Abstract
We extend Brzozowski derivatives and partial derivatives from regular expressions to \(\omega \)-regular expressions and establish their basic properties. We observe that the existing derivative-based automaton constructions do not scale to \(\omega \)-regular expressions. We define a new variant of the partial derivative that operates on linear factors and prove that this variant gives rise to a translation from \(\omega \)-regular expressions to nondeterministic Büchi automata.
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Antimirov, V.M.: Rewriting regular inequalities. In: Reichel, H. (ed.) FCT 1995. LNCS, vol. 965, pp. 116–125. Springer, Heidelberg (1995)
Antimirov, V.M.: Partial derivatives of regular expressions and finite automaton constructions. Theoretical Computer Science 155(2), 291–319 (1996)
Brzozowski, J.A.: Derivatives of regular expressions. J. ACM 11(4), 481–494 (1964)
Caron, P., Champarnaud, J.-M., Mignot, L.: Partial derivatives of an extended regular expression. In: Dediu, A.-H., Inenaga, S., Martín-Vide, C. (eds.) LATA 2011. LNCS, vol. 6638, pp. 179–191. Springer, Heidelberg (2011)
Kleene, S.C.: Representation of events in nerve nets and finite automata. Automata Studies (1956)
Park, D.: Concurrency and automata on infinite sequences. In: Deussen, P. (ed.) Theoretical Computer Science. LNCS, vol. 104, pp. 167–183. Springer, Heidelberg (2003)
Redziejowski, R.R.: Construction of a deterministic \(\omega \)-automaton using derivatives. Informatique Théorique et Applications 33(2), 133–158 (1999)
Redziejowski, R.R.: An improved construction of deterministic omega-automaton using derivatives. Fundam. Inform. 119(3–4), 393–406 (2012)
Roşu, G., Viswanathan, M.: Testing extended regular language membership incrementally by rewritin. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol. 2706, pp. 499–514. Springer, Heidelberg (2003)
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Thiemann, P., Sulzmann, M. (2015). From \(\omega \)-Regular Expressions to Büchi Automata via Partial Derivatives. In: Dediu, AH., Formenti, E., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2015. Lecture Notes in Computer Science(), vol 8977. Springer, Cham. https://doi.org/10.1007/978-3-319-15579-1_22
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DOI: https://doi.org/10.1007/978-3-319-15579-1_22
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