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Choiceless polynomial time

Andreas Blass, Yuri Gurevich, Saharon Shelah
1999 Annals of Pure and Applied Logic  
Turing machines deÿne polynomial time (PTime) on strings but cannot deal with structures like graphs directly, and there is no known, easily computable string encoding of isomorphism classes of structures  ...  This question can be recast as follows: Does there exist a logic that captures polynomial time (without presuming the presence of a linear order)? Earlier, one of us conjectured a negative answer.  ...  Choiceless polynomial time.  ... 
doi:10.1016/s0168-0072(99)00005-6 fatcat:gqnccerwmfd5pdyvg6k33q72ue

Choiceless polynomial time [article]

Andreas Blass, Yuri Gurevich, Saharon Shelah
1997 arXiv   pre-print
Turing machines define polynomial time (PTime) on strings but cannot deal with structures like graphs directly, and there is no known, easily computable string encoding of isomorphism classes of structures  ...  This question can be recast as follows: Does there exist a logic that captures polynomial time (without presuming the presence of a linear order)? Earlier, one of us conjectured the negative answer.  ...  We call the fragment Choiceless Polynomial Time (CPTime). The idea is to eliminate arbitrary choice by means of parallel execution.  ... 
arXiv:math/9705225v1 fatcat:5i3bafda25ezvnjyqwxd47e2uy

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.  ...  Definition of Choiceless Polynomial Time Intuitively, Choiceless Polynomial Time (CPT) is the polynomial-time fragment of BGS-logic.  ... 
doi:10.1007/978-3-319-23534-9_11 fatcat:n6rczztse5g4nezyzahgrmis3q

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).  ...  In this paper, we consider the logic Choiceless Polynomial Time and a specific problem, called the CFI-query.  ...  Secondly, | tc(x i )| is bounded by a polynomial in |A|. Additionally, since the logic is called Choiceless Polynomial Time, also the length of any run must be polynomially bounded in |A|.  ... 
arXiv:2107.03778v1 fatcat:5wuqyd46yrfv5d64ko3jvadsze

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.  ...  Our main result is that PIL has precisely the same expressive power as Choiceless Polynomial Time.  ...  CHOICELESS POLYNOMIAL TIME Choiceless Polynomial Time operates on hereditarily finite sets. Thus we first recall some basic notions of set theory.  ... 
doi:10.1109/lics.2015.68 dblp:conf/lics/GradelPSK15 fatcat:o6zudj655jdxzk54icw22ulauu

Choiceless Polynomial Time Computation and the Zero-One Law [chapter]

Andreas Blass, Yuri Gurevich
2000 Lecture Notes in Computer Science  
In fact, it was shown that choiceless polynomial timeCPTime, the complexity class defined by BGS programs subject to a polynomial time bound, does not contain the parity problem: Given a set, determine  ...  Thus, Theorem 2 can be viewed as a zero-one law for choiceless polynomial space computation.  ... 
doi:10.1007/3-540-44622-2_2 fatcat:gagfzqignfgnnfz4zrn5osr6bq

Canonization for Bounded and Dihedral Color Classes in Choiceless Polynomial Time [article]

Moritz Lichter an Pascal Schweitzer
2020 arXiv   pre-print
We present a canonization procedure for graphs with dihedral color classes of bounded size in the logic of Choiceless Polynomial Time (CPT), which then captures PTime on this class of structures.  ...  However, important for us is that the normal form is definable in choiceless polynomial time (CPT).  ...  A polynomial-time canonization algorithm implies a polynomial-time isomorphism test.  ... 
arXiv:2010.12182v1 fatcat:o6nbddqtbje4hd7xzt6qoamhbm

