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A Certified Module to Study Digital Images with the Kenzo System
[chapter]

2012
*
Lecture Notes in Computer Science
*

The proof is carried out using ACL2, a system

doi:10.1007/978-3-642-27549-4_15
fatcat:ynkiskuvrvapne5ogt72torv2e
*for*proving properties of programs written in (a subset of) Common Lisp. ... The*description*of the main function in charge of this task is shown here:*simplicial*-*complex*-generator ls: From a list of simplexes, ls, this function generates the associated*simplicial**complex*, that ...*For*each p we obtain two triangles which are two facets of the*simplicial**complex*associated with I. ...##
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Knowledge and simplicial complexes
[article]

2020
*
arXiv
*
pre-print

*Simplicial*

*complexes*are a versatile and convenient paradigm on which to build all the tools and techniques of the

*logic*of knowledge, on the assumption that initial epistemic models can be described in ... We give a survey on how to interpret all such notions on

*simplicial*

*complexes*, building upon the foundations laid in prior work by Goubault and others. ... In this work we further explore and survey what the

*logic*of knowledge can contribute to the

*description*of

*simplicial*

*complexes*and their dynamic evolution. ...

##
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Page 4406 of Mathematical Reviews Vol. , Issue 90H
[page]

1990
*
Mathematical Reviews
*

Formulas relating HW;(p) and SW;(p) are known (and mentioned in the paper)

*for*i = 1, 2, 3, but not*for*i = 4.*For*the proofs the author uses*simplicial*algebraic topology in Grothendieck sites. ... Second, the author states that his*complex*I(r) is the same as the*complex*that Lichtenbaum and Milne would call I'(r)[—2r]. ...##
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Higher Čech Theory

2004
*
K-theory
*

We introduce a notion of 'cover of level n'

doi:10.1007/s10977-004-0840-0
fatcat:47pb6w6tlvghdbenrdpnqwqndi
*for*a topological space, or more generally any Grothendieck site, with the key property that*simplicial*homotopy classes computed along the filtered diagram ... Our approach is purely*simplicial*and combinatorial. Mathematics Subject Classifications (2000): 18G55, 55N30 ... Duskin*for*several email messages and generous*simplicial*guidance; this work could not have started without his definitions and insights. ...##
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Formalization of a normalization theorem in simplicial topology

2012
*
Annals of Mathematics and Artificial Intelligence
*

*simplicial*set, and a smaller chain

*complex*

*for*the same

*simplicial*set, called the normalized chain

*complex*. ... In this paper we present a complete formalization of the Normalization Theorem, a result in Algebraic

*Simplicial*Topology stating that there exists a homotopy equivalence between the chain

*complex*of a ... Acknowledgements We thank the anonymous referees

*for*their careful revision and useful feedback. ...

##
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Geometric Model Checking of Continuous Space
[article]

2022
*
arXiv
*
pre-print

The Spatial

arXiv:2105.06194v2
fatcat:w6sqisekjndgrnhrsydoaokftq
*Logic*of Closure Spaces, SLCS, extends Modal*Logic*with reachability connectives that, in turn, can be used*for*expressing interesting spatial properties, such as "being near to" or "being ... Topological Spatial Model Checking is a recent paradigm where model checking techniques are developed*for*the topological interpretation of Modal*Logic*. ... We use the*terminology*cells in this way*for*the purposes of this paper; there is no relation between such cells and the so-called cell*complexes*of algebraic topology. ...##
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Incidence Simplicial Matrices Formalized in Coq/SSReflect
[chapter]

2011
*
Lecture Notes in Computer Science
*

*Simplicial*

*complexes*are at the heart of Computational Algebraic Topology, since they give a concrete, combinatorial

*description*of otherwise rather abstract objects which makes many important topological ... In this paper we present a formalization in the COQ theorem prover of

*simplicial*

*complexes*and their incidence matrices as well as the main theorem that gives meaning to the definition of homology groups ...

*Simplicial*

*complexes*provide a purely combinatorial

*description*of topological spaces which admit a triangulation. ...

##
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Cosimplicial C-infinity rings and the de Rham complex of Euclidean space
[article]

2013
*
arXiv
*
pre-print

We also analyse the notion of R-module (following Quillen)

arXiv:1310.7407v1
fatcat:gckdfjfkfrckbhzwnkezdfwns4
*for*a (co-)*simplicial*C-infinity ring R. ... We prove that the cosimplicial abelian group associated to the de Rham*complex*of Euclidean space has the structure of a cosimplicial C-infinity ring. ... I give explanation of this*terminology*in the corresponding section. ...##
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Stacky fans and tropical moduli in polymake
[article]

2021
*
arXiv
*
pre-print

*For*instance, the next

*logical*step would be to analyse the cells of type (020) and (111) in M pl 3 . D.Bunnett and M. ...

