Seminars

Many natural computational problems, such as satisfiability and
systems of equations, can be expressed in a unified way as constraint
satisfaction problems (CSPs). In this talk I will show that the usual
reductions preserving the complexity of the constraint satisfaction
problem preserve also its proof complexity. As an application, I will
present two gap theorems, which say that CSPs that admit small size
refutations in some classical proof systems are exactly the constraint
satisfaction problems which can be solved by Datalog.

This is joint work with Albert Atserias.

As an extension of word transformations, tree transformations have numerous applications in computer science : XSLT transformations, Unix packages installation and removal, databases queries... Likewise, there are many formal models to describe these transformations. However, the proof of formal properies on these models is often difficult, or even undecidable.
In this talk, I will be interested in one of the simplest model for tree transformations, namely deterministic top-down tree transducers (DTOP). It has been known for a while that the equivalence problem of DTOPs can be solved via an earliest normal form comparison algorithm, that is in 2EXPTIME. However, when applying this algorithm to practical cases, it seemed that the worst case was not bound to happen often, if ever.
I will present a new algorithm for the problem, based on the search of counterexamples via the expansion and unification of a set of rules over states of DTOPs. The most interesting feature of this algorithm is that it runs in exponential time, thus proving that the equivalence problem of DTOPs is in fact EXPTIME-complete.

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.

Abstract:
In this talk, I will present a connection between the streaming complexity and the circuit complexity of regular languages through a notion of streaming by block . This result provides tight constructions of boolean circuits computing an automaton, thanks to some classical and recent results on the circuit complexity of regular languages. I will apply this framework to the schema validation in streaming of XML-documents.

Abstract: Higher-order constructions make their way into main stream
programming languages like Java, C++, python, rust... These
constructions bring new challenges to the verification of programs as
they make their control flow more complex.

In this talk, I will present how methods coming from denotational
semantics can prove decidable the verification of certain properties of
higher-order programs. These properties are expressed by means of finite
state automata of the possibly infinite execution trees generated by the
programs and can capture safety properties but also liveness and
fairness properties.

Higher-order pushdown systems and ground tree rewriting systems can
be seen as extensions of suffix word rewriting systems. Both classes
generate infinite graphs with interesting logical
properties. Indeed, the satisfaction of any formula written in
monadic second order logic (respectively first order logic with
reachability predicates) can be decided on such a graph.

The purpose of this talk is to propose a common extension to both
higher-order stack operations and ground tree rewriting. We introduce a model
of higher-order ground tree rewriting over trees labelled by
higher-order stacks (henceforth called stack trees), which syntactically
coincides with ordinary ground tree rewriting at order 1 and with the dynamics
of higher-order pushdown automata over unary trees. The infinite
graphs generated by this class have a decidable first order logic with
reachability.

Formally, an order n stack tree is a tree labelled by order n-1 stacks.
Operations of ground stack tree rewriting are represented by a certain class
of connected DAGs labelled by a set of basic operations over stack trees
describing of the relative application positions of the basic
operations appearing on it. Applying a DAG to a stack tree t intuitively
amounts to paste its input vertices to some leaves of t and to simplify
the obtained structure, applying the basic operations labelling the edges of the
DAG to the leaves they are appended to, until either a new stack tree is
obtained or the process fails, in which case the application of the DAG to t
at the chosen position is deemed impossible. This model is a common extension
to those of higher-order stack operations presented by Carayol and of ground tree
transducers presented by Dauchet and Tison.

As further results we can define a notion of recognisable sets of
operations through a generalisation. The proof that the graphs generated
by a ground stack tree rewriting system have a decidable first order theory
with reachability is inspired by the technique of finite set interpretations
presented by Colcombet and Loding.

Abstract: Separation logic is used as an assertion language for
Hoare-style proof systems about programs with pointers,
and there is an ongoing quest for understanding its
complexity and expressive power. There are also
a lot of activities to develop verification methods
with decision procedures for fragments of practical use.

Actually, there exist many variants for separation
logic that can be viewed as fragments of second-order logic,
as well as variants of modal or temporal logics in which
models can be updated dynamically.

In this talk, after introducing first principles on separation logic,
issues related to decidability, computational complexity and expressive
power are discussed. We provide several tight relationships with
second-order logics, interval temporal logics or data logics, depending
on the variants of the logic and on the syntactic resources available.

Initial architects envinsioned RDF as a knowledge representation language, freeing users from syntactic limitations and revolutionizing the way information was exchanged.
While inference and description logic are applied to RDF, the foundation of simple assertions composed of global, unambiguous identifiers, has many more mondane and practical applications.
Distributed contributions to large (web-scale) data graphs demands adaptation of tree and stream-based validation techniques to operate over a graph.
Shape Expressions performs an ordered traversal of RDF graphs to
1 validate of structural constraints.
2 perform generative semantic actions.