10 research outputs found
Temporal Logics on Words with Multiple Data Values
The paper proposes and studies temporal logics for attributed words, that is, data words with a (finite) set of (attribute,value)-pairs at each position. It considers a basic logic which is a semantical fragment of the logic of Demri and Lazic with operators for navigation into the future and the past. By reduction to the emptiness problem for data automata it is shown that this basic logic is decidable. Whereas the basic logic only allows navigation to positions where a fixed data value occurs, extensions are studied that also allow navigation to positions with different data values. Besides some undecidable results it is shown that the extension by a certain UNTIL-operator with an inequality target condition remains decidable
Ordered Navigation on Multi-attributed Data Words
We study temporal logics and automata on multi-attributed data words.
Recently, BD-LTL was introduced as a temporal logic on data words extending LTL
by navigation along positions of single data values. As allowing for navigation
wrt. tuples of data values renders the logic undecidable, we introduce ND-LTL,
an extension of BD-LTL by a restricted form of tuple-navigation. While complete
ND-LTL is still undecidable, the two natural fragments allowing for either
future or past navigation along data values are shown to be Ackermann-hard, yet
decidability is obtained by reduction to nested multi-counter systems. To this
end, we introduce and study nested variants of data automata as an intermediate
model simplifying the constructions. To complement these results we show that
imposing the same restrictions on BD-LTL yields two 2ExpSpace-complete
fragments while satisfiability for the full logic is known to be as hard as
reachability in Petri nets
An automaton over data words that captures EMSO logic
We develop a general framework for the specification and implementation of
systems whose executions are words, or partial orders, over an infinite
alphabet. As a model of an implementation, we introduce class register
automata, a one-way automata model over words with multiple data values. Our
model combines register automata and class memory automata. It has natural
interpretations. In particular, it captures communicating automata with an
unbounded number of processes, whose semantics can be described as a set of
(dynamic) message sequence charts. On the specification side, we provide a
local existential monadic second-order logic that does not impose any
restriction on the number of variables. We study the realizability problem and
show that every formula from that logic can be effectively, and in elementary
time, translated into an equivalent class register automaton
Reasoning about Data Repetitions with Counter Systems
We study linear-time temporal logics interpreted over data words with
multiple attributes. We restrict the atomic formulas to equalities of attribute
values in successive positions and to repetitions of attribute values in the
future or past. We demonstrate correspondences between satisfiability problems
for logics and reachability-like decision problems for counter systems. We show
that allowing/disallowing atomic formulas expressing repetitions of values in
the past corresponds to the reachability/coverability problem in Petri nets.
This gives us 2EXPSPACE upper bounds for several satisfiability problems. We
prove matching lower bounds by reduction from a reachability problem for a
newly introduced class of counter systems. This new class is a succinct version
of vector addition systems with states in which counters are accessed via
pointers, a potentially useful feature in other contexts. We strengthen further
the correspondences between data logics and counter systems by characterizing
the complexity of fragments, extensions and variants of the logic. For
instance, we precisely characterize the relationship between the number of
attributes allowed in the logic and the number of counters needed in the
counter system.Comment: 54 page
A Hypersequent Calculus with Clusters for Data Logic over Ordinals
We study freeze tense logic over well-founded data streams. The logic features past-and future-navigating modalities along with freeze quantifiers, which store the datum of the current position and test data (in)equality later in the formula. We introduce a decidable fragment of that logic, and present a proof system that is sound for the whole logic, and complete for this fragment. Technically, this is a hy-persequent system enriched with an ordering, clusters, and annotations. The proof system is tailored for proof search, and yields an optimal coNP complexity for validity and a small model property for our fragment
Automata Column: The Complexity of Reachability in Vector Addition Systems
International audienceThe program of the 30th Symposium on Logic in Computer Science held in 2015 in Kyoto included two contributions on the computational complexity of the reachability problem for vector addition systems: Blondin, Finkel, Göller, Haase, and McKenzie [2015] attacked the problem by providing the first tight complexity bounds in the case of dimension 2 systems with states, while Leroux and Schmitz [2015] proved the first complexity upper bound in the general case. The purpose of this column is to present the main ideas behind these two results, and more generally survey the current state of affairs
Playing with Repetitions in Data Words Using Energy Games
We introduce two-player games which build words over infinite alphabets, and
we study the problem of checking the existence of winning strategies. These
games are played by two players, who take turns in choosing valuations for
variables ranging over an infinite data domain, thus generating
multi-attributed data words. The winner of the game is specified by formulas in
the Logic of Repeating Values, which can reason about repetitions of data
values in infinite data words. We prove that it is undecidable to check if one
of the players has a winning strategy, even in very restrictive settings.
However, we prove that if one of the players is restricted to choose valuations
ranging over the Boolean domain, the games are effectively equivalent to
single-sided games on vector addition systems with states (in which one of the
players can change control states but cannot change counter values), known to
be decidable and effectively equivalent to energy games.
Previous works have shown that the satisfiability problem for various
variants of the logic of repeating values is equivalent to the reachability and
coverability problems in vector addition systems. Our results raise this
connection to the level of games, augmenting further the associations between
logics on data words and counter systems
Playing with Repetitions in Data Words Using Energy Games
We introduce two-player games which build words over infinite alphabets, and
we study the problem of checking the existence of winning strategies. These
games are played by two players, who take turns in choosing valuations for
variables ranging over an infinite data domain, thus generating
multi-attributed data words. The winner of the game is specified by formulas in
the Logic of Repeating Values, which can reason about repetitions of data
values in infinite data words. We prove that it is undecidable to check if one
of the players has a winning strategy, even in very restrictive settings.
However, we prove that if one of the players is restricted to choose valuations
ranging over the Boolean domain, the games are effectively equivalent to
single-sided games on vector addition systems with states (in which one of the
players can change control states but cannot change counter values), known to
be decidable and effectively equivalent to energy games.
Previous works have shown that the satisfiability problem for various
variants of the logic of repeating values is equivalent to the reachability and
coverability problems in vector addition systems. Our results raise this
connection to the level of games, augmenting further the associations between
logics on data words and counter systems