Abstract
Operator precedence languages, designated as Floyd’s Languages (FL) to honor their inventor, are a classical deterministic context-free family. FLs are known to be a boolean family, and have been recently shown to strictly include the Visibly Pushdown Languages (VPDL); the latter are FLs characterized by operator precedence relations determined by the alphabet partition. In this paper we give the non-obvious proves that FLs have the same closure properties that motivated the introduction of VPDLs, namely under reversal, concatenation and Kleene’s star. Thus, rather surprisingly, the historical FL family turns out to be the largest known deterministic context-free family that includes the VPDL and has the same closure properties needed for applications to model checking and for defining mark-up languages such as HTML. As a corollary, an extended regular expression of precedence-compatible FLs is a FL and a deterministic parser for it can be algorithmically obtained.
Partially supported by PRIN 2007TJNZRE-002, CNR-IEIIT and ESF AutoMathA.
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References
Alur, R., Madhusudan, P.: Visibly pushdown languages. In: STOC: ACM Symposium on Theory of Computing, STOC (2004)
Alur, R., Madhusudan, P.: Adding nesting structure to words. J. ACM 56(3) (2009)
Berstel, J., Boasson, L.: Balanced grammars and their languages. In: Brauer, W., Ehrig, H., Karhumäki, J., Salomaa, A. (eds.) Formal and Natural Computing. LNCS, vol. 2300, pp. 3–25. Springer, Heidelberg (2002)
Caucal, D.: Synchronization of pushdown automata. In: Ibarra, O.H., Dang, Z. (eds.) DLT 2006. LNCS, vol. 4036, pp. 120–132. Springer, Heidelberg (2006)
Crespi Reghizzi, S.: The mechanical acquisition of precedence grammars. PhD thesis, University of California UCLA, School of Engineering (1970)
Crespi-Reghizzi, S., Guida, G., Mandrioli, D.: Operator precedence grammars and the noncounting property. SICOMP: SIAM Journ. on Computing 10, 174–191 (1981)
Crespi-Reghizzi, S., Mandrioli, D.: Algebraic properties of structured context-free languages: old approaches and novel developments. In: WORDS 2009 - 7th Int. Conf. on Words, preprints (2009), http://arXiv.org/abs/0907.2130
Crespi-Reghizzi, S., Mandrioli, D., Martin, D.F.: Algebraic properties of operator precedence languages. Information and Control 37(2), 115–133 (1978)
Fischer, M.J.: Some properties of precedence languages. In: STOC ’69: Proc. first annual ACM Symp. on Theory of Computing, pp. 181–190. ACM, New York (1969)
Floyd, R.W.: Syntactic analysis and operator precedence. J. ACM 10(3), 316–333 (1963)
Grune, D., Jacobs, C.J.: Parsing techniques: a practical guide. Springer, New York (2008)
McNaughton, R.: Parenthesis grammars. J. ACM 14(3), 490–500 (1967)
McNaughton, R., Papert, S.: Counter-free Automata. MIT Press, Cambridge (1971)
Nowotka, D., Srba, J.: Height-deterministic pushdown automata. In: Kučera, L., Kučera, A. (eds.) MFCS 2007. LNCS, vol. 4708, pp. 125–134. Springer, Heidelberg (2007)
Salomaa, A.K.: Formal Languages. Academic Press, London (1973)
Thatcher, J.: Characterizing derivation trees of context-free grammars through a generalization of finite automata theory. Journ. of Comp. and Syst. Sc. 1, 317–322 (1967)
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Crespi Reghizzi, S., Mandrioli, D. (2010). Operator Precedence and the Visibly Pushdown Property. In: Dediu, AH., Fernau, H., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2010. Lecture Notes in Computer Science, vol 6031. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13089-2_18
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