
Capturing Logarithmic Space and Polynomial Time on Chordal ClawFree Graphs
We show that the class of chordal clawfree graphs admits LREC=definabl...
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Deep Weisfeiler Leman
We introduce the framework of Deep Weisfeiler Leman algorithms (DeepWL),...
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Insignificant Choice Polynomial Time
In the late 1980s Gurevich conjectured that there is no logic capturing ...
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Limitations of the InvertibleMap Equivalences
This note draws conclusions that arise by combining two recent papers, b...
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Ranking Bracelets in Polynomial Time
The main result of the paper is the first polynomialtime algorithm for ...
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Globally Optimal Joint Uplink Base Station Association and Beamforming
The joint base station (BS) association and beamforming problem has been...
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Choiceless Polynomial Time, Symmetric Circuits and CaiFürerImmerman Graphs
Choiceless Polynomial Time (CPT) is currently the only candidate logic f...
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Separating Rank Logic from Polynomial Time
In the search for a logic capturing polynomial time the most promising candidates are Choiceless Polynomial Time (CPT) and rank logic. Rank logic extends fixedpoint logic with counting by a rank operator over prime fields. We show that the isomorphism problem for CFI graphs over ℤ_2^i cannot be defined in rank logic, even if the base graph is totally ordered. However, CPT can define this isomorphism problem. We thereby separate rank logic from CPT and in particular from polynomial time.
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