Filters








27 Hits in 3.7 sec

Continuity of Functional Transducers: A Profinite Study of Rational Functions [article]

Michaël Cadilhac, Olivier Carton, Charles Paperman
2020 arXiv   pre-print
A word-to-word function is continuous for a class of languages V if its inverse maps V_languages to V.  ...  Here, we report on the decidability of continuity for functional transducers and some standard classes of regular languages.  ...  In this section, we study the consequence of variety (non)inclusion on the inclusion of the related classes of continuous rational functions.  ... 
arXiv:1802.10555v3 fatcat:z3mtd24t3veslco6zealikafme

Continuity of Functional Transducers: A Profinite Study of Rational Functions

Michaël Cadilhac, Olivier Carton, Charles Paperman
2018 Logical Methods in Computer Science  
A word-to-word function is continuous for a class of languages~$\mathcal{V}$ if its inverse maps $\mathcal{V}$_languages to~$\mathcal{V}$.  ...  Here, we report on the decidability of continuity for functional transducers and some standard classes of regular languages.  ...  In this section, we study the consequence of variety (non)inclusion on the inclusion of the related classes of continuous rational functions.  ... 
doi:10.23638/lmcs-16(1:24)2020 fatcat:d7juean75ba2dmiumaeigiu7k4

Continuity and Rational Functions

Michaël Cadilhac, Olivier Carton, Charles Paperman, Marc Herbstritt
2017 International Colloquium on Automata, Languages and Programming  
A word-to-word function is continuous for a class of languages V if its inverse maps V_languages to V.  ...  Here, we report on the decidability of continuity for functional transducers and some standard classes of regular languages.  ...  In a first part, we study when the structure of the transducer is relevant to continuity, and in a second, when the (non)inclusion of variety relates to (non)inclusion of the class of continuous rational  ... 
doi:10.4230/lipics.icalp.2017.115 dblp:conf/icalp/CadilhacCP17 fatcat:72umguybzrburd2oornfgapckm

Automata as p-adic Dynamical Systems [article]

Livat Tyapaev
2018 arXiv   pre-print
,p-1}, where p is a prime number, coincide with the continuous transformation (with respect to the p-adic metric) of a ring Z_p of p-adic integers.  ...  The objects of the study are non-Archimedean dynamical systems generated by automata mappings on the space Z_p.  ...  We can consider an automaton function f : Z p → Z p as an algebraic dynamical system on a measurable and a metric space Z p of p-adic integers, which, actually, is a profinite algebra with the structure  ... 
arXiv:1709.02644v2 fatcat:xzs6j7qpird6hh7e2wnojlrzwi

Quantifiers on languages and codensity monads

Mai Gehrke, Daniela Petrisan, Luca Reggio
2017 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)  
Our construction yields, in particular, a new characterisation of the profinite monad of the free S-semimodule monad for finite and commutative semirings S, which generalises our earlier insight that the  ...  In particular, we provide a general construction on recognisers corresponding to adding one layer of various kinds of quantifiers and prove a related Reutenauer-type theorem.  ...  We would also like to thank the Simons Institute for the Theory of Computing for the opportunity to present this work.  ... 
doi:10.1109/lics.2017.8005140 dblp:conf/lics/GehrkePR17 fatcat:wsyfdp6u2favvfohjdmkwzix2a

Operations preserving regular languages

Jean Berstel, Luc Boasson, Olivier Carton, Bruno Petazzoni, Jean-Eric Pin
2006 Theoretical Computer Science  
Our approach relies on a detailed study of various residual notions, notably residually ultimately periodic sequences and residually rational transductions.  ...  By a natural generalization, denote by L[s], where L is a language, the set of all words of L filtered by s.  ...  The class of cyclically ultimately periodic functions has been studied by Siefkes [16] , who gave in particular a recursion scheme for producing such functions.  ... 
doi:10.1016/j.tcs.2005.11.034 fatcat:ynzgubzkffftfpy2xziv7sfme4

Quantifiers on languages and codensity monads [article]

Mai Gehrke, Daniela Petrisan, Luca Reggio
2019 arXiv   pre-print
Our construction hinges on a measure-theoretic characterisation of the profinite monad of the free S-semimodule monad for finite and commutative semirings S, which generalises our earlier insight that  ...  In particular, we provide a general construction on recognisers corresponding to adding one layer of various kinds of quantifiers and prove a corresponding Reutenauer-type theorem.  ...  , the study of profinite monads in formal language theory.  ... 
arXiv:1702.08841v3 fatcat:35gre5ddqfhgbbcadv67yi45am

Recognisable languages over monads [article]

Mikołaj Bojańczyk
2015 arXiv   pre-print
The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set.  ...  The goal of this paper is to propose monads as a unifying framework for discussing existing algebras and designing new algebras.  ...  Unravelling the classical definition of uniform continuity, a function f : A n → A is uniformly continuous with respect to L-distance if for every finite set K ⊆ L there is some finite set M ⊆ L such that  ... 
arXiv:1502.04898v1 fatcat:2in7ckqcvje7ddulnd7nmfn5jm

