Grohe, Martin and Grußien, Berit and Hernich, André and Laubner, Bastian - L-Recursion and a new Logic for Logarithmic Space

lmcs:938 - Logical Methods in Computer Science, March 13, 2013, Volume 9, Issue 1
L-Recursion and a new Logic for Logarithmic Space

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

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.


Source : oai:arXiv.org:1212.6567
DOI : 10.2168/LMCS-9(1:11)2013
Volume: Volume 9, Issue 1
Published on: March 13, 2013
Submitted on: March 7, 2012
Keywords: Computer Science - Logic in Computer Science,Computer Science - Computational Complexity


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