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Choiceless Polynomial Time on Structures with Small Abelian Colour Classes [chapter]

F. Abu Zaid, E. Grädel, M. Grohe, W. Pakusa
2014 Lecture Notes in Computer Science  
Theorem CPT = P on q-bounded structures with Abelian colours. Theorem CPT = P on q-bounded structures with Abelian colours.  ...  q-bounded structures Beyond Abelian groups: does CPT capture P on q-bounded structures with solvable colours? Theorem CPT = P on q-bounded structures with Abelian colours.  ... 
doi:10.1007/978-3-662-44522-8_5 fatcat:w3g4zwluvfgqxhbda7lsiqrity

Is Polynomial Time Choiceless? [chapter]

Erich Grädel, Martin Grohe
2015 Lecture Notes in Computer Science  
Nevertheless, together with Andreas Blass and Saharon Shelah, he has also proposed what still seems to be the most promising candidate for a logic for polynomial time, namely Choiceless Polynomial Time  ...  A long time ago, Yuri Gurevich made precise the problem of whether there is a logic capturing polynomial-time on arbitrary finite structures, and conjectured that no such logic exists.  ...  It is still open whether Choiceless Polynomial Time captures Ptime on all classes of finite structures with bounded colour class size.  ... 
doi:10.1007/978-3-319-23534-9_11 fatcat:n6rczztse5g4nezyzahgrmis3q

Characterising Choiceless Polynomial Time with First-Order Interpretations

Erich Gradel, Wied Pakusa, Svenja Schalthofer, Lukasz Kaiser
2015 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science  
Choiceless Polynomial Time (CPT) is one of the candidates in the quest for a logic for polynomial time.  ...  We present here alternative characterisations of Choiceless Polynomial Time (with and without counting) based on iterated first-order interpretations.  ...  This implies in particular that CPT captures polynomial time on structures of colour class size two.  ... 
doi:10.1109/lics.2015.68 dblp:conf/lics/GradelPSK15 fatcat:o6zudj655jdxzk54icw22ulauu

Definability of Cai-Fürer-Immerman Problems in Choiceless Polynomial Time

Wied Pakusa, Svenja Schalthöfer, Erkal Selman
2018 ACM Transactions on Computational Logic  
Choiceless Polynomial Time (CPT) is one of the most promising candidates in the search for a logic capturing Ptime.  ...  The strength of Choiceless Polynomial Time is its ability to perform isomorphism-invariant computations over structures, using hereditarily finite sets as data structures.  ...  CPT captures Ptime on structures with bounded colour class size if the colour classes have Abelian automorphism groups.  ... 
doi:10.1145/3154456 fatcat:b4nso4uqa5eqlfofh7lgczf2km

Choiceless Polynomial Time, Symmetric Circuits and Cai-Fürer-Immerman Graphs [article]

Benedikt Pago
2021 arXiv   pre-print
Choiceless Polynomial Time (CPT) is currently the only candidate logic for capturing PTIME (that is, it is contained in PTIME and has not been separated from it).  ...  Our result implicitly extends this to preorders with colour classes of polylogarithmic size (plus some unordered additional structure).  ...  This generalises the choiceless CFI-algorithm from [16] , which works on preordered base graphs with logarithmically-sized colour classes.  ... 
arXiv:2107.03778v1 fatcat:5wuqyd46yrfv5d64ko3jvadsze

Rank logic is dead, long live rank logic! [article]

Erich Grädel, Wied Pakusa
2015 arXiv   pre-print
Motivated by the search for a logic for polynomial time, we study rank logic (FPR) which extends fixed-point logic with counting (FPC) by operators that determine the rank of matrices over finite fields  ...  This solves an open question posed by Dawar and Holm and also implies that rank logic, in its original definition with a distinct rank operator for every field, fails to capture polynomial time.  ...  A negative answer to this last question would provide a class of structures on which FPR * is strictly weaker than Choiceless Polynomial Time (which captures Ptime on this class [1] ).  ... 
arXiv:1503.05423v1 fatcat:coz4qftg65go7dcttf6t3guwwa

Approximations of Isomorphism and Logics with Linear-Algebraic Operators [article]

Anuj Dawar, Erich Grädel, Wied Pakusa
2019 arXiv   pre-print
It follows that there are polynomial-time properties of graphs which are not definable in the infinitary logic with all Q-linear-algebraic operators and finitely many variables, which implies that no extension  ...  The intuition is that two graphs G and H which are equivalent with respect to k-Q-IM-equivalence cannot be distinguished by a refinement of k-tuples given by linear operators acting on vector spaces over  ...  The class C is not just decidable in PTIME, but also definable in choiceless polynomial time (CPT) (see [30] ).  ... 
arXiv:1902.06648v2 fatcat:dmyz6u4rqnhv3olcegxtmfe4oq

Deep Learning for Computer Vision (Dagstuhl Seminar 17391) Body-Centric Computing (Dagstuhl Seminar 17392)

Jeremy Blackburn, Emiliano De Cristofaro, Michael Sirivianos, Thorsten Strufe, Adnan Darwiche, Pierre Marquis, Dan Suciu, Stefan, Ute Schmid, Stephen Muggleton, Rishabh Singh, Daniel Cremers (+7 others)
and personal growth to deepen their understanding and engagement with their own bodies.  ...  We believe the reason for this is due to limited knowledge about how to understand, analyse and correlate the vast amount of data from the various sensors worn by individuals and populations in real-time  ...  The three survey talks were given by Wied Pakusa (Oxford) on recent achievements concerning the quest for a logic for polynomial time, focussing on Rank Logic and on Choiceless Polynomial Time, Dan Suciu  ...