484 research outputs found
Deterministic Automata for Unordered Trees
Automata for unordered unranked trees are relevant for defining schemas and
queries for data trees in Json or Xml format. While the existing notions are
well-investigated concerning expressiveness, they all lack a proper notion of
determinism, which makes it difficult to distinguish subclasses of automata for
which problems such as inclusion, equivalence, and minimization can be solved
efficiently. In this paper, we propose and investigate different notions of
"horizontal determinism", starting from automata for unranked trees in which
the horizontal evaluation is performed by finite state automata. We show that a
restriction to confluent horizontal evaluation leads to polynomial-time
emptiness and universality, but still suffers from coNP-completeness of the
emptiness of binary intersections. Finally, efficient algorithms can be
obtained by imposing an order of horizontal evaluation globally for all
automata in the class. Depending on the choice of the order, we obtain
different classes of automata, each of which has the same expressiveness as
CMso.Comment: In Proceedings GandALF 2014, arXiv:1408.556
The Complexity of Enriched Mu-Calculi
The fully enriched μ-calculus is the extension of the propositional
μ-calculus with inverse programs, graded modalities, and nominals. While
satisfiability in several expressive fragments of the fully enriched
μ-calculus is known to be decidable and ExpTime-complete, it has recently
been proved that the full calculus is undecidable. In this paper, we study the
fragments of the fully enriched μ-calculus that are obtained by dropping at
least one of the additional constructs. We show that, in all fragments obtained
in this way, satisfiability is decidable and ExpTime-complete. Thus, we
identify a family of decidable logics that are maximal (and incomparable) in
expressive power. Our results are obtained by introducing two new automata
models, showing that their emptiness problems are ExpTime-complete, and then
reducing satisfiability in the relevant logics to these problems. The automata
models we introduce are two-way graded alternating parity automata over
infinite trees (2GAPTs) and fully enriched automata (FEAs) over infinite
forests. The former are a common generalization of two incomparable automata
models from the literature. The latter extend alternating automata in a similar
way as the fully enriched μ-calculus extends the standard μ-calculus.Comment: A preliminary version of this paper appears in the Proceedings of the
33rd International Colloquium on Automata, Languages and Programming (ICALP),
2006. This paper has been selected for a special issue in LMC
Relating timed and register automata
Timed automata and register automata are well-known models of computation
over timed and data words respectively. The former has clocks that allow to
test the lapse of time between two events, whilst the latter includes registers
that can store data values for later comparison. Although these two models
behave in appearance differently, several decision problems have the same
(un)decidability and complexity results for both models. As a prominent
example, emptiness is decidable for alternating automata with one clock or
register, both with non-primitive recursive complexity. This is not by chance.
This work confirms that there is indeed a tight relationship between the two
models. We show that a run of a timed automaton can be simulated by a register
automaton, and conversely that a run of a register automaton can be simulated
by a timed automaton. Our results allow to transfer complexity and decidability
results back and forth between these two kinds of models. We justify the
usefulness of these reductions by obtaining new results on register automata.Comment: In Proceedings EXPRESS'10, arXiv:1011.601
Limit Synchronization in Markov Decision Processes
Markov decision processes (MDP) are finite-state systems with both strategic
and probabilistic choices. After fixing a strategy, an MDP produces a sequence
of probability distributions over states. The sequence is eventually
synchronizing if the probability mass accumulates in a single state, possibly
in the limit. Precisely, for 0 <= p <= 1 the sequence is p-synchronizing if a
probability distribution in the sequence assigns probability at least p to some
state, and we distinguish three synchronization modes: (i) sure winning if
there exists a strategy that produces a 1-synchronizing sequence; (ii)
almost-sure winning if there exists a strategy that produces a sequence that
is, for all epsilon > 0, a (1-epsilon)-synchronizing sequence; (iii) limit-sure
winning if for all epsilon > 0, there exists a strategy that produces a
(1-epsilon)-synchronizing sequence.
We consider the problem of deciding whether an MDP is sure, almost-sure,
limit-sure winning, and we establish the decidability and optimal complexity
for all modes, as well as the memory requirements for winning strategies. Our
main contributions are as follows: (a) for each winning modes we present
characterizations that give a PSPACE complexity for the decision problems, and
we establish matching PSPACE lower bounds; (b) we show that for sure winning
strategies, exponential memory is sufficient and may be necessary, and that in
general infinite memory is necessary for almost-sure winning, and unbounded
memory is necessary for limit-sure winning; (c) along with our results, we
establish new complexity results for alternating finite automata over a
one-letter alphabet
Enriched MU-Calculi Module Checking
The model checking problem for open systems has been intensively studied in
the literature, for both finite-state (module checking) and infinite-state
(pushdown module checking) systems, with respect to Ctl and Ctl*. In this
paper, we further investigate this problem with respect to the \mu-calculus
enriched with nominals and graded modalities (hybrid graded Mu-calculus), in
both the finite-state and infinite-state settings. Using an automata-theoretic
approach, we show that hybrid graded \mu-calculus module checking is solvable
in exponential time, while hybrid graded \mu-calculus pushdown module checking
is solvable in double-exponential time. These results are also tight since they
match the known lower bounds for Ctl. We also investigate the module checking
problem with respect to the hybrid graded \mu-calculus enriched with inverse
programs (Fully enriched \mu-calculus): by showing a reduction from the domino
problem, we show its undecidability. We conclude with a short overview of the
model checking problem for the Fully enriched Mu-calculus and the fragments
obtained by dropping at least one of the additional constructs
Synchronizing Data Words for Register Automata
Register automata (RAs) are finite automata extended with a finite set of
registers to store and compare data from an infinite domain. We study the
concept of synchronizing data words in RAs: does there exist a data word that
sends all states of the RA to a single state?
For deterministic RAs with k registers (k-DRAs), we prove that inputting data
words with 2k+1 distinct data from the infinite data domain is sufficient to
synchronize. We show that the synchronization problem for DRAs is in general
PSPACE-complete, and it is NLOGSPACE-complete for 1-DRAs. For nondeterministic
RAs (NRAs), we show that Ackermann(n) distinct data (where n is the size of the
RA) might be necessary to synchronize. The synchronization problem for NRAs is
in general undecidable, however, we establish Ackermann-completeness of the
problem for 1-NRAs.
Another main result is the NEXPTIME-completeness of the length-bounded
synchronization problem for NRAs, where a bound on the length of the
synchronizing data word, written in binary, is given. A variant of this last
construction allows to prove that the length-bounded universality problem for
NRAs is co-NEXPTIME-complete
Alternating register automata on finite words and trees
We study alternating register automata on data words and data trees in
relation to logics. A data word (resp. data tree) is a word (resp. tree) whose
every position carries a label from a finite alphabet and a data value from an
infinite domain. We investigate one-way automata with alternating control over
data words or trees, with one register for storing data and comparing them for
equality. This is a continuation of the study started by Demri, Lazic and
Jurdzinski. From the standpoint of register automata models, this work aims at
two objectives: (1) simplifying the existent decidability proofs for the
emptiness problem for alternating register automata; and (2) exhibiting
decidable extensions for these models. From the logical perspective, we show
that (a) in the case of data words, satisfiability of LTL with one register and
quantification over data values is decidable; and (b) the satisfiability
problem for the so-called forward fragment of XPath on XML documents is
decidable, even in the presence of DTDs and even of key constraints. The
decidability is obtained through a reduction to the automata model introduced.
This fragment contains the child, descendant, next-sibling and
following-sibling axes, as well as data equality and inequality tests
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