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Closure under union and composition of iterated rational transductions

D. Simplot, A. Terlutte
2000 RAIRO - Theoretical Informatics and Applications  
We proceed our work on iterated transductions by studying the closure under union and composition of some classes of iterated functions.  ...  We analyze this closure for the classes of lengthpreserving rational functions, length-preserving subsequential functions and length-preserving sequential functions with terminal states.  ...  We also thank Jacques Sakarovitch for useful remarks on a previous version of this paper.  ... 
doi:10.1051/ita:2000114 fatcat:hrklbf53uzginltsstkjpnopw4

Iteration of rational transductions

Alain Terlutte, David Simplot
2000 RAIRO - Theoretical Informatics and Applications  
Hence, we study the smallest family of transductions containing lengthpreserving rational transductions and closed under union, composition and iteration.  ...  The purpose of this paper is to show connections between iterated length-preserving rational transductions and linear space computations.  ...  We w ould like to thank Michel Latteux for supervising this work and his constant encouragements and help during the redaction.  ... 
doi:10.1051/ita:2000109 fatcat:pc57ljoikrbilgkofhjkg7cqra

Iterated relabeling tree transducers

Z. Fülöp, A. Terlutte
2002 Theoretical Computer Science  
In this paper we consider the closure UCI (Rel) of the class of relabeling tree transformations, under U = union, C = composition and I = iteration.  ...  We give a characterization of UCI (Rel) in terms of a short expression built up from Rel with composition and iteration.  ...  Besides, several interesting results were obtained on the closure of length-preserving rational transductions and of length-preserving functional rational transductions with respect to union, composition  ... 
doi:10.1016/s0304-3975(01)00181-5 fatcat:ctonaueuxrc3vloxv7e7a7xmre

Iterating transducers

Dennis Dams, Yassine Lakhnech, Martin Steffen
2002 The Journal of Logic and Algebraic Programming  
finite-state representation T * • A for the transduction of A under T's transitive closure.  ...  The construction builds a quotient of an underlying infinite-state transducer T <ω , using a novel behavioural equivalence based on past and future bisimulations on finite approximations of T <ω .  ...  Furthermore thanks to Kedar Namjoshi, Kai Baukus, and Karsten Stahl for inspiring discussions and suggestions, and careful reading of earlier versions of this document.  ... 
doi:10.1016/s1567-8326(02)00025-5 fatcat:oesc7b2evvdqnmxhcjepz2n63m

Page 7408 of Mathematical Reviews Vol. , Issue 2001J [page]

2001 Mathematical Reviews  
(F-LILL-FI; Villeneuve d’Ascq Closure under union and composition of iterated rational transductions. (English and French summaries) Theor. Inform. Appl. 34 (2000), no. 3, 183-212.  ...  The authors study Z@(,), the smallest class of transductions containing ¥, which is closed under union and composition.  ... 

Two iteration theorems for some families of languages

L. Boasson
1973 Journal of computer and system sciences (Print)  
However, o~ and c# are closely related: o~" is the full AFL generated by Di* [13] . Consequently, from a result of [11] restated in [3], o~-is the closer of under union, product, and star operation.  ...  In the first part of this paper, we recall some notations, terminology, and properties we use about Dyck languages and rational transductions.  ...  As a consequence of the fact that the rational transductions are closed under composition [8] , (6(~) = {L' I L' = ~'L, L s ~ and ~-is a rational transduction}.  ... 
doi:10.1016/s0022-0000(73)80036-4 fatcat:5krg636fgncdzl7w2dvrpjpg5y

Page 4191 of Mathematical Reviews Vol. , Issue 2001F [page]

2001 Mathematical Reviews  
This class is by defi- nition the smallest one containing length-preserving transductions which is stable under union, composition and iteration.  ...  Moreover, this class is stable under intersection and difference, which leads to another characterization of it: this is the smallest family closed under union, intersection, iteration and difference that  ... 

