7,350 research outputs found
Queries with Guarded Negation (full version)
A well-established and fundamental insight in database theory is that
negation (also known as complementation) tends to make queries difficult to
process and difficult to reason about. Many basic problems are decidable and
admit practical algorithms in the case of unions of conjunctive queries, but
become difficult or even undecidable when queries are allowed to contain
negation. Inspired by recent results in finite model theory, we consider a
restricted form of negation, guarded negation. We introduce a fragment of SQL,
called GN-SQL, as well as a fragment of Datalog with stratified negation,
called GN-Datalog, that allow only guarded negation, and we show that these
query languages are computationally well behaved, in terms of testing query
containment, query evaluation, open-world query answering, and boundedness.
GN-SQL and GN-Datalog subsume a number of well known query languages and
constraint languages, such as unions of conjunctive queries, monadic Datalog,
and frontier-guarded tgds. In addition, an analysis of standard benchmark
workloads shows that most usage of negation in SQL in practice is guarded
negation
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
On product, generic and random generic quantum satisfiability
We report a cluster of results on k-QSAT, the problem of quantum
satisfiability for k-qubit projectors which generalizes classical
satisfiability with k-bit clauses to the quantum setting. First we define the
NP-complete problem of product satisfiability and give a geometrical criterion
for deciding when a QSAT interaction graph is product satisfiable with positive
probability. We show that the same criterion suffices to establish quantum
satisfiability for all projectors. Second, we apply these results to the random
graph ensemble with generic projectors and obtain improved lower bounds on the
location of the SAT--unSAT transition. Third, we present numerical results on
random, generic satisfiability which provide estimates for the location of the
transition for k=3 and k=4 and mild evidence for the existence of a phase which
is satisfiable by entangled states alone.Comment: 9 pages, 5 figures, 1 table. Updated to more closely match published
version. New proof in appendi
Orbit decidability, applications and variations
We present the notion of orbit decidability into a more general framework,
exploring interesting generalizations and variations of this algorithmic
problem. A recent theorem by Bogopolski-Martino-Ventura gave a renovated
protagonism to this notion and motivated several interesting algebraic
applications
Strategy Logic with Imperfect Information
We introduce an extension of Strategy Logic for the imperfect-information
setting, called SLii, and study its model-checking problem. As this logic
naturally captures multi-player games with imperfect information, the problem
turns out to be undecidable. We introduce a syntactical class of "hierarchical
instances" for which, intuitively, as one goes down the syntactic tree of the
formula, strategy quantifications are concerned with finer observations of the
model. We prove that model-checking SLii restricted to hierarchical instances
is decidable. This result, because it allows for complex patterns of
existential and universal quantification on strategies, greatly generalises
previous ones, such as decidability of multi-player games with imperfect
information and hierarchical observations, and decidability of distributed
synthesis for hierarchical systems. To establish the decidability result, we
introduce and study QCTL*ii, an extension of QCTL* (itself an extension of CTL*
with second-order quantification over atomic propositions) by parameterising
its quantifiers with observations. The simple syntax of QCTL* ii allows us to
provide a conceptually neat reduction of SLii to QCTL*ii that separates
concerns, allowing one to forget about strategies and players and focus solely
on second-order quantification. While the model-checking problem of QCTL*ii is,
in general, undecidable, we identify a syntactic fragment of hierarchical
formulas and prove, using an automata-theoretic approach, that it is decidable.
The decidability result for SLii follows since the reduction maps hierarchical
instances of SLii to hierarchical formulas of QCTL*ii
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Petri net equivalence
Determining whether two Petri nets are equivalent is an interesting problem from both practical and theoretical standpoints. Although it is undecidable in the general case, for many interesting nets the equivalence problem is solvable. This paper explores, mostly from a theoretical point of view, some of the issues of Petri net equivalence, including both reachability sets and languages. Some new definitions of reachability set equivalence are described which allow the markings of some places to be treated identically or ignored, analogous to the Petri net languages in which multiple transitions may be labeled with the same symbol or with the empty string. The complexity of some decidable Petri net equivalence problems is analyzed
PDDLStream: Integrating Symbolic Planners and Blackbox Samplers via Optimistic Adaptive Planning
Many planning applications involve complex relationships defined on
high-dimensional, continuous variables. For example, robotic manipulation
requires planning with kinematic, collision, visibility, and motion constraints
involving robot configurations, object poses, and robot trajectories. These
constraints typically require specialized procedures to sample satisfying
values. We extend PDDL to support a generic, declarative specification for
these procedures that treats their implementation as black boxes. We provide
domain-independent algorithms that reduce PDDLStream problems to a sequence of
finite PDDL problems. We also introduce an algorithm that dynamically balances
exploring new candidate plans and exploiting existing ones. This enables the
algorithm to greedily search the space of parameter bindings to more quickly
solve tightly-constrained problems as well as locally optimize to produce
low-cost solutions. We evaluate our algorithms on three simulated robotic
planning domains as well as several real-world robotic tasks.Comment: International Conference on Automated Planning and Scheduling (ICAPS)
202
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