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Pro-aperiodic monoids via saturated models
[article]

2017
*
arXiv
*
pre-print

We apply Stone duality and

arXiv:1609.07736v2
fatcat:ma3tvz37ercrdon3ejdlrq5rty
*model*theory to study the structure theory of free*pro*-*aperiodic**monoids*. ... Stone duality implies that elements of the free*pro*-*aperiodic**monoid*may be viewed as elementary equivalence classes of pseudofinite words. ... In this paper, we use Stone duality and*saturated**models*to obtain most of the known structural results about free*pro*-*aperiodic**monoids*, as well as some new ones. ...##
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Editors: Heribert Vollmer and Brigitte Vallée; Article No. 39

*
licensed under Creative Commons License CC-BY 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)
*
unpublished

We apply Stone duality and

fatcat:v5sone23ofcfll3ugxc52vjz34
*model*theory to study the structure theory of free*pro*-*aperiodic**monoids*. ...*Model*theory provides us with*saturated*words in each such class, i.e., words in which all possible factorizations are realized. ... Since finite words and W 3 are weakly 39:8*Pro*-*Aperiodic**Monoids**via**Saturated**Models**saturated*, the word W 3 is in fact ω-*saturated*. Since |W 3 | is countable, W 3 is countably*saturated*. ...##
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The linear nature of pseudowords

2019
*
Publicacions matemàtiques
*

We show that, in the case of the pseudovariety of

doi:10.5565/publmat6321901
fatcat:o2kcos6iu5cvxjcigvsgosyiye
*aperiodic*finite semigroups, the pseudoword can be recovered from the labeled linear order. ... They worked specially with*saturated**models*. In our paper, the*models*that appear in the image of the representation are not*saturated*in general. ... Consider the pseudoword a ω of the free*pro*-*aperiodic*semigroup Ω {a} A. Then F(a ω ) has only one stationary point, namely (a ω , a ω ). ...##
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The linear nature of pseudowords
[article]

2017
*
arXiv
*
pre-print

We show that, in the case of the pseudovariety of

arXiv:1702.08083v2
fatcat:ehnnxkdohbhzdeuvgvwtnp5bom
*aperiodic*finite semigroups, the pseudoword can be recovered from the labeled linear order. ... They worked specially with*saturated**models*. In our paper, the*models*that appear in the image of the representation are not*saturated*in general. ... Consider the pseudoword a ω of the free*pro*-*aperiodic*semigroup Ω {a} A. Then F(a ω ) has only one stationary point, namely (a ω , a ω ). ...##
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A Cook's tour of duality in logic: from quantifiers, through Vietoris, to measures
[article]

2020
*
arXiv
*
pre-print

To be more precise, (Schützenberger, 1965) shows that the star-free languages are precisely those recognised by (finite)

arXiv:2007.15415v1
fatcat:d7fs2d66tffg3m7o5ob6xz6tt4
*aperiodic**monoids*. ... However, it was introduced, not*via*logic and duality, but rather*via*the connection between automata and finite semigroups, where the multiplication available on the profinite*monoid*also plays a fundamental ... the propositional logic having as atoms p ≥q ϕ and p <q ϕ, for each ϕ ∈ FO ω and q ∈ [0, 1] ∩ Q, and the following inference rules (along with the usual ones for the Boolean connectives): The intended*models*...##
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Noncommutative stable homotopy and stable infinity categories

2015
*
Journal of Topology and Analysis (JTA)
*

Along the way we obtain infinity categorical

doi:10.1142/s1793525315500077
fatcat:zxlajtrcyrblrg4duzayvdn7ca
*models*for some well-known bivariant homology theories like KK-theory, E-theory, and connective E-theory*via*suitable (co)localizations. ... In a subsequent project we are going to construct a*model*structure on*Pro*ω (SC * δ ), whose homotopy category will contain HoSC * as a full subcategory. ... There is a*monoidal*exact p-localization functor NSH → NSH p . ...##
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Profinite semigroups and applications
[chapter]

*
Structural Theory of Automata, Semigroups, and Universal Algebra
*

[79] ) A language over a finite alphabet is star-free if and only if it is recognized by a finite

doi:10.1007/1-4020-3817-8_1
fatcat:xix2tppzybhgli5gmxzqbmdkf4
*aperiodic**monoid*. ... Hence we have N ↔ N*via*Eilenberg's correspondence. ...##
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Towards a pseudoequational proof theory
[article]

2017
pre-print

clearly sound, is also shown to be complete in many instances, such as when Σ defines a locally finite variety, a pseudovariety of groups, more generally, of completely simple semigroups, or of commutative

doi:10.4171/pm/2012
arXiv:1708.09681v1
fatcat:pzw6pvxqhjhhtfymz4x6roxh7i
*monoids*... Note also that a finite monogenic additive*monoid*M carries a natural structure of semiring*via*the natural additive homomorphism N → M . ... Our first example is given by the pseudoidentity x ω+1 = x ω , which defines the pseudovariety A of all finite*aperiodic**monoids*. ...##
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Collaborating institutions
[chapter]

2016
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The Financial System We Need
*

We define the distribution of the process through an irreducible

doi:10.18356/b4968a28-en
fatcat:v75hvlhqebfglfsx7q4qwwlc34
*aperiodic*matrix, which we can suppose stochastic. ... The requirement of advanced skilled professionals has led many people to study*via*web. ... The*model*for noisy images is: let f be the observed image and let us assume that f =f +n, being f a noise-free image n a noise signal (n ∼ N (0, σ)). ...##
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Limits to parallel computation: P-completeness theory

1996
*
ChoiceReviews
*

The re- A.8.27

doi:10.5860/choice.33-3959
fatcat:qjoueeu225gr7jvwdf6gkoxfbq
*Aperiodic**Monoid*Membership Variety B 2 A.9 Geometry (AMonMEMB) A.9.1 Plane Sweep Triangulation (PST) Given: duction involves constructing "geometric" gadgets for routing (left and right ... Reference: Beaudry, McKenzie, and Thérien [29].Hint: The reduction is from a variant of Generability, Problem A.6.7.Remarks: The lattice of*aperiodic**monoid*varieties is partitioned in [29] into the following ...##
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Some Fundamental Theorems in Mathematics
[article]

2022
*
arXiv
*
pre-print

It is for cancellative

arXiv:1807.08416v4
fatcat:lw7lbsxyznfrnaozilxapihmdy
*monoids*(the statement a * x = b * x implies a = b in the*monoid*) that the*monoid*is also contained isomorphically inside the group. ... The*monoid*structure belongs to a collection of mathematical structures magmas ⊃ semigroups ⊃*monoids*⊃ groups. A*monoid*is commutative, if x * y = y * x for all x, y ∈ X. ...##
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On Graphs, Groups and Geometry
[article]

2022
*
arXiv
*
pre-print

The

arXiv:2205.14097v1
fatcat:6fmpzkmuhzfrbcy4n466jw2iem
*pro*-finite completion of G has fractal Hausdorff dimension 5/8. ... Using only a*monoid*structures for example and to look for the natural numbers (N, +), would not an option for us. ...