Regular and First-Order List Functions

Mikołaj Bojańczyk, Laure Daviaud, Shankara Narayanan Krishna
2018 Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science - LICS '18  
Acknowledgements This research has been supported by the European Research Council (ERC) under the European Union Horizon 2020 research and innovation programme (ERC consolidator grant LIPA, agreement  ...  no. 683080) and the EPSRC grant EP/P020992/1 (Solving Parity Games in Theory and Practice).  ...  Thanks to Lemma 4.4 and the closure of first-order list function under composition, it is now sufficient to prove that the bottom three functions of Lemma 4.8 are first-order list functions, in order  ... 
doi:10.1145/3209108.3209163 dblp:conf/lics/BojanczykDK18 fatcat:rt2bucyjhbeyffbsn2pad5qi2m

Synchronization of musical words

Marc Chemillier
2004 Theoretical Computer Science  
This leads to the study of closure properties of rational languages of ÿnite words under superimposition and iterated superimposition.  ...  The rationality of the transduction associated with the superimposition appears to be a powerful argument in the proof of these properties.  ...  Closure properties for rational languages In this section, we study closure properties of rational languages under both the superimposition and the iterated superimposition.  ... 
doi:10.1016/s0304-3975(03)00309-8 fatcat:ovmduaaccngppi2m7ymrvbyp6e

Linearly bounded infinite graphs

Arnaud Carayol, Antoine Meyer
2006 Acta Informatica  
We present some of their structural properties as well as alternative characterizations in terms of rewriting systems and context-sensitive transductions.  ...  Finally, we compare these graphs to rational graphs, which are another class of automata accepting the context-sensitive languages, and prove that in the bounded-degree case, rational graphs are a strict  ...  Proof The closure under union follows from that of context-sensitive languages.  ... 
doi:10.1007/s00236-006-0022-z fatcat:3hialx5b5rao7pduyhjvhtgcda

Regular and First Order List Functions [article]

Mikolaj Bojanczyk, Laure Daviaud, Krishna Shankara Narayanan
2018 arXiv   pre-print
Our main results are that first-order list functions are exactly the same as first-order transductions, under a suitable encoding of the inputs; and the regular list functions are exactly the same as MSO-transductions  ...  them together using four combinators (most importantly, composition of functions).  ...  It is clear that fo-transductions are closed under disjoint union and composition. Moreover, map and pairing can be handled the same way.  ... 
arXiv:1803.06168v1 fatcat:4ugqdwlsjjd73nnurdqgeexalq

Formal Methods of Transformations (Dagstuhl Seminar 17142)

Emmanuel Filiot, Sebastian Maneth, Helmut Seidl, Marc Herbstritt
2017 Dagstuhl Reports  
The goal of this Dagstuhl seminar was to gather researchers working on the theory and practice of transformations (also know as transductions) of word and tree structures, which are realised by transducers  ...  This seminar was motivated by recent advances and breakthrough results, both in the settings of words and trees.  ...  Deterministic two-way transducers define the robust class of regular functions which, among other good properties, is closed under composition.  ... 
doi:10.4230/dagrep.7.4.23 dblp:journals/dagstuhl-reports/FiliotMS17 fatcat:2kwm6o7h2banfjp5y5nb4wimvm

Polyregular Functions [article]

Mikołaj Bojańczyk
2018 arXiv   pre-print
functions as well as two extra functions called squaring and iterated reverse 3. a fragment of the lambda-calculus, which has a list type constructor and limited forms of iteration such as map but not  ...  The class has four equivalent definitions: 1. deterministic two-way transducers with pebbles; 2 the smallest class of string-to-string functions that is closed under composition, contains all sequential  ...  (We need to use closure of good languages under unions, because the number of iterations could be ≤ Q , but closure under unions is an easy corollary of the if-then-else construction in Sublemma 6.6.)  ... 
arXiv:1810.08760v1 fatcat:dkoy677fgnabxjmkeicdp4fcby

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

Jean-Éric Pin
2020 Lecture Notes in Computer Science  
Another good source of tough questions is the recent book 200 Problems in Formal Languages and Automata Theory [36] . Surprisingly, there are very few exercises related to starfree languages.  ...  Most books of automata theory [9, 23, 29, 45, 49] offer exercises on regular languages, including some difficult ones.  ...  Uniformly continuous transductions are closed under composition and they are also closed under direct product.  ... 
doi:10.1007/978-3-030-40608-0_5 fatcat:mzoyw7mckzgxnhyggsxiq4bhoa

Fair expressions and regular languages over lists

L. Breveglieri
1997 RAIRO - Theoretical Informatics and Applications  
From statements 7.7 and 7.4 it follows that RLL and sRLL are closed under rational and simple rational list transduction, respectively.  ...  of rational transductions.  ... 
doi:10.1051/ita/1997310100151 fatcat:fjraryffu5ahtlwgizqfkq3bo4
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