Seminars

Counter-Example-Guided Abstraction Refinement (CEGAR) has been very successful in model checking.
Since then, it has been applied to many different problems. It is especially proved to be a highly successful practical approach for solving the PSPACE complete QBF problem. In this paper, we propose a new CEGAR-like approach for tackling PSPACE complete problems that we call RECAR (Recursive Explore and Check Abstraction Refinement). We show that this generic approach is sound and complete. Then we propose a specific implementation of the RECAR approach to solve the modal logic K satisfiability problem. We implemented both CEGAR and RECAR approaches for the modal logic K satisfiability problem within the solver MoSaiC. We compared experimentally those approaches to the state-of-the-art solvers for that problem. The RECAR approach outperforms the CEGAR one for that problem and also compares favorably against the state-of-the-art on the benchmarks considered.

In database management, one of the principal task is to optimize the queries to evaluate them efficiently. It is in particular the case for recursive queries for which their evaluation can lead to crawl all the database. In particular, one of the main question is to minimize the queries in order to avoid to evaluate useless parts of the query. The core theoretical question around this line of work is the problem of inclusion of a query in another. Interestedly, this question is related to an important question in IA which is to answer a query when the data is incomplete but rules are given to derive new information. This problem is called certain query answering. In both context, if both problem are undecidable in general, there are fragments based on guardedness that are decidable due to the fact there exists witness of the problems that have a bounded tree width and that their encoding in trees is regular. Furthermore, the queries can be translated in MSO. In both contexts, Courcelle’s Theorems imply the decidability of both problems. I will present to the different results on the translation of logic class of formula for our problems into tree automata to obtain tight bounds to the problems of inclusion of recursive queries or certain query answering.

Abstract:

We show that equivalence of deterministic top-down tree-to-string transducers is decidable,
thus solving a long standing open problem in formal language theory.
We also present efficient algorithms for subclasses:
polynomial time for total transducers with unary output alphabet (over a given top-down regular domain language),
and co-randomized polynomial time for linear transducers, these results are obtained using techniques from multi-linear algebra.
For our main result, we prove that equivalence can be certified by means of inductive invariants using polynomial ideals.
This allows us to construct two semi-algorithms, one searching for a proof of equivalence, one for a witness of non-equivalence.

Abstract: We consider the problem of computing a conjunctive query on a large database in a parallel setting with p servers. Unlike traditional query processing, the complexity is no longer dominated by the number of disk accesses. Typically, a query is evaluated by a sufficiently large number of servers such that the entire data can be kept in the main memory of these servers. The dominant cost becomes that of communicating data and synchronizing among the servers.
I will present some interesting results in [1, 2, 3, 4] dealing with the communication complexity of massively parallel computation of a query. The computation is performed in "rounds".
First, I will present the Massively Parallel Communication (MPC) model to analyze the tradeoff between the number of rounds and the amount of communication required in a massively parallel computing environment.
Then I will present the HyperCube (HC) algorithm that computes a full conjunctive query q in one round.
I will discuss the communication complexity [2]. The main result is the optimal load O(m/p1/τ ) where τ is the fractional vertex cover of the hypergraph of q and m the input data size.

References
[1] Parallel Evaluation of Conjunctive Queries. Paris Koutris, Dan Suciu PODS2011
[2] Communication Steps for Parallel Query Processing. Paul Beame, Paris Koutris, Dan Suciu PODS2013
[3] Skew in Parallel Query Processing. Paul Beame, Paris Koutris Dan Suciu PODS'2014
[4] Worst-Case Optimal Algorithms for Parallel Query Processing. Paris Koutris, Paul Beame, Dan Suciu ICDT2016

Abstract:
The challenge that we tackle in this thesis is the problem of how to answer
XPath queries on XML streams with low latency, full coverage, high time
efficiency, and low memory costs. We first propose to approximate earli-
est query answering for navigational XPath queries by compilation to early
nested word automata. It turns out that this leads to almost optimal la-
tency and memory consumption. Second, we contribute a formal semantics
of XPath 3.0. It is obtained by mapping XPath to the new query language
λXP that we introduce. We then show how to compile λXP queries to net-
works of early nested word automata, and develop streaming algorithms for
the latter. Thereby we obtain a streaming algorithm that indeed covers all of
XPath 3.0. Third, we develop an algorithm for projecting XML streams with
respect to the query defined by an early nested word automaton. Thereby
we are able to make our streaming algorithms highly time efficient. We have
implemented all our algorithms with the objective to obtain an industrially
applicable streaming tool. It turns out that our algorithms outperform all
previous approaches in time efficiency, coverage, and latency.