215 research outputs found
Partially Ordered Two-way B\"uchi Automata
We introduce partially ordered two-way B\"uchi automata and characterize
their expressive power in terms of fragments of first-order logic FO[<].
Partially ordered two-way B\"uchi automata are B\"uchi automata which can
change the direction in which the input is processed with the constraint that
whenever a state is left, it is never re-entered again. Nondeterministic
partially ordered two-way B\"uchi automata coincide with the first-order
fragment Sigma2. Our main contribution is that deterministic partially ordered
two-way B\"uchi automata are expressively complete for the first-order fragment
Delta2. As an intermediate step, we show that deterministic partially ordered
two-way B\"uchi automata are effectively closed under Boolean operations.
A small model property yields coNP-completeness of the emptiness problem and
the inclusion problem for deterministic partially ordered two-way B\"uchi
automata.Comment: The results of this paper were presented at CIAA 2010; University of
Stuttgart, Computer Scienc
On finitely ambiguous B\"uchi automata
Unambiguous B\"uchi automata, i.e. B\"uchi automata allowing only one
accepting run per word, are a useful restriction of B\"uchi automata that is
well-suited for probabilistic model-checking. In this paper we propose a more
permissive variant, namely finitely ambiguous B\"uchi automata, a
generalisation where each word has at most accepting runs, for some fixed
. We adapt existing notions and results concerning finite and bounded
ambiguity of finite automata to the setting of -languages and present a
translation from arbitrary nondeterministic B\"uchi automata with states to
finitely ambiguous automata with at most states and at most accepting
runs per word
Ambiguity, Weakness, and Regularity in Probabilistic B\"uchi Automata
Probabilistic B\"uchi automata are a natural generalization of PFA to
infinite words, but have been studied in-depth only rather recently and many
interesting questions are still open. PBA are known to accept, in general, a
class of languages that goes beyond the regular languages. In this work we
extend the known classes of restricted PBA which are still regular, strongly
relying on notions concerning ambiguity in classical omega-automata.
Furthermore, we investigate the expressivity of the not yet considered but
natural class of weak PBA, and we also show that the regularity problem for
weak PBA is undecidable
Unambiguous Separators for Tropical Tree Automata
In this paper we show that given a max-plus automaton (over trees, and with real weights) computing a function f and a min-plus automaton (similar) computing a function g such that f ? g, there exists effectively an unambiguous tropical automaton computing h such that f ? h ? g.
This generalizes a result of Lombardy and Mairesse of 2006 stating that series which are both max-plus and min-plus rational are unambiguous. This generalization goes in two directions: trees are considered instead of words, and separation is established instead of characterization (separation implies characterization). The techniques in the two proofs are very different
One Theorem to Rule Them All: A Unified Translation of LTL into {\omega}-Automata
We present a unified translation of LTL formulas into deterministic Rabin
automata, limit-deterministic B\"uchi automata, and nondeterministic B\"uchi
automata. The translations yield automata of asymptotically optimal size
(double or single exponential, respectively). All three translations are
derived from one single Master Theorem of purely logical nature. The Master
Theorem decomposes the language of a formula into a positive boolean
combination of languages that can be translated into {\omega}-automata by
elementary means. In particular, Safra's, ranking, and breakpoint constructions
used in other translations are not needed
How Deterministic are Good-For-Games Automata?
In GFG automata, it is possible to resolve nondeterminism in a way that only
depends on the past and still accepts all the words in the language. The
motivation for GFG automata comes from their adequacy for games and synthesis,
wherein general nondeterminism is inappropriate. We continue the ongoing effort
of studying the power of nondeterminism in GFG automata. Initial indications
have hinted that every GFG automaton embodies a deterministic one. Today we
know that this is not the case, and in fact GFG automata may be exponentially
more succinct than deterministic ones.
We focus on the typeness question, namely the question of whether a GFG
automaton with a certain acceptance condition has an equivalent GFG automaton
with a weaker acceptance condition on the same structure. Beyond the
theoretical interest in studying typeness, its existence implies efficient
translations among different acceptance conditions. This practical issue is of
special interest in the context of games, where the Buchi and co-Buchi
conditions admit memoryless strategies for both players. Typeness is known to
hold for deterministic automata and not to hold for general nondeterministic
automata.
We show that GFG automata enjoy the benefits of typeness, similarly to the
case of deterministic automata. In particular, when Rabin or Streett GFG
automata have equivalent Buchi or co-Buchi GFG automata, respectively, then
such equivalent automata can be defined on a substructure of the original
automata. Using our typeness results, we further study the place of GFG
automata in between deterministic and nondeterministic ones. Specifically,
considering automata complementation, we show that GFG automata lean toward
nondeterministic ones, admitting an exponential state blow-up in the
complementation of a Streett automaton into a Rabin automaton, as opposed to
the constant blow-up in the deterministic case
On the Succinctness of Good-for-MDPs Automata
Good-for-MDPs and good-for-games automata are two recent classes of
nondeterministic automata that reside between general nondeterministic and
deterministic automata. Deterministic automata are good-for-games, and
good-for-games automata are good-for-MDPs, but not vice versa. One of the
question this raises is how these classes relate in terms of succinctness.
Good-for-games automata are known to be exponentially more succinct than
deterministic automata, but the gap between good-for-MDPs and good-for-games
automata as well as the gap between ordinary nondeterministic automata and
those that are good-for-MDPs have been open. We establish that these gaps are
exponential, and sharpen this result by showing that the latter gap remains
exponential when restricting the nondeterministic automata to separating safety
or unambiguous reachability automata.Comment: 18 page
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