*For*instance, the second barycentric subdivision of a finite symmetric ∆-

*complex*yields a finite

*simplicial*

*complex*on which the group action is regular [4, Definition II.1.2 and Exercise III.5], which ...

##
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A simplicial complex model of dynamic epistemic logic for fault-tolerant distributed computing
[article]

2017
*
arXiv
*
pre-print

Then we use dynamic epistemic

arXiv:1703.11005v2
fatcat:2j5mgeumrrgq5hqqh3ujovuzwu
*logic*to study how the*simplicial**complex*epistemic model changes after the agents communicate with each other. ...*For*each state of the Kripke model there is a facet in the*complex*, with one vertex per agent. ... Sergio Rajsbaum would like to acknowledge the Ecole Polytechnique*for*financial support through the 2016-2017 Visiting Scholar Program. ...##
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Enriched categories and models for spaces of evolving states

2008
*
Theoretical Computer Science
*

We model both the 'space' and the directed paths by a

doi:10.1016/j.tcs.2008.06.029
fatcat:toiz5ntwcrgo5hnsym6zyqv4du
*simplicially*enriched category, and show how to adapt some classical constructions to produce a differential graded enrichment. ... That structure is, however, non-commutative and computational techniques*for*handling it are more*complex*than*for*, say,*simplicial*vector spaces or chain*complexes*. ... The*terminology*'chain*complex*(of vector spaces)' is usually considered to be synonymous with 'non-negatively graded dgvs', whilst a cochain*complex*is a 'non-positively graded dgvs'. ...##
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Shellability is NP-Complete

2018
*
International Symposium on Computational Geometry
*

*For*d ≥ 3, the problem is already NP-hard

*for*pure d-dimensional

*simplicial*

*complexes*that are cones (hence contractible). ... We prove that

*for*every d ≥ 2, deciding if a pure, d-dimensional,

*simplicial*

*complex*is shellable is NP-hard, hence NP-complete. ... This is a purely combinatorial

*description*of a

*simplicial*

*complex*and a natural input model

*for*computational questions. 9 A (finite) geometric

*simplicial*

*complex*is a finite collection K of geometric ...

##
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Sheafifiable homotopy model categories

2000
*
Mathematical proceedings of the Cambridge Philosophical Society (Print)
*

If a Quillen model category can be specified using a certain

doi:10.1017/s0305004100004722
fatcat:2x5gqilwpfbnzbptncdflwstt4
*logical*syntax (intuitively, "is algebraic/combinatorial enough"), so that it can be defined in any category of sheaves, then the satisfaction ... This suggests that one borrows the*logical**description*of weak equivalences and one of the classes of cofibrations and fibrations. ... It is quite ironic to observe that while the simple (inductive) injective replacement arguments break down*for*unbounded*complexes*, the proof strategy of 3.13 can only apply to a category of*complexes*...##
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Computability of homotopy groups of nilpotent complexes

1987
*
Journal of Pure and Applied Algebra
*

In Section 6 we obtain the rewards of the application of

doi:10.1016/0022-4049(87)90106-x
fatcat:ej3rwx35bzbdnmtciiw2epbfim
*logic*.*For*a nilpotent*complex*, the Postnikov tower does not directly yield a presentation of x,X. ... A*simplicial*set X is called locally finite if the set of n-simplices X" is finite*for*all n 2 0. Let Y be a Kan*complex*and let Hom,(l, Y) be the*simplicial*path*complex*. ... Each*complex*Yn,r,q will be a subcomplex of Y,,i, and*for*q> n, a q-deformation retract of Yn,j. ...##
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Freeness conditions for quasi 3-crossed modules and complexes of using simplicial algebras with CW−bases

2013
*
Mathematical Sciences
*

Quasi 3-crossed

doi:10.1186/2251-7456-7-35
fatcat:cazwzgr76zbrlnyvvmwalqvpnu
*complexes*are introduced and similar freeness results are given*for*these are discussed. ... Using free*simplicial*algebras with given CW−basis, it is shown how to construct a free or totally free quasi 3-crossed module on suitable construction data. ... The following notation and*terminology*is due to [6] . We give an explicit*description*of the construction of a totally free 2-crossed module. ...
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