1,515 research outputs found
Topological Complexity of omega-Powers : Extended Abstract
This is an extended abstract presenting new results on the topological
complexity of omega-powers (which are included in a paper "Classical and
effective descriptive complexities of omega-powers" available from
arXiv:0708.4176) and reflecting also some open questions which were discussed
during the Dagstuhl seminar on "Topological and Game-Theoretic Aspects of
Infinite Computations" 29.06.08 - 04.07.08
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
There Exist some Omega-Powers of Any Borel Rank
Omega-powers of finitary languages are languages of infinite words
(omega-languages) in the form V^omega, where V is a finitary language over a
finite alphabet X. They appear very naturally in the characterizaton of regular
or context-free omega-languages. Since the set of infinite words over a finite
alphabet X can be equipped with the usual Cantor topology, the question of the
topological complexity of omega-powers of finitary languages naturally arises
and has been posed by Niwinski (1990), Simonnet (1992) and Staiger (1997). It
has been recently proved that for each integer n > 0, there exist some
omega-powers of context free languages which are Pi^0_n-complete Borel sets,
that there exists a context free language L such that L^omega is analytic but
not Borel, and that there exists a finitary language V such that V^omega is a
Borel set of infinite rank. But it was still unknown which could be the
possible infinite Borel ranks of omega-powers. We fill this gap here, proving
the following very surprising result which shows that omega-powers exhibit a
great topological complexity: for each non-null countable ordinal alpha, there
exist some Sigma^0_alpha-complete omega-powers, and some Pi^0_alpha-complete
omega-powers.Comment: To appear in the Proceedings of the 16th EACSL Annual Conference on
Computer Science and Logic, CSL 2007, Lausanne, Switzerland, September 11-15,
2007, Lecture Notes in Computer Science, (c) Springer, 200
The omega-inequality problem for concatenation hierarchies of star-free languages
The problem considered in this paper is whether an inequality of omega-terms
is valid in a given level of a concatenation hierarchy of star-free languages.
The main result shows that this problem is decidable for all (integer and half)
levels of the Straubing-Th\'erien hierarchy
The FO^2 alternation hierarchy is decidable
We consider the two-variable fragment FO^2[<] of first-order logic over
finite words. Numerous characterizations of this class are known. Th\'erien and
Wilke have shown that it is decidable whether a given regular language is
definable in FO^2[<]. From a practical point of view, as shown by Weis, FO^2[<]
is interesting since its satisfiability problem is in NP. Restricting the
number of quantifier alternations yields an infinite hierarchy inside the class
of FO^2[<]-definable languages. We show that each level of this hierarchy is
decidable. For this purpose, we relate each level of the hierarchy with a
decidable variety of finite monoids. Our result implies that there are many
different ways of climbing up the FO^2[<]-quantifier alternation hierarchy:
deterministic and co-deterministic products, Mal'cev products with definite and
reverse definite semigroups, iterated block products with J-trivial monoids,
and some inductively defined omega-term identities. A combinatorial tool in the
process of ascension is that of condensed rankers, a refinement of the rankers
of Weis and Immerman and the turtle programs of Schwentick, Th\'erien, and
Vollmer
Remarks on Parikh-recognizable omega-languages
Several variants of Parikh automata on infinite words were recently
introduced by Guha et al. [FSTTCS, 2022]. We show that one of these variants
coincides with blind counter machine as introduced by Fernau and Stiebe
[Fundamenta Informaticae, 2008]. Fernau and Stiebe showed that every
-language recognized by a blind counter machine is of the form
for Parikh recognizable languages , but
blind counter machines fall short of characterizing this class of
-languages. They posed as an open problem to find a suitable
automata-based characterization. We introduce several additional variants of
Parikh automata on infinite words that yield automata characterizations of
classes of -language of the form for all
combinations of languages being regular or Parikh-recognizable. When
both and are regular, this coincides with B\"uchi's classical
theorem. We study the effect of -transitions in all variants of
Parikh automata and show that almost all of them admit
-elimination. Finally we study the classical decision problems
with applications to model checking.Comment: arXiv admin note: text overlap with arXiv:2302.04087,
arXiv:2301.0896
10501 Abstracts Collection -- Advances and Applications of Automata on Words and Trees
From 12.12.2010 to 17.12.2010, the Dagstuhl Seminar 10501
``Advances and Applications of Automata on Words and Trees\u27\u27 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
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