176 research outputs found
Two-Way Parikh Automata
Parikh automata extend automata with counters whose values can only be tested at the end of the computation, with respect to membership into a semi-linear set. Parikh automata have found several applications, for instance in transducer theory, as they enjoy a decidable emptiness problem.
In this paper, we study two-way Parikh automata. We show that emptiness becomes undecidable in the non-deterministic case. However, it is PSpace-C when the number of visits to any input position is bounded and the semi-linear set is given as an existential Presburger formula. We also give tight complexity bounds for the inclusion, equivalence and universality problems. Finally, we characterise precisely the complexity of those problems when the semi-linear constraint is given by an arbitrary Presburger formula
Proceedings of JAC 2010. Journées Automates Cellulaires
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
Three Applications to Rational Relations of the High Undecidability of the Infinite Post Correspondence Problem in a Regular omega-Language
It was noticed by Harel in [Har86] that "one can define -complete
versions of the well-known Post Correspondence Problem". We first give a
complete proof of this result, showing that the infinite Post Correspondence
Problem in a regular -language is -complete, hence located
beyond the arithmetical hierarchy and highly undecidable. We infer from this
result that it is -complete to determine whether two given infinitary
rational relations are disjoint. Then we prove that there is an amazing gap
between two decision problems about -rational functions realized by
finite state B\"uchi transducers. Indeed Prieur proved in [Pri01, Pri02] that
it is decidable whether a given -rational function is continuous, while
we show here that it is -complete to determine whether a given
-rational function has at least one point of continuity. Next we prove
that it is -complete to determine whether the continuity set of a
given -rational function is -regular. This gives the exact
complexity of two problems which were shown to be undecidable in [CFS08].Comment: To appear in: Special Issue: Frontier Between Decidability and
Undecidability and Related Problems, International Journal of Foundations of
Computer Scienc
Quantum computation with devices whose contents are never read
In classical computation, a "write-only memory" (WOM) is little more than an
oxymoron, and the addition of WOM to a (deterministic or probabilistic)
classical computer brings no advantage. We prove that quantum computers that
are augmented with WOM can solve problems that neither a classical computer
with WOM nor a quantum computer without WOM can solve, when all other resource
bounds are equal. We focus on realtime quantum finite automata, and examine the
increase in their power effected by the addition of WOMs with different access
modes and capacities. Some problems that are unsolvable by two-way
probabilistic Turing machines using sublogarithmic amounts of read/write memory
are shown to be solvable by these enhanced automata.Comment: 32 pages, a preliminary version of this work was presented in the 9th
International Conference on Unconventional Computation (UC2010
Reversible Two-Party Computations
Deterministic synchronous systems consisting of two finite automata running
in opposite directions on a shared read-only input are studied with respect to
their ability to perform reversible computations, which means that the automata
are also backward deterministic and, thus, are able to uniquely step the
computation back and forth. We study the computational capacity of such devices
and obtain on the one hand that there are regular languages that cannot be
accepted by such systems. On the other hand, such systems can accept even
non-semilinear languages. Since the systems communicate by sending messages, we
consider also systems where the number of messages sent during a computation is
restricted. We obtain a finite hierarchy with respect to the allowed amount of
communication inside the reversible classes and separations to general, not
necessarily reversible, classes. Finally, we study closure properties and
decidability questions and obtain that the questions of emptiness, finiteness,
inclusion, and equivalence are not semidecidable if a superlogarithmic amount
of communication is allowed.Comment: In Proceedings AFL 2023, arXiv:2309.0112
Separating Automatic Relations
We study the separability problem for automatic relations (i.e., relations on finite words definable by synchronous automata) in terms of recognizable relations (i.e., finite unions of products of regular languages). This problem takes as input two automatic relations R and R\u27, and asks if there exists a recognizable relation S that contains R and does not intersect R\u27. We show this problem to be undecidable when the number of products allowed in the recognizable relation is fixed. In particular, checking if there exists a recognizable relation S with at most k products of regular languages that separates R from R\u27 is undecidable, for each fixed k ? 2. Our proofs reveal tight connections, of independent interest, between the separability problem and the finite coloring problem for automatic graphs, where colors are regular languages
The many facets of string transducers
Regular word transductions extend the robust notion of regular languages from a qualitative to a quantitative reasoning. They were already considered in early papers of formal language theory, but turned out to be much more challenging. The last decade brought considerable research around various transducer models, aiming to achieve similar robustness as for automata and languages. In this paper we survey some older and more recent results on string transducers. We present classical connections between automata, logic and algebra extended to transducers, some genuine definability questions, and review approaches to the equivalence problem
Separating Automatic Relations
We study the separability problem for automatic relations (i.e., relations on
finite words definable by synchronous automata) in terms of recognizable
relations (i.e., finite unions of products of regular languages). This problem
takes as input two automatic relations and , and asks if there exists a
recognizable relation that contains and does not intersect . We
show this problem to be undecidable when the number of products allowed in the
recognizable relation is fixed. In particular, checking if there exists a
recognizable relation with at most products of regular languages that
separates from is undecidable, for each fixed . Our proofs
reveal tight connections, of independent interest, between the separability
problem and the finite coloring problem for automatic graphs, where colors are
regular languages.Comment: Long version of a paper accepted at MFCS 202
Unification and Logarithmic Space
We present an algebraic characterization of the complexity classes Logspace
and Nlogspace, using an algebra with a composition law based on unification.
This new bridge between unification and complexity classes is rooted in proof
theory and more specifically linear logic and geometry of interaction. We show
how to build a model of computation in the unification algebra and then, by
means of a syntactic representation of finite permutations in the algebra, we
prove that whether an observation (the algebraic counterpart of a program)
accepts a word can be decided within logarithmic space. Finally, we show that
the construction naturally corresponds to pointer machines, a convenient way of
understanding logarithmic space computation.Comment: arXiv admin note: text overlap with arXiv:1402.432
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