L-Recursion and a new Logic for Logarithmic Space

Authors Martin Grohe, Berit Grußien, André Hernich, Bastian Laubner

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Martin Grohe
Berit Grußien
André Hernich
Bastian Laubner

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Martin Grohe, Berit Grußien, André Hernich, and Bastian Laubner. L-Recursion and a new Logic for Logarithmic Space. In Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 12, pp. 277-291, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)


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 closure logic STC and transitive closure logic (with or without counting). LREC is strictly contained in fixed-point logic with counting FPC. We also study an extension LREC= of LREC that has nicer closure properties and is more expressive than both LREC and STC, but is still contained in FPC and has a data complexity in LOGSPACE. Our main results are that LREC captures LOGSPACE on the class of directed trees and that LREC= captures LOGSPACE on the class of interval graphs.
  • descriptive complexity
  • logarithmic space
  • fixed-point logics


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