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The complexity of random ordered structures

Joel H. Spencer, Katherine St. John
2008 Annals of Pure and Applied Logic  
Verbitsky, How complex are 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.  ... 
doi:10.1016/j.apal.2007.11.010 fatcat:vnyo6aeskbcjbm6ekx43hjbdma

Learning directed probabilistic logical models: ordering-search versus structure-search

Daan Fierens, Jan Ramon, Maurice Bruynooghe, Hendrik Blockeel
2008 Annals of Mathematics and Artificial Intelligence  
We conclude that there is no significant difference between 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).  ... 
doi:10.1007/s10472-009-9134-9 fatcat:pt5zatdj3rcb3biyyabrgv3any

Randomisation and Derandomisation in Descriptive Complexity Theory

Kord Eickmeyer, Martin Grohe, Anuj Dawar
2011 Logical Methods in Computer Science  
Similarly, we present a query on 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.  ... 
doi:10.2168/lmcs-7(3:14)2011 fatcat:ez6mz5hh3fcoda6ka726764rre

A zero-one law for logic with a fixed-point operator

Andreas Blass, Yuri Gurevich, Dexter Kozen
1985 Information and Control  
Contrary to what one might expect, our equivalence result does not allow us to transfer PSPACE completeness 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  ... 
doi:10.1016/s0019-9958(85)80027-9 fatcat:pvnvemhlybfx5bq43zxugi4s2y

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

Valentin Goranko, Bruce Kapron
2003 Archive for Mathematical Logic  
We study 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.  ... 
doi:10.1007/s001530100135 fatcat:guydqwklyrfdhnagfs44rznyzy

Zero-One Laws [chapter]

Leonid Libkin
2004 Elements of Finite Model Theory  
We can generalize this train 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.  ... 
doi:10.1007/978-3-662-07003-1_12 fatcat:4hpoz4wtlffidplb5gjc3bvd74

Book review: Descriptive complexity, by Neil Immerman

W. Klonowski
2001 Discrete Dynamics in Nature and Society  
Application 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.  ... 
doi:10.1155/s1026022601000061 fatcat:svibibixhjderjixlvkog2zdze

Random Satisfiability: A Higher-Order Logical Approach in Discrete Hopfield Neural Network

Syed Anayet Karim, Nur Ezlin Zamri, Alyaa Alway, Mohd Shareduwan Mohd Kasihmuddin, Ahmad Izani Md Ismail, Mohd Asyraf Mansor, Nik Fathihah Abu Hassan
2021 IEEE Access  
This paper proposes 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.  ... 
doi:10.1109/access.2021.3068998 fatcat:x2eerlvq4fcrxmn5tngye7mzdu

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 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.  ... 
doi:10.1017/jsl.2021.105 fatcat:c53lyik6evfpbf6rlrfgjaelii

JSL volume 86 issue 4 Cover and Front matter

2021 Journal of Symbolic Logic (JSL)  
They should also consult the more general guidelines for the submission of manuscripts at  ...  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.  ... 
doi:10.1017/jsl.2021.104 fatcat:qnlbng6eknalxaxvdcvah6bw5a

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]

Phokion G. Kolaitis, Moshe Y. Vardi
2000 Lecture Notes in Computer Science  
In this survey, we consider fragments 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.  ... 
doi:10.1007/3-540-44612-5_6 fatcat:ndxqxpfoffcozpybdt4zym3idm

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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