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On the dualization in distributive lattices and related problems
[article]

2020
*
arXiv
*
pre-print

*In*this paper, we study

*the*

*dualization*

*in*

*distributive*

*lattices*, a generalization of

*the*well-known hypergraph

*dualization*

*problem*. ... This

*in*particular allows us to study

*the*complexity of

*the*

*problem*under various combined restrictions

*on*graph classes

*and*poset types, including bipartite, split,

*and*co-bipartite graphs,

*and*variants ... We show that

*the*obtained

*problem*is equivalent to

*the*

*dualization*

*in*

*distributive*

*lattices*. ...

##
###
Dualization in Lattices Given by Ordered Sets of Irreducibles
[article]

2015
*
arXiv
*
pre-print

However, if

arXiv:1504.01145v2
fatcat:n5zsomhlpnbdviuo4urk4ewve4
*the**lattice*is*distributive*,*dualization*is shown to be possible*in*subexponential time. ...*Dualization*of a monotone Boolean function*on*a finite*lattice*can be represented by transforming*the*set of its minimal 1 to*the*set of its maximal 0 values. ...*The*second author was supported by*the*Basic Research Program of*the*National Research University Higher School of Economics (Moscow, Russia)*and*Russian Foundation for Basic Research. ...##
###
The Involutive Quantaloid of Completely Distributive Lattices
[article]

2020
*
arXiv
*
pre-print

Let sLatt be

arXiv:1911.01085v3
fatcat:rk6ewzmn3jc7rlnb3ua6sdk7ui
*the*category of sup-*lattices**and*join-continuous functions*and*let cdLatt be*the*full subcategory of sLatt whose objects are*the*completely*distributive**lattices*. ... We prove*the*following result: Q(L) is an involutive (that is, non-commutative cyclic -autonomous) quantale if*and*only if L is a completely*distributive**lattice*. ...*The*author is thankful to Srecko Brlek, Claudia Muresan,*and*André Joyal for*the*fruitful discussions these scientists shared with him*on*this topic during winter 2018. ...##
###
Dualization in lattices given by implicational bases
[article]

2020
*
arXiv
*
pre-print

*Lattices*that share this property include

*distributive*

*lattices*coded by

*the*ideals of an interval order, when both

*the*independent-width

*and*

*the*size of

*the*premises equal

*one*. ... It was recently proved that

*the*

*dualization*

*in*

*lattices*given by implicational bases is impossible

*in*output-polynomial time unless P=NP. ... Acknowledgement

*The*first author would like to thank Simon Vilmin for extensive discussions

*on*

*the*topic of this paper. ...

##
###
Beyond Hypergraph Dualization
[chapter]

2016
*
Encyclopedia of Algorithms
*

For

doi:10.1007/978-1-4939-2864-4_719
fatcat:uzler4wr6vbobozpcrtnid6ipa
*distributive**lattices*class which contains boolean*lattice**and**the*product of chains,*the**dualization*is open. 3. ...*The*Trans-Enum*problem*can also be formulated as a*dualization**problem**in*posets. Let (P, ≤) be a poset (i.e. ≤ is a reflexive, antisymmetric,*and*transitive*relation**on**the*set P ). ...##
###
Beyond Hypergraph Dualization
[chapter]

2014
*
Encyclopedia of Algorithms
*

*The*Trans-Enum

*problem*can also be formulated as a

*dualization*

*problem*

*in*posets. Let (P, ≤) be a poset (i.e. ≤ is a reflexive, antisymmetric,

*and*transitive

*relation*

*on*

*the*set P ). ... For

*distributive*

*lattices*class which contains boolean

*lattice*

*and*

*the*product of chains,

*the*

*dualization*is open. sch(R)

*and*c ∈ D. Let Q r be

*the*set of all possible conjunctive queries over R. ...

##
###
Translating between the representations of a ranked convex geometry
[article]

2021
*
arXiv
*
pre-print

Quite surprisingly, we show that

arXiv:1907.09433v2
fatcat:zshldvesr5d6hjoyvdf4dpxb7m
*the**problem**in*this context is already harder than*the**dualization**in**distributive**lattices*, a generalization of*the*well-known hypergraph*dualization**problem*for which ...*In*Horn logic, these are respectively known as*the*Horn expressions*and**the*characteristic models. ...*In*Section 3 we give hardness results*in*acyclic convex geometries*in**relation*with*the**dualization**problem**in**distributive**lattices*. ...##
###
Dualizing Clones as Models of Lawvere Theories

