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The complexity of random ordered structures

2008
*
Annals of Pure and Applied Logic
*

Verbitsky, How complex are

doi:10.1016/j.apal.2007.11.010
fatcat:vnyo6aeskbcjbm6ekx43hjbdma
*random*graphs in first*order**logic*?*Random**Structures*and Algorithms 26 (2005) 119-145]*of*D(G p (n)) = log 1/ p n + O(lg lg n). ... We show that for*random*bit strings, U p (n), with probability, p = 1 2 ,*the*first*order*quantifier depth D(U p (n)) needed to distinguish non-isomorphic*structures*is Θ(lg lg n), with high probability ... Acknowledgments*The*second author gratefully acknowledges support from NSF ITR 01-21651 and MRI 02-15942 and*the*hospitality*of**the*Centre de Recerca Matemàtica, Barcelona, Spain. ...##
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Learning directed probabilistic logical models: ordering-search versus structure-search

2008
*
Annals of Mathematics and Artificial Intelligence
*

We conclude that there is no significant difference between

doi:10.1007/s10472-009-9134-9
fatcat:pt5zatdj3rcb3biyyabrgv3any
*the*two algorithms in terms*of*quality*of**the*learnt models while*ordering*-search is significantly faster. ... This problem has been tackled before by upgrading*the**structure*-search algorithm initially proposed for Bayesian networks. ...*of**the**logical*predicates and an assignment*of*values to all ground*random*variables (as determined by*the**random*variable declarations). ...##
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Randomisation and Derandomisation in Descriptive Complexity Theory

2011
*
Logical Methods in Computer Science
*

Similarly, we present a query on

doi:10.2168/lmcs-7(3:14)2011
fatcat:ez6mz5hh3fcoda6ka726764rre
*ordered**structures*which is definable in BPFO but not in monadic second-*order**logic*, and a query on additive*structures*which is definable in BPFO but not in FO. ... Finally, we note that BPIFP+C,*the*probabilistic version*of*fixed-point*logic*with counting, captures*the*complexity class BPP, even on unordered*structures*. ... Acknowledgements We would like to thank Nicole Schweikardt and Dieter van Melkebeek for helpful comments on an earlier version*of*this paper. ...##
###
A zero-one law for logic with a fixed-point operator

1985
*
Information and Control
*

Contrary to what one might expect, our equivalence result does not allow us to transfer PSPACE completeness

doi:10.1016/s0019-9958(85)80027-9
fatcat:pvnvemhlybfx5bq43zxugi4s2y
*of**the*theory*of**random**structures*from first-*order**logic*to*the*fixed-point operators. ... We show that any formula in these extended*logics*is equivalent, in*random**structures*(i.e., with probability approaching 1 as*the**structures*get larger), to a first-*order*formula. ...*THE*COMPLEXITY*OF**THE*FO + IFP THEORY*OF**RANDOM**STRUCTURES**The*proofs*of**the*zero-one laws for first-*order**logic*and for FO + IFP show that a sentence is true in*random*(countably infinite)*structures*...##
###
Page 3690 of Mathematical Reviews Vol. , Issue 99f
[page]

1999
*
Mathematical Reviews
*

*the*second

*order*monadic properties

*of*a

*random*mapping. ... Second-

*order*monadic

*logic*extends first-

*order*

*logic*by allowing quantification over subsets

*of*

*the*universe. ...

##
###
The modal logic of the countable random frame

2003
*
Archive for Mathematical Logic
*

We study

doi:10.1007/s001530100135
fatcat:guydqwklyrfdhnagfs44rznyzy
*the*modal*logic*ML r*of**the*countable*random*frame, which is contained in and 'approximates'*the*modal*logic**of*almost sure frame validity, i.e.*the**logic**of*those modal principles which are valid ... Therefore*the*analog*of*Fagin's transfer theorem for almost sure validity in first-*order**logic*fails for modal*logic*. ...*The*work*of*Valentin Goranko was done during his sabbatical leave to*the*University*of*Victoria, BC, Canada, and supported in part by NSERC. ...##
###
Zero-One Laws
[chapter]

2004
*
Elements of Finite Model Theory
*

We can generalize this train

doi:10.1007/978-3-662-07003-1_12
fatcat:4hpoz4wtlffidplb5gjc3bvd74
*of*thought to prove*the*zero-one law for first-*order**logic*over general*structures*, once we know how to build up an analogue to*the**random*graph: a homogeneous*random**structure*... We will then use a related but much more general construction known as a Fraïssé limit in*order*to prove*the*zero-one law for first-*order**logic*over*the**structures**of*any purely relational vocabulary. ...##
###
Book review: Descriptive complexity, by Neil Immerman

