137 research outputs found
First-Order Provenance Games
We propose a new model of provenance, based on a game-theoretic approach to
query evaluation. First, we study games G in their own right, and ask how to
explain that a position x in G is won, lost, or drawn. The resulting notion of
game provenance is closely related to winning strategies, and excludes from
provenance all "bad moves", i.e., those which unnecessarily allow the opponent
to improve the outcome of a play. In this way, the value of a position is
determined by its game provenance. We then define provenance games by viewing
the evaluation of a first-order query as a game between two players who argue
whether a tuple is in the query answer. For RA+ queries, we show that game
provenance is equivalent to the most general semiring of provenance polynomials
N[X]. Variants of our game yield other known semirings. However, unlike
semiring provenance, game provenance also provides a "built-in" way to handle
negation and thus to answer why-not questions: In (provenance) games, the
reason why x is not won, is the same as why x is lost or drawn (the latter is
possible for games with draws). Since first-order provenance games are
draw-free, they yield a new provenance model that combines how- and why-not
provenance
Semiring Provenance for B\"uchi Games: Strategy Analysis with Absorptive Polynomials
This paper presents a case study for the application of semiring semantics
for fixed-point formulae to the analysis of strategies in B\"uchi games.
Semiring semantics generalizes the classical Boolean semantics by permitting
multiple truth values from certain semirings. Evaluating the fixed-point
formula that defines the winning region in a given game in an appropriate
semiring of polynomials provides not only the Boolean information on who wins,
but also tells us how they win and which strategies they might use. This is
well-understood for reachability games, where the winning region is definable
as a least fixed point. The case of B\"uchi games is of special interest, not
only due to their practical importance, but also because it is the simplest
case where the fixed-point definition involves a genuine alternation of a
greatest and a least fixed point.
We show that, in a precise sense, semiring semantics provide information
about all absorption-dominant strategies -- strategies that win with minimal
effort, and we discuss how these relate to positional and the more general
persistent strategies. This information enables further applications such as
game synthesis or determining minimal modifications to the game needed to
change its outcome. Lastly, we discuss limitations of our approach and present
questions that cannot be immediately answered by semiring semantics.Comment: Full version of a paper submitted to GandALF 202
Provenance for Aggregate Queries
We study in this paper provenance information for queries with aggregation.
Provenance information was studied in the context of various query languages
that do not allow for aggregation, and recent work has suggested to capture
provenance by annotating the different database tuples with elements of a
commutative semiring and propagating the annotations through query evaluation.
We show that aggregate queries pose novel challenges rendering this approach
inapplicable. Consequently, we propose a new approach, where we annotate with
provenance information not just tuples but also the individual values within
tuples, using provenance to describe the values computation. We realize this
approach in a concrete construction, first for "simple" queries where the
aggregation operator is the last one applied, and then for arbitrary (positive)
relational algebra queries with aggregation; the latter queries are shown to be
more challenging in this context. Finally, we use aggregation to encode queries
with difference, and study the semantics obtained for such queries on
provenance annotated databases
Provenance Circuits for Trees and Treelike Instances (Extended Version)
Query evaluation in monadic second-order logic (MSO) is tractable on trees
and treelike instances, even though it is hard for arbitrary instances. This
tractability result has been extended to several tasks related to query
evaluation, such as counting query results [3] or performing query evaluation
on probabilistic trees [10]. These are two examples of the more general problem
of computing augmented query output, that is referred to as provenance. This
article presents a provenance framework for trees and treelike instances, by
describing a linear-time construction of a circuit provenance representation
for MSO queries. We show how this provenance can be connected to the usual
definitions of semiring provenance on relational instances [20], even though we
compute it in an unusual way, using tree automata; we do so via intrinsic
definitions of provenance for general semirings, independent of the operational
details of query evaluation. We show applications of this provenance to capture
existing counting and probabilistic results on trees and treelike instances,
and give novel consequences for probability evaluation.Comment: 48 pages. Presented at ICALP'1
- …