2,661 research outputs found
Alternating weak automata from universal trees
An improved translation from alternating parity automata on infinite words to alternating weak automata is given. The blow-up of the number of states is related to the size of the smallest universal ordered trees and hence it is quasi-polynomial, and it is polynomial if the asymptotic number of priorities is at most logarithmic in the number of states. This is an exponential improvement on the translation of Kupferman and Vardi (2001) and a quasi-polynomial improvement on the translation of Boker and Lehtinen (2018). Any slightly better such translation would (if - like all presently known such translations - it is efficiently constructive) lead to algorithms for solving parity games that are asymptotically faster in the worst case than the current state of the art (Calude, Jain, Khoussainov, Li, and Stephan, 2017; Jurdzinski and Lazic, 2017; and Fearnley, Jain, Schewe, Stephan, and Wojtczak, 2017), and hence it would yield a significant breakthrough
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
Distributed Graph Automata and Verification of Distributed Algorithms
Combining ideas from distributed algorithms and alternating automata, we
introduce a new class of finite graph automata that recognize precisely the
languages of finite graphs definable in monadic second-order logic. By
restricting transitions to be nondeterministic or deterministic, we also obtain
two strictly weaker variants of our automata for which the emptiness problem is
decidable. As an application, we suggest how suitable graph automata might be
useful in formal verification of distributed algorithms, using Floyd-Hoare
logic.Comment: 26 pages, 6 figures, includes a condensed version of the author's
Master's thesis arXiv:1404.6503. (This version of the article (v2) is
identical to the previous one (v1), except for minor changes in phrasing.
Index problems for game automata
For a given regular language of infinite trees, one can ask about the minimal
number of priorities needed to recognize this language with a
non-deterministic, alternating, or weak alternating parity automaton. These
questions are known as, respectively, the non-deterministic, alternating, and
weak Rabin-Mostowski index problems. Whether they can be answered effectively
is a long-standing open problem, solved so far only for languages recognizable
by deterministic automata (the alternating variant trivializes).
We investigate a wider class of regular languages, recognizable by so-called
game automata, which can be seen as the closure of deterministic ones under
complementation and composition. Game automata are known to recognize languages
arbitrarily high in the alternating Rabin-Mostowski index hierarchy; that is,
the alternating index problem does not trivialize any more.
Our main contribution is that all three index problems are decidable for
languages recognizable by game automata. Additionally, we show that it is
decidable whether a given regular language can be recognized by a game
automaton
On the Borel Inseparability of Game Tree Languages
The game tree languages can be viewed as an automata-theoretic counterpart of
parity games on graphs. They witness the strictness of the index hierarchy of
alternating tree automata, as well as the fixed-point hierarchy over binary
trees. We consider a game tree language of the first non-trivial level, where
Eve can force that 0 repeats from some moment on, and its dual, where Adam can
force that 1 repeats from some moment on. Both these sets (which amount to one
up to an obvious renaming) are complete in the class of co-analytic sets. We
show that they cannot be separated by any Borel set, hence {\em a fortiori} by
any weakly definable set of trees. This settles a case left open by
L.Santocanale and A.Arnold, who have thoroughly investigated the separation
property within the -calculus and the automata index hierarchies. They
showed that separability fails in general for non-deterministic automata of
type , starting from level , while our result settles
the missing case
On the Complexity of ATL and ATL* Module Checking
Module checking has been introduced in late 1990s to verify open systems,
i.e., systems whose behavior depends on the continuous interaction with the
environment. Classically, module checking has been investigated with respect to
specifications given as CTL and CTL* formulas. Recently, it has been shown that
CTL (resp., CTL*) module checking offers a distinctly different perspective
from the better-known problem of ATL (resp., ATL*) model checking. In
particular, ATL (resp., ATL*) module checking strictly enhances the
expressiveness of both CTL (resp., CTL*) module checking and ATL (resp. ATL*)
model checking. In this paper, we provide asymptotically optimal bounds on the
computational cost of module checking against ATL and ATL*, whose upper bounds
are based on an automata-theoretic approach. We show that module-checking for
ATL is EXPTIME-complete, which is the same complexity of module checking
against CTL. On the other hand, ATL* module checking turns out to be
3EXPTIME-complete, hence exponentially harder than CTL* module checking.Comment: In Proceedings GandALF 2017, arXiv:1709.0176
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
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