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Noetherian Spaces in Verification
[chapter]

2010
*
Lecture Notes in Computer Science
*

*Noetherian*

*spaces*are a topological concept that generalizes well quasiorderings. ... We explore applications to infinite-state

*verification*problems, and show how this stimulated the search for infinite procedures à la Karp-Miller. ... Introduction The purpose of this paper is to given a gentle introduction to the theory of

*Noetherian*

*spaces*,

*in*the context of

*verification*of infinite-state systems. ...

##
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Well Quasi-Orders in Computer Science (Dagstuhl Seminar 16031)

2016
*
Dagstuhl Reports
*

of Well quasi-orders (known as the Wqo-Theory) and several fields of Computer Science (

doi:10.4230/dagrep.6.1.69
dblp:journals/dagstuhl-reports/Goubault-Larrecq16
fatcat:o3uwzu5ptfavfes6kgexpi4a6q
*Verification*and Termination of Infinite-State Systems, Automata and Formal Languages, Term Rewriting and Proof Theory ...*In*this seminar, we brought together several communities from Computer Science and Mathematics*in*order to facilitate the knowledge transfer between Mathematicians and Computer Scientists as well as between ... resonated with*verification*(e.g.,*Noetherian**spaces*), and all participated actively*in*vivid sessions of setting up and discussing open questions. ...##
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On Noetherian Spaces

2007
*
22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)
*

Our starting point is that this notion generalizes that of well-quasi order,

doi:10.1109/lics.2007.34
dblp:conf/lics/Goubault-Larrecq07
fatcat:53hobcjvjbbb3bo4ql34pxqjwm
*in*the sense that an Alexandroff-discrete*space*is*Noetherian*iff its specialization quasi-ordering is well. ... A topological*space*is*Noetherian*iff every open is compact. ... We hope that*Noetherian**spaces*will be valuable*in**verification**in*the future. ...##
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Page 3379 of Mathematical Reviews Vol. , Issue 92f
[page]

1992
*
Mathematical Reviews
*

Since it is undecidable

*in*general whether a finite*Noetherian*trace replacement system is confluent [P. Narendran and the reviewer, Inform. Process. ...*In*more detail, the the- sis presents the following results: (1) a compositional and modular trace semantics for speed-independent circuits, (2) a definition of*verification*based on safe substitution, ...##
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Noetherian Quasi-Polish Spaces
[article]

2017
*
arXiv
*
pre-print

*In*the presence of suitable power

*spaces*, compactness of X can be characterized as the singleton {X} being open

*in*the

*space*O(X) of open subsets of X. ... Within the setting of Quasi-Polish

*spaces*, we can fully characterize the ∇-compact

*spaces*: A Quasi-Polish

*space*is

*Noetherian*iff it is ∇-compact. ... The second author thanks Paul Shafer for explaining results pertaining to

*Noetherian*

*spaces*

*in*reverse mathematics. ...

##
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Topologically defined classes of commutative rings

1980
*
Annali di Matematica Pura ed Applicata
*

*In*Section 2, we apply the techniques and results of the preceeding section to build up spectral

*spaces*(~ attaching 7> (ef. [13]) a spectral

*space*which has only one minimal point to another spectral ... Some results stated

*in*this section, relevant essentially to the topologieM and ordering properties of these

*spaces*, are easily deduced (*) Entrato

*in*:Redazione il 15 novembre 1978. ... ( 7 ) 7 Spec (D~) is a

*noetherian*

*space*if, and only if, Spec (D) and Spec (V) are

*noetherian*

*spaces*. ...

##
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Extending coherent and quasi-coherent sheaves on generically closed spaces

1984
*
Journal of Algebra
*

The advantage of these

doi:10.1016/0021-8693(84)90241-2
fatcat:xaaak7nj5bb3lf3sh66hjo4hxq
*spaces*is that for a*Noetherian*ring the generically closed subsets of Spec(R) correspond bijectively to idempotent kernel functors*in*R-mod. ... This also works for locally*Noetherian*schemes X by restricting attention to a covering by*Noetherian*afline*spaces*. We assume from hereon that all schemes considered are*Noetherian*. Any T.T. ...##
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The maximal ideal space of a noetherian ring

1976
*
Journal of Pure and Applied Algebra
*

*In*particular, this gives a complete characterization of the maximal ideal

*spaces*of countable

*Noetherian*rings. ... Let R be a commutative

*Noetherian*ring with prime ideal

*space*spec @). ... Moh, of a

*Noetherian*ring whose maximal ideal

*space*V is countable but has uncountably many closed sets. ...

