L-Recursion and a new Logic for Logarithmic Space

@article{Grohe2012LRecursionAA,
  title={L-Recursion and a new Logic for Logarithmic Space},
  author={Martin Grohe and Berit Gru{\ss}ien and Andr{\'e} Hernich and Bastian Laubner},
  journal={Log. Methods Comput. Sci.},
  year={2012},
  volume={9}
}
We extend first-order logic with counting by a new operator that allows it to formalise a limited form of recursion which can be evaluated in logarithmic space. The resulting logic LREC has a data complexity in LOGSPACE, and it defines LOGSPACE-complete problems like deterministic reachability and Boolean formula evaluation. We prove that LREC is strictly more expressive than deterministic transitive closure logic with counting and incomparable in expressive power with symmetric transitive… Expand
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