Generalized One-Unambiguity. In: Mauri, G., Leporati, A. (eds) Developments in Language Theory. DLT 2011. Lecture Notes in Computer Science, vol 6795. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22321-1_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-22321-1_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22320-4
Online ISBN: 978-3-642-22321-1
eBook Packages: Computer ScienceComputer Science (R0)