2014
*
Electronical Notes in Theoretical Computer Science
*

be beneficial for

doi:10.1016/j.entcs.2014.02.005
fatcat:d7eyy7ksevckhjt6sfajempv3m
*the*classical*problem*of studying*the**lattice*of clones*on*a given set. ...*In*this paper, we argue that*the*possibility of applying duality theory might be such a reason,*and*we support this claim by outlining how treating*and**dualizing*clones as models of Lawvere theories can ...*Dualizing**the*bounded*distributive**lattice*from Example 5.3 as a*distributive**lattice*without*the*constants 0, 1 would for instance look as displayed*in*Figure 1 . ...##
###
Page 83 of Mathematical Reviews Vol. , Issue 2002A
[page]

2002
*
Mathematical Reviews
*

Different cases of dualities are considered: For a cardinal « any «-

*dualizable*algebra B via a cer- A. Priestley for bounded*distributive**lattices*have been ex- NUMBER THEORY A. ...*The*digraph (G,—) corresponds to*the*groupoid whose underlying set is G*and**in*which xy = x if*and*only if x A set G equipped with an equivalence*relation*p can be given*the*structure of a quasitrivial ...##
###
Approaches to the sign problem in lattice field theory

2016
*
International Journal of Modern Physics A
*

We here review

doi:10.1142/s0217751x16430077
fatcat:6f2zoufbwvg6fdhgalal4d74pe
*the*sign*problem**in**lattice*field theories, focussing*on*two more recent methods:*Dualization*to world-line type of representations*and**the*density-of-states approach. ... Various strategies to overcome this so-called Sign*Problem*or Complex Action*Problem*were proposed during*the*last thirty years. ... Sulejmanpasic,*and*A. Rago for discussions. KL is supported by*the*Leverhulme Trust (grant RPG-2014-118)*and*STFC (grant ST/L000350/1). CG is supported by DFG TRR55,*and*FWF grant I 1452-N27. ...##
###
A GENERAL DUALITY THEORY FOR CLONES

2013
*
International journal of algebra and computation
*

Kearnes Inspired by work of Mašulović, we outline a general duality theory for clones that will allow us to

doi:10.1142/s0218196713500021
fatcat:5gqotzd6yzhg3jyg6gmx33as3q
*dualize*any given clone, together with its*relational*counterpart*and**the*relationship between ... Afterwards, we put*the*approach to work*and*illustrate it by producing some specific results for concrete examples as well as some general results that come from studying*the*duals of clones*in*a rather ... Indeed, every step towards a richer duality theory for*relational*structures provides us with a new opportunity to obtain more results for clones over sets by using*the*machinery introduced*in*this paper ...##
###
:{unav)

2012
*
Reliable Computing
*

*The*purpose of this paper is to inquire

*the*connection between maximal inner interval estimates of

*the*solution sets to interval linear system

*and*solutions of

*the*

*dualization*equation

*in*Kaucher interval ...

*The*results of our work are as follows: 1) a criterion of inner interval estimate of

*the*solution set, 2) a criterion for a solution of

*dualization*equation to be a maximal inner interval estimate of

*the*...

*Lattice*structure. "⊆", "≤" are partial order

*relations*

*on*IR defined by

*the*order

*relation*"≤"

*on*R (see Figures 1

*and*2 ): x ⊆ y deƒ ⇐⇒ (x ≥ y

*and*x ≤ y), x ≤ y deƒ ⇐⇒ (x ≤ y

*and*x ≤ y). "∨", "∧" are ...

##
###
Page 4940 of Mathematical Reviews Vol. , Issue 2003g
[page]

2003
*
Mathematical Reviews
*

Algebraically, a BL-algebra is a bounded

*distributive**lattice*having also*the*structure of a commutative monoid*and**one*additional binary implication, with all*the*basic operations connected by certain ... It turns out that*the*kernels of such mappings are congruence*relations**on**the*(absolutely free) term algebra of*the*considered type. ...##
###
Open problems from NCS 2018

2019
*
The Art of Discrete and Applied Mathematics
*

Thus

doi:10.26493/2590-9770.1332.594
fatcat:4vmhj7dl5zhkxeyobknctef274
*the*reader is invited to refer back to*the*relevant article. It is hoped that*in**the*months to follow some of these*problems*will be solved, or at least, considerable light will be shed*on*them. ... All participants*in**the*workshop NCS 2018 were invited to submit a list of open*problems*, typically*problems*relevant to*the*subject matter of their talk. ... Background For an antilattice N , a congruence θ is an equivalence*relation**on*N that is compatible with both ∧*and*∨. Congruence*relations*form a*lattice*, Con(N ). 9 Joao Pita Costa*Problem*9.3. ...##
###
Page 5985 of Mathematical Reviews Vol. , Issue 97J
[page]

1997
*
Mathematical Reviews
*

A fundamental

*problem**in**the*theory of natural dualities is to determine which finite algebras M are*dualizable*,*in**the*sense that there is a structure M = (M;G, H, R, 7 ) yielding a natural duality*on*... For example, if M has a*lattice*reduct, it is sufficient to choose R to be S(M?). Herein lies*the**problem*, for even when M is ...
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