Characterizations of the LL(k) property

Extended abstract
  • Seppo Sippu
  • Eljas Soisalon-Soininen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 85)


Characterizations of the LL(k) property for context-free grammars are given, which lead to efficient algorithms for testing an arbitrary context-free grammar for the LL(k) property. The characterizations are based on succinct nondeterministic representations of a finite-state automaton used for constructing a canonical LL(k) parser. The resulting testing algorithms are usually of the same order to time complexity as their LR(k) counterparts. For example, one characterization (the LR(k) counterpart of which has been used by Hunt, Szymanski and Ullman for obtaining the fastest known algorithm for LR(k) testing) implies an 0(nk+2) algorithm for LL(k) testing, where n is the size of the grammar in question and k is considered to be a fixed integer. This time bound for LL(k) testing has previously only been obtained indirectly, by a linear time-bounded reduction of LL(k) testing to LR(k) testing. Moreover, it is shown that the LL(k) property allows an especially convenient characterization, one which allows an 0(nk+1) algorithm for LL(k) testing. This new time bound suggests that the LL(k) property might be strictly easier to test than the LR(k) property.


Accessible State General String Nondeterministic Automaton Succinct Representation Terminal String 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1980

Authors and Affiliations

  • Seppo Sippu
    • 1
  • Eljas Soisalon-Soininen
    • 2
  1. 1.Department of Computer ScienceUniversity of HelsinkiHelsinki 25Finland
  2. 2.Department of MathematicsUniversity of California at Santa BarbaraSanta BarbaraUSA

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