180 research outputs found

    Transductions Computed by One-Dimensional Cellular Automata

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    Cellular automata are investigated towards their ability to compute transductions, that is, to transform inputs into outputs. The families of transductions computed are classified with regard to the time allowed to process the input and to compute the output. Since there is a particular interest in fast transductions, we mainly focus on the time complexities real time and linear time. We first investigate the computational capabilities of cellular automaton transducers by comparing them to iterative array transducers, that is, we compare parallel input/output mode to sequential input/output mode of massively parallel machines. By direct simulations, it turns out that the parallel mode is not weaker than the sequential one. Moreover, with regard to certain time complexities cellular automaton transducers are even more powerful than iterative arrays. In the second part of the paper, the model in question is compared with the sequential devices single-valued finite state transducers and deterministic pushdown transducers. It turns out that both models can be simulated by cellular automaton transducers faster than by iterative array transducers.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249

    Transforming a Single-Valued Transducer Into a Mealy Machine

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    AbstractThis article deals with the transformation of a single-valued finite transducer into a Mealy machine. The following results are obtained: (1) LetMbe a single-valued real-time (or “letter-to-word”) transducer withnstates, input alphabetΣ, and output alphabetΔwhich is equivalent to some Mealy machineM′. Then,Mcan be effectively transformed into such anM′ having at most 2n+1·min{#Σ, #Δ}n−1states. A similar result holds ifMis not real time. As an important side effect three “Mealy” properties are obtained which characterize the fact that the given transducerMis equivalent to some Mealy machine. (2) The upper bound in result (1) improves to 2n−1 ifMis known to be a letter-to-letter transducer. (3) For every integert⩾2 and every odd integern⩾3 there is a single-valued real-time transducerMwithnstates and input and output alphabets of cardinalitytsuch thatMis equivalent to some Mealy machineM′ and every suchM′ has at leastt(n−1)/2states. (4) Ift=3, then result (3) holds true with letter-to-letter transducers rather than real-time transducers and with a lower bound of 2(n−1)/2. (5) It is a PSPACE-complete problem to decide whether or not a given single-valued transducerMis equivalent to some Mealy machine. The problem remains PSPACE-complete ifMis known to be a letter-to-letter transducer

    Two-wayness: Automata and Transducers

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    This PhD is about two natural extensions of Finite Automata (FA): the 2-way fa (2FA) and the 2-way transducers (2T). It is well known that 2FA s are computably equivalent to FAs, even in their nondeterministic (2nfa) variant. However, in the field of descriptional complexity, some questions remain. Raised by Sakoda and Sipser in 1978, the question of the cost of the simulation of 2NFA by 2DFA (the deterministic variant of 2FA) is still open. In this manuscript, we give an answer in a restricted case in which the nondeterministic choices of the simulated 2NFA may occur at the boundaries of the input tape only (2ONFA). We show that every 2ONFA can be simulated by a 2DFA of subexponential (but superpolynomial) size. Under the assumptions L=NL, this cost is reduced to the polynomial level. Moreover, we prove that the complementation and the simulation by a halting 2ONFA is polynomial. We also consider the anologous simulations for alternating devices. Providing a one-way write-only output tape to FAs leads to the notion of transducer. Contrary to the case of finite automata which are acceptor, 2-way transducers strictly extends the computational power of 1-way one, even in the case where both the input and output alphabets are unary. Though 1-way transducers enjoy nice properties and characterizations (algebraic, logical, etc. . . ), 2-way variants are less known, especially the nondeterministic case. In this area, this manuscript gives a new contribution: an algebraic characterization of the relations accepted by two-way transducers when both the input and output alphabets are unary. Actually, it can be reformulated as follows: each unary two-way transducer is equivalent to a sweeping (and even rotating) transducer. We also show that the assumptions made on the size of the alphabets are required, that is, sweeping transducers weakens the 2-way transducers whenever at least one of the alphabet is non-unary. On the path, we discuss on the computational power of some algebraic operations on word relations, introduced in the aim of describing the behavior of 2-way transducers or, more generally, of 2-way weighted automata. In particular, the mirror operation, consisting in reversing the input word in order to describe a right to left scan, draws our attention. Finally, we study another kind of operations, more adapted for binary word relations: the composition. We consider the transitive closure of relations. When the relation belongs to some very restricted sub-family of rational relations, we are able to compute its transitive closure and we set its complexity. This quickly becomes uncomputable when higher classes are considered