2001
*
Discrete Dynamics in Nature and Society
*

Application

doi:10.1155/s1026022601000061
fatcat:svibibixhjderjixlvkog2zdze
*of*descriptive complexity to databases is obvious relational databases are finite*logical**structure*and languages like SQL are simple extensions*of*first-*order**logic*. ... Very uniform classes, e.g., To be input to a computer a*structure*must be encoded as a character string. Encoding imposes an*ordering**of**the**structure*. ...##
###
Random Satisfiability: A Higher-Order Logical Approach in Discrete Hopfield Neural Network

2021
*
IEEE Access
*

This paper proposes

doi:10.1109/access.2021.3068998
fatcat:x2eerlvq4fcrxmn5tngye7mzdu
*Random*3 Satisfiability (RAN3SAT) with three types*of**logical*combinations (k =1, 3, k =2, 3, and k =1, 2, 3) to report*the*behaviors*of*multiple*logical**structures*. ... To resolve this problem,*the*advantage*of*introducing nonsystematic satisfiability*logic*is important to improve*the*flexibility*of**the**logical**structure*. ...*The*work by [21] explains how RANkSAT is extended for nonsystematic*logical*rule by emphasizing*random**structure*with higher*orders**of*k and reporting*the*behavior*of*more*logical*combination. ...##
###
JSL volume 86 issue 4 Cover and Back matter

2021
*
Journal of Symbolic Logic (JSL)
*

p-adic valuation v p , Q and SF Q are defined likewise for rational numbers, and < denotes

doi:10.1017/jsl.2021.105
fatcat:c53lyik6evfpbf6rlrfgjaelii
*the*natural*ordering*on each*of*these domains. ... We consider*the**structures*(Z; SF Z ), (Z; <, SF Z ), (Q; SF Q ), and (Q; <, SF Q ) where Z is*the*additive group*of*integers, SF Z is*the*set*of*a ∈ Z such that vp(a) < 2 for every prime p and corresponding ... We will introduce a first-*order*notion*of*genericity which captures*the*partial*randomness*in*the*interaction between SF Z and*the*additive*structure*on Z. ...##
###
JSL volume 86 issue 4 Cover and Front matter

2021
*
Journal of Symbolic Logic (JSL)
*

They should also consult

doi:10.1017/jsl.2021.104
fatcat:qnlbng6eknalxaxvdcvah6bw5a
*the*more general guidelines for*the*submission*of*manuscripts at http://www.aslonline.org/journals-journal-guide.html. ... These instructions include*the*Association's standards about previous publication and plagiarism as well as information about copyrights and electronic copies*of*published papers. ... We will introduce a first-*order*notion*of*genericity which captures*the*partial*randomness*in*the*interaction between SF Z and*the*additive*structure*on Z. ...##
###
Page 636 of Mathematical Reviews Vol. , Issue 95b
[page]

1995
*
Mathematical Reviews
*

Lynch [

*Random**Structures*Algorithms 3 (1992), no. 1, 33-53; MR 92j:03029] proved that, for any sentence A*of**the*first-*order*theory*of*graphs, /4(c) = lim,—.. ...*Random**Structures*Algorithms 5 (1994), no. 1, 191-204. J. F. ...##
###
Page 03 of Mathematical Reviews Vol. , Issue 94d
[page]

1994
*
Mathematical Reviews
*

Some

*of**the*important features*of*these*logics*are: (i) both*the*formulas and*the**structures*for*the**logics*reflect*the*fact that a system is composed out*of*a number*of*participating sequential agents ... small index property for w-stable w-categorical*structures*and for*the**random*graph. ...##
###
0–1 Laws for Fragments of Existential Second-Order Logic: A Survey
[chapter]

2000
*
Lecture Notes in Computer Science
*

In this survey, we consider fragments

doi:10.1007/3-540-44612-5_6
fatcat:ndxqxpfoffcozpybdt4zym3idm
*of*existential second-*order**logic*in which we restrict*the*patterns*of*first-*order*quantifiers. ...*The*probability*of*a property on*the*collection*of*all finite relational*structures*is*the*limit as Ò ½*of**the*fraction*of**structures*with Ò elements satisfying*the*property, provided*the*limit exists. ...*of*second-*order**logic*considered here. ...##
###
Page 2429 of Mathematical Reviews Vol. , Issue 2000d
[page]

2000
*
Mathematical Reviews
*

This expository article shows how such results have been extended by numerous authors to more powerful

*logics*and to*the*class*of**random**structures*known as*random*graphs. ... It states that, for every sentence in*the*language,*the*probability that it holds for a*random**structure*approaches a limit as*the*size*of**the**structure*grows. ...
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