Abstract
In this paper, we consider the monadic second order logic (MSO) and two of its extensions, namely Counting MSO (CMSO) and Presburger MSO (PMSO), interpreted over unranked and unordered trees. We survey classes of tree automata introduced for the logics PMSO and CMSO as well as other related formalisms; we gather results from the literature and sometimes clarify or fill the remaining gaps between those various formalisms. Finally, we complete our study by adapting these classes of automata for capturing precisely the expressiveness of the logic MSO.
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Carme, J., Niehren, J., Tommasi, M.: Querying Unranked Trees with Stepwise Tree Automata. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol. 3091, pp. 105–118. Springer, Heidelberg (2004)
Colcombet, T.: Rewriting in the partial algebra of typed terms modulo AC. Electronic Notes in Theoretical Computer Science, vol. 68. Elsevier Science Publishers, Amsterdam (2002)
Comon, H., Dauchet, M., Gilleron, R., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree Automata Techniques and Applications (1997), Available on: http://www.grappa.univ-lille3.fr/tata (release October 1, 2002)
Courcelle, B.: The Monadic Second-Order Logic of Graphs. I. Recognizable Sets of Finite Graphs. IC 85(1), 12–75 (1990)
Courcelle, B.: The monadic second order logic of graphs VI: on several representations of graphs by relational structures. Discrete Applied Mathematics 54(2-3), 117–149 (1994)
Courcelle, B.: Basic notions of universal algebra for language theory and graph grammars. Theoretical Computer Science 163, 1–54 (1996)
Dal-Zilio, S., Lugiez, D.: XML Schema, Tree Logic and Sheaves Automata. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol. 2706, pp. 246–263. Springer, Heidelberg (2003)
Dal-Zilio, S., Lugiez, D., Meyssonnier, C.: A logic you can count on. In: 31st Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (2004)
Gaubert, S., Giua, A.: Petri net languages and infinite subsets of Nm. Journal of Computer System Sciences 59(3), 373–391 (1999)
Guaiana, G., Restivo, A., Salemi, S.: On Aperiodic Trace Languages. In: Jantzen, M., Choffrut, C. (eds.) STACS 1991. LNCS, vol. 480, pp. 76–88. Springer, Heidelberg (1991)
Klaedtke, F., Rueß, H.: Monadic Second-Order Logics with Cardinalities. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, Springer, Heidelberg (2003)
Mezei, J., Wright, J.B.: Algebraic automata and context-free sets. Information and Control 11(2-3), 3–29 (1967)
Neven, F., Schwentick, T.: Query automata over finite trees. Theoretical Computer Science 275(1-2), 633–674 (2002)
Niehren, J., Podelski, A.: Feature Automata and Recognizable Sets of Feature Trees. In: Gaudel, M.-C., Jouannaud, J.-P. (eds.) CAAP 1993, FASE 1993, and TAPSOFT 1993. LNCS, vol. 668, pp. 356–375. Springer, Heidelberg (1993)
Ohsaki, H.: Beyond Regularity: Equational Tree Automata for Associative and Commutative Theories. In: Fribourg, L. (ed.) CSL 2001 and EACSL 2001. LNCS, vol. 2142, pp. 539–553. Springer, Heidelberg (2001)
Ohsaki, H., Takai, T.: Decidability and Closure Properties of Equational Tree Languages. In: Tison, S. (ed.) RTA 2002. LNCS, vol. 2378, pp. 114–128. Springer, Heidelberg (2002)
Parikh, R.J.: On context-free languages. Journal of the ACM 13(4), 570–581 (1966)
Seidl, H., Schwentick, T., Muscholl, A.: Numerical Document Queries. In: Twenty-Second ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pp. 155–166. ACM Press, New York (2003)
Thatcher, J.W., Wright, J.B.: Generalized finite automata with an application to a decision problem of second-order logic. Mathematical System Theory 2, 57–82 (1968)
Verma, K.N.: Two-Way Equational Tree Automata for AC-like Theories: Decidability and Closure Properties. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol. 2706, pp. 180–197. Springer, Heidelberg (2003)
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Boneva, I., Talbot, JM. (2005). Automata and Logics for Unranked and Unordered Trees. In: Giesl, J. (eds) Term Rewriting and Applications. RTA 2005. Lecture Notes in Computer Science, vol 3467. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-32033-3_36
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DOI: https://doi.org/10.1007/978-3-540-32033-3_36
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