Solving linear programs without breaking abstractions

We show that the ellipsoid method for solving linear programs can be implemented in a way that respects the symmetry of the program being solved. That is to say, there is an algorithmic implementation of the method that does not distinguish, or make choices, between variables or constraints in the program unless they are distinguished by properties definable from the program. In particular, we demonstrate that the solvability of linear programs can be expressed in fixed-point logic with counting (FPC) as long as the program is given by a separation oracle that is itself definable in FPC. We use this to show that the size of a maximum matching in a graph is definable in FPC. This settles an open problem first posed by Blass, Gurevich and Shelah [Blass et al. 1999]. On the way to defining a suitable separation oracle for the maximum matching program, we provide FPC formulas defining canonical maximum flows and minimum cuts in undirected capacitated graphs.Research supported by EPSRC grant EP/H026835.This is the author accepted manuscript. The final version is available from ACM via http://dx.doi.org/10.1145/282289

IST Austria Thesis

Many security definitions come in two flavors: a stronger “adaptive” flavor, where the adversary can arbitrarily make various choices during the course of the attack, and a weaker “selective” flavor where the adversary must commit to some or all of their choices a-priori. For example, in the context of identity-based encryption, selective security requires the adversary to decide on the identity of the attacked party at the very beginning of the game whereas adaptive security allows the attacker to first see the master public key and some secret keys before making this choice. Often, it appears to be much easier to achieve selective security than it is to achieve adaptive security. A series of several recent works shows how to cleverly achieve adaptive security in several such scenarios including generalized selective decryption [Pan07][FJP15], constrained PRFs [FKPR14], and Yao’s garbled circuits [JW16]. Although the above works expressed vague intuition that they share a common technique, the connection was never made precise. In this work we present a new framework (published at Crypto ’17 [JKK+17a]) that connects all of these works and allows us to present them in a unified and simplified fashion. Having the framework in place, we show how to achieve adaptive security for proxy re-encryption schemes (published at PKC ’19 [FKKP19]) and provide the first adaptive security proofs for continuous group key agreement protocols (published at S&P ’21 [KPW+21]). Questioning optimality of our framework, we then show that currently used proof techniques cannot lead to significantly better security guarantees for "graph-building" games (published at TCC ’21 [KKPW21a]). These games cover generalized selective decryption, as well as the security of prominent constructions for constrained PRFs, continuous group key agreement, and proxy re-encryption. Finally, we revisit the adaptive security of Yao’s garbled circuits and extend the analysis of Jafargholi and Wichs in two directions: While they prove adaptive security only for a modified construction with increased online complexity, we provide the first positive results for the original construction by Yao (published at TCC ’21 [KKP21a]). On the negative side, we prove that the results of Jafargholi and Wichs are essentially optimal by showing that no black-box reduction can provide a significantly better security bound (published at Crypto ’21 [KKPW21c])

Arboreal Categories and Equi-resource Homomorphism Preservation Theorems

The classical homomorphism preservation theorem, due to {\L}o\'s, Lyndon and Tarski, states that a first-order sentence $\phi$ is preserved under homomorphisms between structures if, and only if, it is equivalent to an existential positive sentence $\psi$. Given a notion of (syntactic) complexity of sentences, an "equi-resource" homomorphism preservation theorem improves on the classical result by ensuring that $\psi$ can be chosen so that its complexity does not exceed that of $\phi$. We describe an axiomatic approach to equi-resource homomorphism preservation theorems based on the notion of arboreal category. This framework is then employed to establish novel homomorphism preservation results, and improve on known ones, for various logic fragments, including first-order, guarded and modal logics.Comment: 44 pages. v3: expanded the Introduction, added a new Section 8, changed the title to reflect the focus of the pape

Intention in the World of the Apparatus

My aim is to describe how the technical image, which is at the very core of our culture today, is in fact a technologically aided method of thinking (or imagining) which has outstripped our powers to control it and as a result come to absolutely dominate our lives. Further, through this domination, the technical image has created a type of visual culture that has ensnared us silently. Not only are we, in essence, “non-existing” if we refuse to participate in this global image network but the network and computational visual culture has evolved and become complex to the point we are often times no longer able to create meaning within it at all.Rather that meaning is created on a blistering scale by algorithms which although “dumb” in some sense, are actually able to create things which begin to confuse us in regards to aesthetic value

Neural Generative Models and Representation Learning for Information Retrieval

Information Retrieval (IR) concerns about the structure, analysis, organization, storage, and retrieval of information. Among different retrieval models proposed in the past decades, generative retrieval models, especially those under the statistical probabilistic framework, are one of the most popular techniques that have been widely applied to Information Retrieval problems. While they are famous for their well-grounded theory and good empirical performance in text retrieval, their applications in IR are often limited by their complexity and low extendability in the modeling of high-dimensional information. Recently, advances in deep learning techniques provide new opportunities for representation learning and generative models for information retrieval. In contrast to statistical models, neural models have much more flexibility because they model information and data correlation in latent spaces without explicitly relying on any prior knowledge. Previous studies on pattern recognition and natural language processing have shown that semantically meaningful representations of text, images, and many types of information can be acquired with neural models through supervised or unsupervised training. Nonetheless, the effectiveness of neural models for information retrieval is mostly unexplored. In this thesis, we study how to develop new generative models and representation learning frameworks with neural models for information retrieval. Specifically, our contributions include three main components: (1) Theoretical Analysis: We present the first theoretical analysis and adaptation of existing neural embedding models for ad-hoc retrieval tasks; (2) Design Practice: Based on our experience and knowledge, we show how to design an embedding-based neural generative model for practical information retrieval tasks such as personalized product search; And (3) Generic Framework: We further generalize our proposed neural generative framework for complicated heterogeneous information retrieval scenarios that concern text, images, knowledge entities, and their relationships. Empirical results show that the proposed neural generative framework can effectively learn information representations and construct retrieval models that outperform the state-of-the-art systems in a variety of IR tasks