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Choiceless polynomial time

1999
*
Annals of Pure and Applied Logic
*

Turing machines deÿne

doi:10.1016/s0168-0072(99)00005-6
fatcat:gqnccerwmfd5pdyvg6k33q72ue
*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*. ...##
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Choiceless polynomial time
[article]

1997
*
arXiv
*
pre-print

Turing machines define

arXiv:math/9705225v1
fatcat:5i3bafda25ezvnjyqwxd47e2uy
*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. ...##
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Is Polynomial Time Choiceless?
[chapter]

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

doi:10.1007/978-3-319-23534-9_11
fatcat:n6rczztse5g4nezyzahgrmis3q
*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. ...##
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Choiceless Polynomial Time, Symmetric Circuits and Cai-Fürer-Immerman Graphs
[article]

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|. ...

##
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Characterising Choiceless Polynomial Time with First-Order Interpretations

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. ...

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

2000
*
Lecture Notes in Computer Science
*

In fact, it was shown that

doi:10.1007/3-540-44622-2_2
fatcat:gagfzqignfgnnfz4zrn5osr6bq
*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. ...##
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Canonization for Bounded and Dihedral Color Classes in Choiceless Polynomial Time
[article]

2020
*
arXiv
*
pre-print

We present a canonization procedure for graphs with dihedral color classes of bounded size in the logic of

arXiv:2010.12182v1
fatcat:o6nbddqtbje4hd7xzt6qoamhbm
*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. ...##
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Choiceless polynomial time, counting and the Cai–Fürer–Immerman graphs

2008
*
Annals of Pure and Applied Logic
*

We consider

doi:10.1016/j.apal.2007.11.011
fatcat:hfmyhfbrevfbfo6uewhwzy5jyu
*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. ...##
###
Choiceless Polynomial Time on Structures with Small Abelian Colour Classes
[chapter]

2014
*
Lecture Notes in Computer Science
*

A i+1 A i ∪ Pot(A i ) States of CPT-programs }

doi:10.1007/978-3-662-44522-8_5
fatcat:w3g4zwluvfgqxhbda7lsiqrity
*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 ...##
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Definability of Cai-Fürer-Immerman Problems in Choiceless Polynomial Time

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). ...

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

2006
*
Electronical Notes in Theoretical Computer Science
*

We consider

doi:10.1016/j.entcs.2005.05.024
fatcat:au55aqwhandrlkdvekciabidke
*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. ...##
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Strong extension axioms and Shelah's zero-one law for choiceless polynomial time

2003
*
Journal of Symbolic Logic (JSL)
*

This paper developed from Shelah's proof of a zero-one law for the complexity class "

doi:10.2178/jsl/1045861507
fatcat:vaizcgxcrbhyjoo7alnzdatniu
*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. ...##
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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 ...

##
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Test Input Data Generation for Choiceless Program Nets

2020
*
ECTI Transactions on Computer and Information Technology
*

Secondly,

doi:10.37936/ecti-cit.2020141.197859
fatcat:vbg3ifwzpfabzmjej2qfld5xma
*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*. ...##
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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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