Katalin Friedl

Hidden translation and orbit coset in quantum computing

We give efficient quantum algorithms for the problems of <sc>Hidden Translation</sc> and <sc>Hidden Subgroup</sc> in a large class of non-abelian groups including solvable groups of constant exponent and of constant length derived series. Our algorithms are recursive. For the base case, we solve efficiently <sc>Hidden Translation</sc> in Z <inf>p</inf>ⁿ, whenever <i>p</i> is a fixed prime. For the induction step, we introduce the problem <sc>Orbit Coset</sc> generalizing both <sc>Hidden Translation</sc> and <sc>Hidden Subgroup</sc>, and prove a powerful self-reducibility result: <sc>Orbit Coset</sc> in a finite group <i>G</i> is reducible to <sc>Orbit Coset</sc> in <i>G/N</i> and subgroups of <i>N</i>, for any solvable normal subgroup <i>N</i> of <i>G</i>.

Adaptive Graph Pattern Matching for Model Transformations using Model-sensitive Search Plans

The current paper makes two contributions for the graph pattern matching problem of model transformation tools. First, model-sensitive search plan generation is proposed for pattern traversal (as an extension to traditional multiplicity and type considerations of existing tools) by estimating the expected performance of search plans on typical instance models that are available at transformation design time. Then, an adaptive approach for graph pattern matching is presented, where the optimal search plan can be selected from previously generated search plans at run-time based on statistical data collected from the current instance model under transformation.

Polynomial time solutions of some problems of computational algebra

The first structure theory in abstract algebra was that of finite dimensional Lie algebras (Cartan-Killing), followed by the structure theory of associative algebras (Wedderburn-Artin). These theories determine, in a non-constructive way, the basic building blocks of the respective algebras (the radical and the simple components of the factor by the radical). In view of the extensive computations done in such algebras, it seems important to design efficient algorithms to find these building blocks. We find polynomial time solutions to a substantial part of these problems. We restrict our attention to algebras over finite fields and over algebraic number fields. We succeed in determining the radical (the “bad part” of the algebra) in polynomial time, using (in the case of prime characteristic) some new algebraic results developed in this paper. For associative algebras we are able to determine the simple components as well. This latter result generalizes factorization of polynomials over the given field. Correspondingly, our algorithm over finite fields is Las Vegas. Some of the results generalize to fields given by oracles. Some fundamental problems remain open. An example: decide whether or not a given rational algebra is a noncommutative field.

Implementing a Graph Transformation Engine in Relational Databases

We present a novel approach to implement a graph transformation engine based on standard relational database management systems (RDBMSs). The essence of the approach is to create database views for each rule and to handle pattern matching by inner join operations while handling negative application conditions by left outer join operations. Furthermore, the model manipulation prescribed by the application of a graph transformation rule is also implemented using elementary data manipulation statements (such as insert, delete). As a result, we obtain a robust and fast transformation engine especially suitable for (1) extending modeling tools with an underlying RDBMS repository and (2) embedding model transformations into large distributed applications where models are frequently persisted in a relational database and transaction handling is required to handle large models consistently.

Quantum Testers for Hidden Group Properties

We construct efficient or query efficient quantum property testers for two existential group properties which have exponential query complexity both for their decision problem in the quantum and for their testing problem in the classical model of computing. These are periodicity in groups and the common coset range property of two functions having identical ranges within each coset of some normal subgroup. Our periodicity tester is efficient in Abelian groups and generalizes, in several aspects, previous periodicity testers. This is achieved by introducing a technique refining the majority correction process widely used for proving robustness of algebraic properties. The periodicity tester in non-Abelian groups and the common coset range tester are query efficient.

On the black-box complexity of sperner's lemma

We present several results on the complexity of various forms of Sperners Lemma in the black-box model of computing. We give a deterministic algorithm for Sperner problems over pseudo-manifolds of arbitrary dimension. The query complexity of our algorithm is linear in the separation number of the skeleton graph of the manifold and the size of its boundary. As a corollary we get an

Graph Transformation in Relational Databases

O(\sqrt{n})

Efficient testing of groups

deterministic query algorithm for the black-box version of the problem 2D-SPERNER, a well studied member of Papadimitrious complexity class PPAD. This upper bound matches the

Hidden Translation and Translating Coset in Quantum Computing

\Omega(\sqrt{n})

Order shattering and Wilson's theorem

deterministic lower bound of Crescenzi and Silvestri. The tightness of this bound was not known before. In another result we prove for the same problem an