LATA 2015: Language and Automata Theory and Applications pp 275-286 | Cite as
Derivatives for Regular Shuffle Expressions
Conference paper
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Abstract
There is a rich variety of shuffling operations ranging from asynchronous interleaving to various forms of synchronizations. We introduce a general shuffling operation which subsumes earlier forms of shuffling. We further extend the notion of a Brzozowski derivative to the general shuffling operation and thus to many earlier forms of shuffling. This extension enables the direct construction of automata from regular expressions involving shuffles that appear in specifications of concurrent systems.
Keywords
Automata and logic Shuffle expressions DerivativesPreview
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References
- 1.Antimirov, V.M.: Rewriting regular inequalities. In: Reichel, H. (ed.) FCT 1995. LNCS, vol. 965, pp. 116–116. Springer, Heidelberg (1995)Google Scholar
- 2.ter Beek, M.H., Martín-Vide, C., Mitrana, V.: Synchronized shuffles. Theor. Comput. Sci. 341(1–3), 263–275 (2005)CrossRefMATHGoogle Scholar
- 3.Brzozowski, J.A.: Derivatives of regular expressions. J. ACM 11(4), 481–494 (1964)CrossRefMATHMathSciNetGoogle Scholar
- 4.Garg, V.K., Ragunath, M.T.: Concurrent regular expressions and their relationship to petri nets. Theor. Comput. Sci. 96(2), 285–304 (1992)CrossRefMATHMathSciNetGoogle Scholar
- 5.Gelade, W.: Succinctness of regular expressions with interleaving, intersection and counting. Theor. Comput. Sci. 411(31–33), 2987–2998 (2010)CrossRefMATHMathSciNetGoogle Scholar
- 6.Grabmayer, C.: Using proofs by coinduction to find “traditional” proofs. In: Fiadeiro, J.L., Harman, N.A., Roggenbach, M., Rutten, J. (eds.) CALCO 2005. LNCS, vol. 3629, pp. 175–193. Springer, Heidelberg (2005) CrossRefGoogle Scholar
- 7.Kumar, A., Verma, A.K.: A novel algorithm for the conversion of parallel regular expressions to non-deterministic finite automata. Applied Mathematics & Information Sciences 8, 95–105 (2014)CrossRefMathSciNetGoogle Scholar
- 8.Latteux, M., Roos, Y.: Synchronized shuffle and regular languages. In: Jewels are Forever, Contributions on Theoretical Computer Science in Honor of arto Salomaa, pp. 35–44. Springer, London (1999)Google Scholar
- 9.Lodaya, K., Mukund, M., Phawade, R.: Kleene theorems for product systems. In: Holzer, M. (ed.) DCFS 2011. LNCS, vol. 6808, pp. 235–247. Springer, Heidelberg (2011) CrossRefGoogle Scholar
- 10.Owens, S., Reppy, J., Turon, A.: Regular-expression derivatives reexamined. Journal of Functional Programming 19(2), 173–190 (2009)CrossRefMATHMathSciNetGoogle Scholar
- 11.de Simone, R.: Langages infinitaires et produit de mixage. Theor. Comput. Sci. 31, 83–100 (1984)CrossRefMATHGoogle Scholar
- 12.Stotts, P.D., Pugh, W.: Parallel finite automata for modeling concurrent software systems. J. Syst. Softw. 27(1), 27–43 (1994)CrossRefGoogle Scholar
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