# 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…

## 7 Citations

Separating LREC from LFP

- Computer ScienceArXiv
- 2021

It is shown that the path systems problem, a classic P-complete problem which is definable in LFP—fixed-point logic—is not defined in LREC = .

Pure Pointer Programs and Tree Isomorphism

- Computer ScienceFoSSaCS
- 2013

It is shown that with counting, purple captures all of logspace on locally ordered graphs, and that without a local ordering, even with counting and nondeterminism, purple cannot solve tree isomorphism.

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

- Mathematics
- 2017

Descriptive complexity theory is concerned with the characterization of complexity classes by means of suitable logics. A central open question is whether there exists a logic that characterizes, or…

Computing With a Fixed Number of Pointers

- 2013

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…

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

- Mathematics, Computer ScienceCSL
- 2017

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.

Definability of summation problems for Abelian groups and semigroups

- Mathematics, Computer Science2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
- 2017

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

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

- Mathematics, Computer ScienceLog. Methods Comput. Sci.
- 2019

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.

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It is proved that LREC is strictly more expressive than deterministic transitive closure logic with counting and incomparable in expressive power with symmetricTransitive closure logic STC and transitiveclosure logic (with or without counting).

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