# 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

#### 7 Citations

Separating LREC from LFP

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Capturing Polynomial Time and Logarithmic Space using Modular Decompositions and Limited Recursion

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Consider the P-complete problem horn which asks whether a given set of Horn clauses is (un)satisfiable. To solve it one keeps a dynamic set of atoms that are forced to be true. Using the clauses one… Expand

Capturing Logarithmic Space and Polynomial Time on Chordal Claw-Free Graphs

- Mathematics, Computer Science
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It is shown that the class of chordal claw-free graphs admits LREC$_=$-definable canonization, a logic that extends first-order logic with counting by an operator that allows it to formalize a limited form of recursion, and that fixed-point Logic with counting captures polynomial time on this graph class. Expand

Definability of summation problems for Abelian groups and semigroups

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The descriptive complexity of summation problems in Abelian groups and semigroups is studied to determine the sum over all elements of X. Expand

Capturing Logarithmic Space and Polynomial Time on Chordal Claw-Free Graphs

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- Log. Methods Comput. Sci.
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It is shown that the class of chordal claw-free graphs admits LREC$_=$-definable canonization, a logic that extends first-order logic with counting by an operator that allows it to formalize a limited form of recursion, and that fixed-point Logic with counting captures polynomial time on this graph class. Expand

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