2,094 research outputs found
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
In the Maze of Data Languages
In data languages the positions of strings and trees carry a label from a
finite alphabet and a data value from an infinite alphabet. Extensions of
automata and logics over finite alphabets have been defined to recognize data
languages, both in the string and tree cases. In this paper we describe and
compare the complexity and expressiveness of such models to understand which
ones are better candidates as regular models
On Pebble Automata for Data Languages with Decidable Emptiness Problem
In this paper we study a subclass of pebble automata (PA) for data languages
for which the emptiness problem is decidable. Namely, we introduce the
so-called top view weak PA. Roughly speaking, top view weak PA are weak PA
where the equality test is performed only between the data values seen by the
two most recently placed pebbles. The emptiness problem for this model is
decidable. We also show that it is robust: alternating, nondeterministic and
deterministic top view weak PA have the same recognition power. Moreover, this
model is strong enough to accept all data languages expressible in Linear
Temporal Logic with the future-time operators, augmented with one register
freeze quantifier.Comment: An extended abstract of this work has been published in the
proceedings of the 34th International Symposium on Mathematical Foundations
of Computer Science (MFCS) 2009}, Springer, Lecture Notes in Computer Science
5734, pages 712-72
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
Bottom-up automata on data trees and vertical XPath
A data tree is a finite tree whose every node carries a label from a finite
alphabet and a datum from some infinite domain. We introduce a new model of
automata over unranked data trees with a decidable emptiness problem. It is
essentially a bottom-up alternating automaton with one register that can store
one data value and can be used to perform equality tests with the data values
occurring within the subtree of the current node. We show that it captures the
expressive power of the vertical fragment of XPath - containing the child,
descendant, parent and ancestor axes - obtaining thus a decision procedure for
its satisfiability problem
An Automata-Theoretic Approach to the Verification of Distributed Algorithms
We introduce an automata-theoretic method for the verification of distributed
algorithms running on ring networks. In a distributed algorithm, an arbitrary
number of processes cooperate to achieve a common goal (e.g., elect a leader).
Processes have unique identifiers (pids) from an infinite, totally ordered
domain. An algorithm proceeds in synchronous rounds, each round allowing a
process to perform a bounded sequence of actions such as send or receive a pid,
store it in some register, and compare register contents wrt. the associated
total order. An algorithm is supposed to be correct independently of the number
of processes. To specify correctness properties, we introduce a logic that can
reason about processes and pids. Referring to leader election, it may say that,
at the end of an execution, each process stores the maximum pid in some
dedicated register. Since the verification of distributed algorithms is
undecidable, we propose an underapproximation technique, which bounds the
number of rounds. This is an appealing approach, as the number of rounds needed
by a distributed algorithm to conclude is often exponentially smaller than the
number of processes. We provide an automata-theoretic solution, reducing model
checking to emptiness for alternating two-way automata on words. Overall, we
show that round-bounded verification of distributed algorithms over rings is
PSPACE-complete.Comment: 26 pages, 6 figure
Automata theory in nominal sets
We study languages over infinite alphabets equipped with some structure that
can be tested by recognizing automata. We develop a framework for studying such
alphabets and the ensuing automata theory, where the key role is played by an
automorphism group of the alphabet. In the process, we generalize nominal sets
due to Gabbay and Pitts
REGISTER GAMES
The complexity of parity games is a long standing open problem that saw a
major breakthrough in 2017 when two quasi-polynomial algorithms were published.
This article presents a third, independent approach to solving parity games in
quasi-polynomial time, based on the notion of register game, a parameterised
variant of a parity game. The analysis of register games leads to a
quasi-polynomial algorithm for parity games, a polynomial algorithm for
restricted classes of parity games and a novel measure of complexity, the
register index, which aims to capture the combined complexity of the priority
assignement and the underlying game graph.
We further present a translation of alternating parity word automata into
alternating weak automata with only a quasi-polynomial increase in size, based
on register games; this improves on the previous exponential translation.
We also use register games to investigate the parity index hierarchy: while
for words the index hierarchy of alternating parity automata collapses to the
weak level, and for trees it is strict, for structures between trees and words,
it collapses logarithmically, in the sense that any parity tree automaton of
size n is equivalent, on these particular classes of structures, to an
automaton with a number of priorities logarithmic in n
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