##
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Noetherian Quasi-Polish spaces

2017
*
Annual Conference for Computer Science Logic
*

*In*particular we would like to thank Jean Goubault-Larrecq and Takayuki Kihara. ... We are grateful to the participants of the Dagstuhl Seminar Well-quasi orders

*in*Computer Science 5 for valuable discussions and inspiration. ...

*Noetherian*

*spaces*were first studied

*in*algebraic geometry. ...

##
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Page 303 of Mathematical Reviews Vol. 46, Issue 2
[page]

1973
*
Mathematical Reviews
*

Chapter 4 gives a presentation of the finiteness theorem for the higher direct images of coherent sheafs on

*Noetherian*separated algebraic*spaces*. ... X is an affine scheme; strong version: if X is a separated*Noetherian*algebraic*space*, and HX, —) is exact for coherent sheafs, then X is affine. (2) Chevalley’s theorem: If X—Y is a finite surjective ...##
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Fixed Points and Noetherian Topologies
[article]

2022
*
arXiv
*
pre-print

*In*the case of

*spaces*that are defined inductively (such as finite words and finite trees), we provide a uniform definition of a divisibility topology using our fixed point theorem. ... While such least fixed point are not

*Noetherian*

*in*general, we prove that under a mild assumption, one can use a topological minimal bad sequence argument to prove that they are. ... Acknowledgements I thank Jean Goubault-Larrecq and Sylvain Schmitz for their help and support

*in*writing this paper. I thank Simon Halfon for his help on transfinite words. ...

##
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Regularization of birational actions of FW groups

2021
*
Confluentes Mathematici (CM)
*

I owe to Michel Brion the argument using equivariant resolution of singularities

doi:10.5802/cml.65
fatcat:pttbg26krnd3vkemovfxlchh2m
*in*Remark 1.2. ...*Verifications*are direct. ... -Let Y be a*noetherian*topological*space*. Let G be a group acting continuously on Y . Let X be a dense open subset of Y . ...##
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Regularization of birational actions of FW groups
[article]

2019
*
arXiv
*
pre-print

Let Y be a

arXiv:1910.07802v1
fatcat:itbpvrp7nzbj7nqs7fohzfxldq
*noetherian*topological*space*. Let G be a group acting continuously on Y . Let X be a dense open subset of Y . ... The second step: a general lemma Recall that a topological*space*is*noetherian*if every nonempty set of closed subsets has a minimal element for inclusion, or equivalently if there is no strictly decreasing ...##
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Finiteness for the k-factor model and chirality varieties

2010
*
Advances in Mathematics
*

Second, chirality varieties inspired by applications

doi:10.1016/j.aim.2009.08.008
fatcat:4fy47ycztnfgxeogd2cvupitne
*in*chemistry. A point*in*such a chirality variety records chirality measurements of all k-subsets among an n-set of ligands. ... For instance, such equations could be used to test whether a given point lies*in*the variety. ... Finally, I thank Mathias Drton for sharing his results with Han Xiao*in*[5] at an early stage. ...##
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Finiteness for the k-factor model and chirality varieties
[article]

2008
*
arXiv
*
pre-print

Second, chirality varieties inspired by applications

arXiv:0811.3503v1
fatcat:yfdxjoeazfen3jkv57ch6h6sui
*in*chemistry. A point*in*such a chirality variety records chirality measurements of all k-subsets among an n-set of ligands. ... For instance, such equations could be used to test whether a given point lies*in*the variety. ... By Lemma 3.5 the*space*Z is Sym(N)-*Noetherian*. ...
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