    Proceedings of JAC 2010. JournĂŠes Automates Cellulaires

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    The second Symposium on Cellular Automata “Journ´ees Automates Cellulaires” (JAC 2010) took place in Turku, Finland, on December 15-17, 2010. The first two conference days were held in the Educarium building of the University of Turku, while the talks of the third day were given onboard passenger ferry boats in the beautiful Turku archipelago, along the route Turku–Mariehamn–Turku. The conference was organized by FUNDIM, the Fundamentals of Computing and Discrete Mathematics research center at the mathematics department of the University of Turku. The program of the conference included 17 submitted papers that were selected by the international program committee, based on three peer reviews of each paper. These papers form the core of these proceedings. I want to thank the members of the program committee and the external referees for the excellent work that have done in choosing the papers to be presented in the conference. In addition to the submitted papers, the program of JAC 2010 included four distinguished invited speakers: Michel Coornaert (Universit´e de Strasbourg, France), Bruno Durand (Universit´e de Provence, Marseille, France), Dora Giammarresi (Universit` a di Roma Tor Vergata, Italy) and Martin Kutrib (Universit¨at Gie_en, Germany). I sincerely thank the invited speakers for accepting our invitation to come and give a plenary talk in the conference. The invited talk by Bruno Durand was eventually given by his co-author Alexander Shen, and I thank him for accepting to make the presentation with a short notice. Abstracts or extended abstracts of the invited presentations appear in the first part of this volume. The program also included several informal presentations describing very recent developments and ongoing research projects. I wish to thank all the speakers for their contribution to the success of the symposium. I also would like to thank the sponsors and our collaborators: the Finnish Academy of Science and Letters, the French National Research Agency project EMC (ANR-09-BLAN-0164), Turku Centre for Computer Science, the University of Turku, and Centro Hotel. Finally, I sincerely thank the members of the local organizing committee for making the conference possible. These proceedings are published both in an electronic format and in print. The electronic proceedings are available on the electronic repository HAL, managed by several French research agencies. The printed version is published in the general publications series of TUCS, Turku Centre for Computer Science. We thank both HAL and TUCS for accepting to publish the proceedings.Siirretty Doriast

    The Realization Problem for finitely generated refinement monoids

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    We show that every finitely generated conical refinement monoid can be represented as the monoid V(R) of isomorphism classes of finitely generated projective modules over a von Neumann regular ring R. To this end, we use the representation of these monoids provided by adaptable separated graphs. Given an adaptable separated graph (E, C) and a field K, we build a von Neumann regular K-algebra Q_K(E,C) and show that there is a natural isomorphism between the separated graph monoid M(E,C) and the monoid V(Q_K(E,C)).The three authors were partially supported by the DGI-MINECO and European Regional Development Fund, jointly, through the grant MTM2017-83487-P. The first and second authors were partially supported by the Generalitat de Catalunya through the grant 2017-SGR-1725. The first author was partially supported by the Beatriu de Pino ́s postdoctoral programme of the Government of Catalonia’s Secretariat for Universities and Research of the Ministry of Economy and Knowledge. The third author was partially supported by PAI III grant FQM-298 of the Junta de Andalucía

    Digital aesthetics: the discrete and the continuous

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    Aesthetic investigations of computation are stuck in an impasse, caused by the difficulty of accounting for the ontological discrepancy between the continuity of sensation and the discreteness of digital technology. This article proposes a theoretical position intended to overcome that deadlock. It highlights how an ontological focus on continuity has entered media studies via readings of Deleuze, which attempt to build a ‘digital aisthesis’ (that is, a theory of digital sensation) by ascribing a ‘virtuality’ to computation. This underpins, in part, the affective turn in digital theory. In contrast to such positions, this article argues for a reconceptualization of formal abstraction in computation, in order to find, within the discreteness of computational formalisms (and not via the coupling of the latter with virtual sensation), an indeterminacy that would make computing aesthetic qua inherently generative. This indeterminacy, it is argued here, can be found by reconsidering, philosophically, Turing’s notion of ‘incomputability’
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