Abstract
We introduce linear expressions for unrestricted dags (directed acyclic graphs) and finite deterministic and nondeterministic automata operating on them. Those dag automata are a conservative extension of the T u,u -automata of Courcelle on unranked, unordered trees and forests. Several examples of dag languages acceptable and not acceptable by dag automata and some closure properties are given.
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Anantharaman, S., Narendran, P., Rusinowitch, M.: Closure properties and decision problems of dag automata. Information Processing Letters 94, 231–240 (2005)
Boneva, I., Talbot, J.-M.: Automata and logic for unranked and unordered trees. In: Giesl, J. (ed.) RTA 2005. LNCS, vol. 3467, pp. 500–515. Springer, Heidelberg (2005)
Bossut, F., Dauchet, M., Warin, B.: A Kleene theorem for a class of planar acyclic graphs. Theor. Comp. Science Center Report HKUST-TCSC 2001-5 117, 251–265 (1995)
Brüggemann-Klein, A., Murata, M., Wood, D.: Regular tree and hedge languages of unranked alphabets. Theor. Comp. Science Center Report HKUST-TCSC 2001 5, 29 (2001)
Charatonik, W.: Automata on dag representations of finite trees. Technical Report MPI-I-1999-2-001, MPI, Univ. Saarbrücken (1999)
Comon, H., Daucher, M., Gilleron, R., Tison, S., Tommasi, M.: Tree automata techniques and application. Available on the Web from 13ux02.univ-lille.fr in directoty tata (1998)
Courcelle, B.: A representation of graphs by algebraic expressions and its use for graph rewriting systems. In: Proc. 3rd Internat. Workshop on Graph-Grammars, pp. 112–132. Springer, Heidelberg (1988)
Courcelle, B.: On recognizable sets and tree automata. In: Aït-Kaci, H., Nivat, M. (eds.) Resolution of Equations in Algebraic Structures, vol. 1, pp. 93–126. Academic Press, London (1989)
Fanchon, J., Morin, R.: Regular sets of pomsets with auitoconcurrency. In: Brim, L., Jančar, P., Křetínský, M., Kucera, A. (eds.) CONCUR 2002. LNCS, vol. 2421, pp. 402–417. Springer, Heidelberg (2002)
Kamimura, T., Slutzki, G.: Parallel and two-way automata on directed ordered acyclic graphs. Inf. Control 49, 10–51 (1981)
Kaminski, M., Pinter, S.: Finite automata on directed graphs. J. Comp. Sys. Sci. 44, 425–446 (1992)
Menzel, J.R., Priese, L., Schuth, M.: Some examples of semi-rational dag languages. In: Ibarra, O.H., Dang, Z. (eds.) DLT 2006. LNCS, vol. 4036, pp. 351–362. Springer Verlag, Heidelberg (2006)
Priese, L.: Semi-rational sets of dags. In: De Felice, C., Restivo, A. (eds.) DLT 2005. LNCS, vol. 3572, pp. 385–396. Springer Verlag, Heidelberg (2005)
Thomas, W.: Finite-state recognizability of graph properties. In: Krob, D. (ed.) Theorie des Automates et Applications, l’Universite de Rouen, France, vol. 172, pp. 147–159 (1992)
Thomas, W.: Automata theory on trees and partial orders. In: Bidoit, M., Dauchet, M. (eds.) CAAP 1997, FASE 1997, and TAPSOFT 1997. LNCS, vol. 1214, pp. 20–34. Springer, Heidelberg (1997)
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Priese, L. (2007). Finite Automata on Unranked and Unordered DAGs. In: Harju, T., Karhumäki, J., Lepistö, A. (eds) Developments in Language Theory. DLT 2007. Lecture Notes in Computer Science, vol 4588. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73208-2_33
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DOI: https://doi.org/10.1007/978-3-540-73208-2_33
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