Abstract
In the theory of automata over infinite alphabets, a central difficulty is that of finding a suitable compromise between expressiveness and algorithmic complexity. We propose an automaton model where we count the multiplicity of data values on an input word. This is particularly useful when such languages represent behaviour of systems with unboundedly many processes, where system states carry such counts as summaries. A typical recognizable language is: “every process does at most k actions labelled a”. We show that emptiness is elementarily decidable, by reduction to the covering problem on Petri nets.
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Autebert, J.-M., Beauquier, J., Boasson, L.: Langages sur des alphabets infinis. Discrete Applied Mathematics 2, 1–20 (1980)
Alur, R., Madhusudan, P.: Adding nesting structure to words. In: Ibarra, O.H., Dang, Z. (eds.) DLT 2006. LNCS, vol. 4036, pp. 1–13. Springer, Heidelberg (2006)
Baclet, M.: Logical characterization of aperiodic data languages. Research Report LSV-03-12, Laboratoire Spécification et Vérification, ENS Cachan, France, 16 p. (September 2003)
Bojanczyk, M., Muscholl, A., Schwentick, T., Segoufin, L., David, C.: Two-variable logic on words with data. In: LICS, pp. 7–16. IEEE Computer Society, Los Alamitos (2006)
Bouyer, P.: A logical characterization of data languages. Inf. Process. Lett. 84(2), 75–85 (2002)
Bouyer, P., Petit, A., Thérien, D.: An algebraic characterization of data and timed languages. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, pp. 248–261. Springer, Heidelberg (2001)
Björklund, H., Schwentick, T.: On notions of regularity for data languages. In: Csuhaj-Varjú, E., Ésik, Z. (eds.) FCT 2007. LNCS, vol. 4639, pp. 88–99. Springer, Heidelberg (2007)
Demri, S., Lazic, R.: Ltl with the freeze quantifier and register automata. In: LICS 2006: Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science, pp. 17–26. IEEE Computer Society, Los Alamitos (2006)
Kaminski, M., Francez, N.: Finite-memory automata. Theor. Comput. Sci. 134(2), 329–363 (1994)
Kaminski, M., Tan, T.: Regular expressions for languages over infinite alphabets. Fundam. Inform. 69(3), 301–318 (2006)
Lipton, R.: The reachability problem requires exponential space. Research Report 62, Yale University (1976)
Lisitsa, A., Potapov, I.: Temporal logic with predicate lambda-abstraction. In: TIME, pp. 147–155 (2005)
Lisitsa, A., Potapov, I.: On the computational power of querying the history. Fundam. Inform. 91(2), 395–409 (2009)
Lisitsa, A., Potapov, I., Saleh, R.: Automata on gauss words. In: LATA, pp. 505–517 (2009)
Neven, F., Schwentick, T., Vianu, V.: Towards regular languages over infinite alphabets. In: Sgall, J., Pultr, A., Kolman, P. (eds.) MFCS 2001. LNCS, vol. 2136, pp. 560–572. Springer, Heidelberg (2001)
Neven, F., Schwentick, T., Vianu, V.: Finite state machines for strings over infinite alphabets. ACM Trans. Comput. Log. 5(3), 403–435 (2004)
Otto, F.: Classes of regular and context-free languages over countably infinite alphabets. Discrete Applied Mathematics 12, 41–56 (1985)
Segoufin, L.: Automata and logics for words and trees over an infinite alphabet. In: Ésik, Z. (ed.) CSL 2006. LNCS, vol. 4207, pp. 41–57. Springer, Heidelberg (2006)
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Manuel, A., Ramanujam, R. (2009). Counting Multiplicity over Infinite Alphabets. In: Bournez, O., Potapov, I. (eds) Reachability Problems. RP 2009. Lecture Notes in Computer Science, vol 5797. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04420-5_14
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DOI: https://doi.org/10.1007/978-3-642-04420-5_14
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