Choiceless polynomial time, counting and the Cai–Fürer–Immerman graphs

Anuj Dawar, David Richerby, Benjamin Rossman
2008 Annals of Pure and Applied Logic  
We consider Choiceless Polynomial Time (CPT), a language introduced by Blass, Gurevich and Shelah, and show that it can express a query originally constructed by Cai, Fürer and Immerman to separate fixed-point  ...  In an attempt to understand the role of choice in defining polynomialtime properties, Blass, Gurevich and Shelah [1] define choiceless polynomial time, CPT, a 'logic' based on a machine model, which  ...  It remains open whether this logic captures all polynomial-time computations.  ... 
doi:10.1016/j.apal.2007.11.011 fatcat:hfmyhfbrevfbfo6uewhwzy5jyu

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  
A i+1 A i ∪ Pot(A i ) States of CPT-programs } Choiceless Polynomial Time: a 0 a 1 · · · a n−1 A 0 ∅ {a 0 , a 1 } · · · A 1 . . . . . .  ...  States of CPT-programs } Choiceless Polynomial Time: set-theoretic operations to manipulate states iterated applications run Heriditarily nite sets Beyond Abelian groups: does CPT capture  ... 
doi:10.1007/978-3-662-44522-8_5 fatcat:w3g4zwluvfgqxhbda7lsiqrity

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.  ...  Choiceless Polynomial Time Choiceless Polynomial Time is a polynomial time restriction of BGS logic (named after Blass, Gurevich and Shelah).  ... 
doi:10.1145/3154456 fatcat:b4nso4uqa5eqlfofh7lgczf2km

Choiceless Polynomial Time, Counting and the Cai–Fürer–Immerman Graphs

Anuj Dawar, David Richerby, Benjamin Rossman
2006 Electronical Notes in Theoretical Computer Science  
We consider Choiceless Polynomial Time ( e CPT), a language introduced by Blass, Gurevich and Shelah, and show that it can express a query originally constructed by Cai, Fürer and Immerman to separate  ...  In the other direction, Blass, Gurevich and Shelah introduce choiceless polynomial time with the aim of characterizing what can be done without choice [1] .  ...  time exists.  ... 
doi:10.1016/j.entcs.2005.05.024 fatcat:au55aqwhandrlkdvekciabidke

Strong extension axioms and Shelah's zero-one law for choiceless polynomial time

Andreas Blass, Yuri Gurevich
2003 Journal of Symbolic Logic (JSL)  
This paper developed from Shelah's proof of a zero-one law for the complexity class "choiceless polynomial time," defined by Shelah and the authors.  ...  The extension axioms, which form the basis for earlier zero-one laws (for first-order logic, fixed-point logic, and finite-variable infinitary logic) are inadequate in the case of choiceless polynomial  ...  We use the latter formulation as the o cial de nition of choiceless polynomial time,CPTime.  ... 
doi:10.2178/jsl/1045861507 fatcat:vaizcgxcrbhyjoo7alnzdatniu

Page 503 of Mathematical Reviews Vol. , Issue 2001A [page]

2001 Mathematical Reviews  
polynomial time.  ...  The paper investi- gates in detail the polynomial time complexity class defined by the machine model, establishing that it is more powerful than some earlier approaches to defining a logic for PTIME, yet  ... 

Test Input Data Generation for Choiceless Program Nets

Wu Biao, Qi-Wei Ge
2020 ECTI Transactions on Computer and Information Technology  
Secondly, polynomial algorithms are proposed to get all constraint conditions of any given choiceless program nets.  ...  Firstly, definitions of program nets are extended and the properties of choiceless program nets are analysed.  ...  Although these input data values are generated by the SMT solver that may take considerable computational time, our algorithms are all polynomial.  ... 
doi:10.37936/ecti-cit.2020141.197859 fatcat:vbg3ifwzpfabzmjej2qfld5xma

Page 2769 of Mathematical Reviews Vol. , Issue 2002D [page]

2002 Mathematical Reviews  
ISBN 3-540-67895-6 Contents: Andreas Blass and Yuri Gurevich, Background, reserve, and Gandy machines (1-17); Andreas Blass and Yuri Gurevich, Choiceless polynomial time computation and the zero-one law  ...  polynomial time logic: inability to express (72-125); Colin Stirling, Schema revisited (126-138); Moshe Y.  ... 
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