469 research outputs found
Advances and applications of automata on words and trees : abstracts collection
From 12.12.2010 to 17.12.2010, the Dagstuhl Seminar 10501 "Advances and Applications of Automata on Words and Trees" was held in Schloss Dagstuhl - Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available
One-Tape Turing Machine Variants and Language Recognition
We present two restricted versions of one-tape Turing machines. Both
characterize the class of context-free languages. In the first version,
proposed by Hibbard in 1967 and called limited automata, each tape cell can be
rewritten only in the first visits, for a fixed constant .
Furthermore, for deterministic limited automata are equivalent to
deterministic pushdown automata, namely they characterize deterministic
context-free languages. Further restricting the possible operations, we
consider strongly limited automata. These models still characterize
context-free languages. However, the deterministic version is less powerful
than the deterministic version of limited automata. In fact, there exist
deterministic context-free languages that are not accepted by any deterministic
strongly limited automaton.Comment: 20 pages. This article will appear in the Complexity Theory Column of
the September 2015 issue of SIGACT New
Forgetting 1-Limited Automata
We introduce and investigate forgetting 1-limited automata, which are
single-tape Turing machines that, when visiting a cell for the first time,
replace the input symbol in it by a fixed symbol, so forgetting the original
contents. These devices have the same computational power as finite automata,
namely they characterize the class of regular languages. We study the cost in
size of the conversions of forgetting 1-limited automata, in both
nondeterministic and deterministic cases, into equivalent one-way
nondeterministic and deterministic automata, providing optimal bounds in terms
of exponential or superpolynomial functions. We also discuss the size
relationships with two-way finite automata. In this respect, we prove the
existence of a language for which forgetting 1-limited automata are
exponentially larger than equivalent minimal deterministic two-way automata.Comment: In Proceedings NCMA 2023, arXiv:2309.0733
Eilenberg Theorems for Free
Eilenberg-type correspondences, relating varieties of languages (e.g. of
finite words, infinite words, or trees) to pseudovarieties of finite algebras,
form the backbone of algebraic language theory. Numerous such correspondences
are known in the literature. We demonstrate that they all arise from the same
recipe: one models languages and the algebras recognizing them by monads on an
algebraic category, and applies a Stone-type duality. Our main contribution is
a variety theorem that covers e.g. Wilke's and Pin's work on
-languages, the variety theorem for cost functions of Daviaud,
Kuperberg, and Pin, and unifies the two previous categorical approaches of
Boja\'nczyk and of Ad\'amek et al. In addition we derive a number of new
results, including an extension of the local variety theorem of Gehrke,
Grigorieff, and Pin from finite to infinite words
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