On LALR(k) testing

  • Seppo Sippu
  • Eljas Soisalon-Soininen
Session 7: G. Rozenberg, Chairman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 115)


The problem of testing whether or not a context-free grammar possesses the LALR(k) property is studied. The uniform problem (i.e. both the subject grammar and the integer k are problem parameters) is shown to be complete for polynomial space (PSPACE) when k is expressed in unary, and complete for nondeterministic (one-level) exponential time (NE) when k is expressed in binary. This solves an open problem by Hunt, Szymanski and Ullman, who showed that for k in binary LR(k), LL(k) and even strong LL(k) testing is NE-complete, and that LALR(k) testing is at least NE-hard. For k in unary the lower bound of the problem follows from the recently obtained result that even for fixed k ≥ 1 (i.e. only the subject grammar is a problem parameter) the problem is PSPACE-hard. Thus, the results lead to the striking conclusion that for k in binary LALR(k) testing is no harder (with respect to polynomial time reductions) than e.g. strong LL(k) testing, and for k in unary no harder than LALR(1) testing.


Deterministic Time Membership Problem General String Valid Item Current Item 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • Seppo Sippu
    • 1
  • Eljas Soisalon-Soininen
    • 1
  1. 1.Department of Computer ScienceUniversity of HelsinkiHelsinki 25Finland

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