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A rational and complete notion of delay for streaming string transducers [article]

Emmanuel Filiot, Ismaël Jecker, Christof Löding, Sarah Winter
2022 arXiv   pre-print
The goal of this work is to provide a similar notion for more complex abstract machines: we introduce a new notion of delay tailored to measure the similarity between streaming string transducers (SST)  ...  The notion of delay between finite transducers is a core element of numerous fundamental results of transducer theory.  ...  of streaming string transducers.  ... 
arXiv:2205.04287v1 fatcat:qtwc3ktioze4zlbsnlpu7stfde

Transducing Markov sequences

Benny Kimelfeld, Christopher Ré
2010 Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems of data - PODS '10  
In particular, it is shown that enumeration in any sub-exponential-approximate order is generally intractable (even for some fixed transducers), and a matching upper bound is obtained through a proposed  ...  Due to this hardness, a special consideration is given to restricted (yet common) classes of transducers that extract matches of a regular expression (subject to prefix and suffix constraints), and it  ...  Acknowledgments We thank Sara Cohen for providing valuable comments and suggestions. We also thank Nimrod Megiddo and Evan Welbourne for useful discussions.  ... 
doi:10.1145/1807085.1807090 dblp:conf/pods/KimelfeldR10 fatcat:5ik7ecckvfgfli744nikuza6ie

On Synthesis of Resynchronizers for Transducers

Sougata Bose, Shankara Narayanan Krishna, Anca Muscholl, Vincent Penelle, Gabriele Puppis, Michael Wagner
2019 International Symposium on Mathematical Foundations of Computer Science  
We show that synthesis of rational resynchronizers is decidable for functional, and even finite-valued, one-way transducers, and undecidable for relational one-way transducers.  ...  We then consider some instances of the following synthesis problem: given transducers T1, T2, construct a rational (resp. regular) resynchronizer R, if it exists, such that T1 is contained in R(T2) under  ...  For two-way transducers (or equivalently, streaming string transducers [1] ) a different formalism is required to capture origin distortion, since the representation of the origin information through  ... 
doi:10.4230/lipics.mfcs.2019.69 dblp:conf/mfcs/BoseKMPP19 fatcat:2su4scmivzdgljhllyxmbfehru

Computable classifications of continuous, transducer, and regular functions [article]

Johanna N.Y. Franklin, Rupert Hölzl, Alexander Melnikov, Keng Meng Ng, Daniel Turetsky
2020 arXiv   pre-print
As one of many consequences, our Σ^0_2-completeness result covers the class of transducer functions as well.  ...  We develop a systematic algorithmic framework that unites global and local classification problems for functional separable spaces and apply it to attack classification problems concerning the Banach space  ...  We also include a single nonaccepting state t for A 0 , and we denote the input stream of A 0 as α ⊕ β.  ... 
arXiv:2010.09499v1 fatcat:nxf4hs5qbfdgxckmggyrvxm6cm

Computing with relational machines

GÉRARD HUET, BENOÎT RAZET
2015 Mathematical Structures in Computer Science  
In a particular case of finite machines, we show that bottom-up search yields an efficient complete simulator.  ...  We propose a relational computing paradigm based on Eilenberg machines, an effective version of Eilenberg's X-machines suitable for general non-deterministic computation.  ...  In this framework we may define computable streams over a parametric datatype data as follows: type stream 'data = [ Void | Stream of 'data and delay 'data ] and delay 'data = unit → stream 'data; This  ... 
doi:10.1017/s0960129515000390 fatcat:t4y4j673b5hnjn4ptcz7ajayie

Synthesizing Computable Functions from Rational Specifications over Infinite Words [article]

Emmanuel Filiot, Sarah Winter
2021 arXiv   pre-print
This entails the decidability of the synthesis problem of computable functions, which we prove to be ExpTime-complete, for a large subclass of rational specifications, namely deterministic rational specifications  ...  In this paper, we consider the synthesis of computable functions of infinite words, for a classical Turing computability notion over infinite inputs.  ...  In Section 4, we introduce a sufficient condition for completeness which yields a (sound and complete) decision procedure for large classes of rational relations.  ... 
arXiv:2103.05674v3 fatcat:q5p5rnhct5cqpa3mwz2a5evqqu

Polyregular Functions [article]

Mikołaj Bojańczyk
2018 arXiv   pre-print
The class of polyregular functions contains known classes of string-to-string transducers, such as the sequential, rational, or regular ones, but goes beyond them because of super-linear growth.  ...  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  ...  I would like to thank the following people for many helpful discussions: Jacek Chrzaszcz, Amina Doumane, Sandra Kiefer, Bartek Klin, Anca Muscholl, Nathan Lhote, Aleksy Schubert, Helmut Seidl, Mahsa Shirmohammadi  ... 
arXiv:1810.08760v1 fatcat:dkoy677fgnabxjmkeicdp4fcby

