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Noetherian Spaces in Verification [chapter]

Jean Goubault-Larrecq
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.  ... 
doi:10.1007/978-3-642-14162-1_2 fatcat:noux7wn3gfcwlkssyf2hnmavti

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

Jean Goubault-Larrecq, Monika Seisenberger, Victor Selivanov, Andreas Weiermann, Marc Herbstritt
2016 Dagstuhl Reports  
of Well quasi-orders (known as the Wqo-Theory) and several fields of Computer Science (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.  ... 
doi:10.4230/dagrep.6.1.69 dblp:journals/dagstuhl-reports/Goubault-Larrecq16 fatcat:o3uwzu5ptfavfes6kgexpi4a6q

On Noetherian Spaces

Jean Goubault-Larrecq
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, 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.  ... 
doi:10.1109/lics.2007.34 dblp:conf/lics/Goubault-Larrecq07 fatcat:53hobcjvjbbb3bo4ql34pxqjwm

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,  ... 

Noetherian Quasi-Polish Spaces [article]

Matthew de Brecht, Arno Pauly
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.  ... 
arXiv:1607.07291v2 fatcat:4dctfac4kff2hckso3x6ghkgoa

Topologically defined classes of commutative rings

Marco Fontana
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.  ... 
doi:10.1007/bf01796550 fatcat:te3oo5itl5fhpmvs2bae2wzzim

Extending coherent and quasi-coherent sheaves on generically closed spaces

F Van Oystaeyen, A Verschoren
1984 Journal of Algebra  
The advantage of these 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.  ... 
doi:10.1016/0021-8693(84)90241-2 fatcat:xaaak7nj5bb3lf3sh66hjo4hxq

The maximal ideal space of a noetherian ring

Sylvia Wiegand, Roger Wiegand
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.  ... 
doi:10.1016/0022-4049(76)90011-6 fatcat:hbflyus3lzg55lkdkh5ju4bbie

Noetherian Quasi-Polish spaces

Matthew De Brecht, Arno Pauly, Marc Herbstritt
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.  ... 
doi:10.4230/lipics.csl.2017.16 dblp:conf/csl/BrechtP17 fatcat:rlpugis7nzfblekknqqxglvzwa

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  ... 

Fixed Points and Noetherian Topologies [article]

Aliaume Lopez
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.  ... 
arXiv:2207.07614v1 fatcat:jhstlgijlzdqrdfrwxw44z4sva

Regularization of birational actions of FW groups

Yves Cornulier
2021 Confluentes Mathematici (CM)  
I owe to Michel Brion the argument using equivariant resolution of singularities 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 .  ... 
doi:10.5802/cml.65 fatcat:pttbg26krnd3vkemovfxlchh2m

Regularization of birational actions of FW groups [article]

Yves Cornulier
2019 arXiv   pre-print
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 .  ...  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  ... 
arXiv:1910.07802v1 fatcat:itbpvrp7nzbj7nqs7fohzfxldq

Finiteness for the k-factor model and chirality varieties

Jan Draisma
2010 Advances in Mathematics  
Second, chirality varieties inspired by applications 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.  ... 
doi:10.1016/j.aim.2009.08.008 fatcat:4fy47ycztnfgxeogd2cvupitne

Finiteness for the k-factor model and chirality varieties [article]

Jan Draisma
2008 arXiv   pre-print
Second, chirality varieties inspired by applications 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.  ... 
arXiv:0811.3503v1 fatcat:yfdxjoeazfen3jkv57ch6h6sui
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