Profinite semigroups [article]

Revekka Kyriakoglou, Dominique Perrin
2017 arXiv   pre-print
We present a survey of results on profinite semigroups and their link with symbolic dynamics.  ...  We develop a series of results, mostly due to Almeida and Costa and we also include some original results on the Sch\"utzenberger groups associated to a uniformly recurrent set.  ...  Since, by [10, Proposition 4.3.2] , the transducer T realizes the decoding function of X, we have αβ(y) 1,1 = ψ(y) for any y ∈ B * . By continuity, we haveαβ(y) 1,1 = ψ(y) for any y ∈ B * .  ... 
arXiv:1703.10088v1 fatcat:nyslcx6iojcb5jf5jw7zrimvwq

How to Prove that a Language Is Regular or Star-Free? [chapter]

Jean-Éric Pin
2020 Lecture Notes in Computer Science  
In this paper, we present various methods to prove that a language is regular or star-free. ∅ c a∅ c c J.-É. Pin-Work supported by the DeLTA project (ANR-16-CE40-0007).  ...  Most books of automata theory [9, 23, 29, 45, 49] offer exercises on regular languages, including some difficult ones.  ...  The transduc- tion is rational if the set {(m, n) ∈ M × N | n ∈ τ (m)} is a rational subset of M × N .  ... 
doi:10.1007/978-3-030-40608-0_5 fatcat:mzoyw7mckzgxnhyggsxiq4bhoa

Extensions of automorphisms of self-similar groups [article]

Francesco Matucci, Pedro V. Silva
2019 arXiv   pre-print
We study the case of the lamplighter group L_k = Z_k Z  ...  In this work we study automorphisms of synchronous self-similar groups, the existence of extensions to automorphisms of the full group of automorphisms of the infinite rooted tree on which these groups  ...  There are two different versions of the rational group, depending on the type of transducers we allow.  ... 
arXiv:1806.09560v2 fatcat:jynmti4llbd5jgvkdu44er74ci

A Mahler's Theorem for Word Functions

Jean-Éric Pin, Christophe Reutenauer, Michael Wagner
2019 International Colloquium on Automata, Languages and Programming  
Let p be a prime number and let Gp be the variety of all languages recognised by a finite p-group. We give a construction process of all Gp-preserving functions from a free monoid to a free group.  ...  Our result follows from a new noncommutative generalization of Mahler's theorem on interpolation series, a celebrated result of p-adic analysis.  ...  In the case of sequential and rational functions, V-preserving functions were first investigated by Schützenberger and the second author [12] .  ... 
doi:10.4230/lipics.icalp.2019.125 dblp:conf/icalp/PinR19 fatcat:qamjeclqwnabvo6z75etmt4awm

From fractal groups to fractal sets [article]

Laurent Bartholdi, Rostislav I. Grigorchuk, Volodymyr V. Nekrashevych
2002 arXiv   pre-print
In particular, it presents a plausible definition of what a "fractal group" should be, and gives many examples of such groups.  ...  In its survey, the paper discusses finite-state transducers, growth of groups and languages, limit spaces of groups, hyperbolic spaces and groups, dynamical systems, Hecke-type operators, C^*-algebras,  ...  Besides playing an important role in the study of growth of finitely generated groups, selfsimilar groups also appear in the study of the Hausdorff dimension of profinite groups.  ... 
arXiv:math/0202001v4 fatcat:axmemqlrbrh53lkllakvx5fage

From Fractal Groups to Fractal Sets [chapter]

Laurent Bartholdi, Rostislav Grigorchuk, Volodymyr Nekrashevych
2003 Fractals in Graz 2001  
In the case of the adding machine action the algebra A Φ is isomorphic to the algebra C(T) with the linear recursion C(T) → M 2 (C(T)) coming from the double self-covering of the circle.  ...  Then Theorem 13.5 implies the well known fact that the Bunce-Deddence algebra is the cross-product algebra of the odometer action on the Cantor space X ω (see [Dav96] ).  ...  The group IMG z 2 − 1 as a typical example Here we present one of the most well-studied examples of an iterated monodromy group of a rational function.  ... 
doi:10.1007/978-3-0348-8014-5_2 fatcat:6kw4fep7s5d6dlvxii44fkkx4q

On the complexity of the word problem for automaton semigroups and automaton groups

Daniele D'Angeli, Emanuele Rodaro, Jan Philipp Wächter
2017 Advances in Applied Mathematics  
In this paper, we study the word problem for automaton semigroups and automaton groups from a complexity point of view.  ...  Finally, we investigate a question asked by Cain about a better upper bound for the length of a word on which two distinct elements of an automaton semigroup must act differently.  ...  Let f : N → R be a function.  ... 
doi:10.1016/j.aam.2017.05.008 fatcat:unsm4lnwcreg3kdzoyykpr5qaa
« Previous Showing results 1 — 15 out of 27 results