Synthesis of Computable Regular Functions of Infinite Words

Vrunda Dave, Emmanuel Filiot, Shankara Narayanan Krishna, Nathan Lhote, Laura Kovács, Igor Konnov
2020 International Conference on Concurrency Theory  
Regular functions from infinite words to infinite words can be equivalently specified by MSO-transducers, streaming ω-string transducers as well as deterministic two-way transducers with look-ahead.  ...  This paper proposes a decision procedure for the following synthesis problem: given a regular function f (equivalently specified by one of the aforementioned transducer model), is f computable and if it  ...  It is a well-behaved class, captured by several models such as streaming ω-string 43:4 Synthesis of Computable Regular Functions of Infinite Words transducers (SST), deterministic two-way Muller transducers  ... 
doi:10.4230/lipics.concur.2020.43 dblp:conf/concur/DaveFKL20 fatcat:dqlhdiqfjjh33olaba5kypewve

Single use register automata for data words [article]

Mikołaj Bojańczyk, Rafał Stefański
2020 arXiv   pre-print
and a variant of streaming string transducers for data words.  ...  Our starting point are register automata for data words, in the style of Kaminski and Francez.  ...  Acknowledgements Supported by the European Research Council under the European Unions Horizon 2020 research and innovation programme (ERC consolidator grant LIPA, agreement no. 683080).  ... 
arXiv:1907.10504v2 fatcat:mgmw6ahfgrahhodmup3xbb2ara

The Calculus of Signal Flow Diagrams I: Linear relations on streams

Filippo Bonchi, Paweł Sobociński, Fabio Zanasi
2017 Information and Computation  
Using universal categorical constructions, we provide a stream semantics and a sound and complete axiomatisation.  ...  We introduce a graphical syntax for signal flow diagrams based on the language of symmetric monoidal categories.  ...  Acknowledgements The first and third authors acknowledge support from ANR 12IS02001 PACE.  ... 
doi:10.1016/j.ic.2016.03.002 fatcat:t3lmoyq4nbgi5gxkybory4cn2a

SD-Regular Transducer Expressions for Aperiodic Transformations

Luc Dartois, Paul Gastin, Shankara Narayanan Krishna
2021 2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)  
FO transductions, aperiodic deterministic two-way transducers, as well as aperiodic streaming string transducers are all equivalent models for first order definable functions.  ...  An SDRTE is a regular expression where Kleene stars are used in a restricted way: they can appear only on aperiodic languages which are prefix codes of bounded synchronization delay.  ...  ACRAs are a generalization of streaming string transducers (SSTs) [6] which make a single left to right pass over the input and use a finite set of variables over strings from the output alphabet.  ... 
doi:10.1109/lics52264.2021.9470738 fatcat:2sl5e2ei2zbhxgwtlpv7za3hz4

Coinduction in Concurrent Timed Systems

Jan Komenda
2010 Electronical Notes in Theoretical Computer Science  
From a coalgebraic viewpoint, behaviours of deterministic partial Mealy automata are causal and length preserving partial functions between finite and infinite sequences of inputs and outputs, called stream  ...  After a study of fundamental properties of functional stream calculus an application to the definition by coinduction of the synchronous product of stream functionals is proposed.  ...  The notion of a timed language is recalled and compared to formal power series and causal stream functions.  ... 
doi:10.1016/j.entcs.2010.07.020 fatcat:ridifg6oijbapbxuldq3l4vfl4

A Generalised Twinning Property for Minimisation of Cost Register Automata

Laure Daviaud, Pierre-Alain Reynier, Jean-Marc Talbot
2016 Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science - LICS '16  
Last, we prove that a similar result holds for finite-valued finitestate transducers, and that the register minimisation problem for the class CRA·c(B * ) is PSPACE-complete.  ...  We introduce a twinning property and a bounded variation property parametrised by an integer k, such that the corresponding notions introduced originally by Choffrut for finite-state transducers are obtained  ...  Beyond weighted automata over infinitary groups, we also prove that our results apply also to transducers from A * to B * . It is known that streaming string transducers (i.e.  ... 
doi:10.1145/2933575.2934549 dblp:conf/lics/DaviaudRT16 fatcat:h5mpy4lpzzabdjugoiz45l4v3m

A categorical approach to open and interconnected dynamical systems

Brendan Fong, Paweł Sobociński, Paolo Rapisarda
2016 Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science - LICS '16  
We develop a sound and complete graphical theory for discrete linear time-invariant dynamical systems.  ...  The graphical syntax, as in previous work, is closely related to the classical notion of signal flow diagrams, differently from previous work, these are understood as multi-input multi-output transducers  ...  We thank Jonathan Mayo, Thabiso Maupong, John Baez, and Jason Erbele for useful discussions.  ... 
doi:10.1145/2933575.2934556 dblp:conf/lics/FongSR16 fatcat:ef7ypvipuravvmzcw57eavwdim

Degree of Sequentiality of Weighted Automata [chapter]

Laure Daviaud, Ismaël Jecker, Pierre-Alain Reynier, Didier Villevalois
2017 Lecture Notes in Computer Science  
Last, we show that these results also hold for word transducers and that the associated decision problem is Pspace-complete.  ...  property, a pattern on the automaton (a new twinning property) and a subclass of cost register automata.  ...  When M is the free monoid (A * , ., ε), this class is a subclass of streaming string transducers [1] and turns out to be equivalent to the class of rational functions on words, i.e. those realized by  ... 
doi:10.1007/978-3-662-54458-7_13 fatcat:io62uuujlbgcpirftv3zhybdfa
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