573 research outputs found
Highly Undecidable Problems For Infinite Computations
We show that many classical decision problems about 1-counter
omega-languages, context free omega-languages, or infinitary rational
relations, are -complete, hence located at the second level of the
analytical hierarchy, and "highly undecidable". In particular, the universality
problem, the inclusion problem, the equivalence problem, the determinizability
problem, the complementability problem, and the unambiguity problem are all
-complete for context-free omega-languages or for infinitary rational
relations. Topological and arithmetical properties of 1-counter
omega-languages, context free omega-languages, or infinitary rational
relations, are also highly undecidable. These very surprising results provide
the first examples of highly undecidable problems about the behaviour of very
simple finite machines like 1-counter automata or 2-tape automata.Comment: to appear in RAIRO-Theoretical Informatics and Application
Advances and applications of automata on words and trees : executive summary
Seminar: 10501 - Advances and Applications of Automata on Words and Trees. The aim of the seminar was to discuss and systematize the recent fast progress in automata theory and to identify important directions for future research. For this, the seminar brought together more than 40 researchers from automata theory and related fields of applications. We had 19 talks of 30 minutes and 5 one-hour lectures leaving ample room for discussions. In the following we describe the topics in more detail
What is known about the Value 1 Problem for Probabilistic Automata?
The value 1 problem is a decision problem for probabilistic automata over
finite words: are there words accepted by the automaton with arbitrarily high
probability? Although undecidable, this problem attracted a lot of attention
over the last few years. The aim of this paper is to review and relate the
results pertaining to the value 1 problem. In particular, several algorithms
have been proposed to partially solve this problem. We show the relations
between them, leading to the following conclusion: the Markov Monoid Algorithm
is the most correct algorithm known to (partially) solve the value 1 problem
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
Randomness for Free
We consider two-player zero-sum games on graphs. These games can be
classified on the basis of the information of the players and on the mode of
interaction between them. On the basis of information the classification is as
follows: (a) partial-observation (both players have partial view of the game);
(b) one-sided complete-observation (one player has complete observation); and
(c) complete-observation (both players have complete view of the game). On the
basis of mode of interaction we have the following classification: (a)
concurrent (both players interact simultaneously); and (b) turn-based (both
players interact in turn). The two sources of randomness in these games are
randomness in transition function and randomness in strategies. In general,
randomized strategies are more powerful than deterministic strategies, and
randomness in transitions gives more general classes of games. In this work we
present a complete characterization for the classes of games where randomness
is not helpful in: (a) the transition function probabilistic transition can be
simulated by deterministic transition); and (b) strategies (pure strategies are
as powerful as randomized strategies). As consequence of our characterization
we obtain new undecidability results for these games
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
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