Logic Characterization of Invisibly Structured Languages: The Case of Floyd Languages

  • Violetta Lonati
  • Dino Mandrioli
  • Matteo Pradella
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7741)


Operator precedence grammars define a classical Boolean and deterministic context-free language family (called Floyd languages or FLs). FLs have been shown to strictly include the well-known Visibly Pushdown Languages, and enjoy the same nice closure properties. In this paper we provide a complete characterization of FLs in terms of a suitable Monadic Second-Order Logic. Traditional approaches to logic characterization of formal languages refer explicitly to the structures over which they are interpreted - e.g, trees or graphs - or to strings that are isomorphic to the structure, as in parenthesis languages. In the case of FLs, instead, the syntactic structure of input strings is “invisible” and must be reconstructed through parsing. This requires that logic formulae encode some typical context-free parsing actions, such as shift-reduce ones.


operator precedence languages deterministic context-free languages monadic second-order logic pushdown automata 


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Violetta Lonati
    • 1
  • Dino Mandrioli
    • 2
  • Matteo Pradella
    • 2
  1. 1.DIUniversità degli Studi di MilanoMilanoItaly
  2. 2.DEIPolitecnico di MilanoMilanoItaly

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