Verification of floating point programs

In this thesis we present an approach to automated verification of floating point programs. Existing techniques for automated generation of correctness theorems are extended to produce proof obligations for accuracy guarantees and absence of floating point exceptions. A prototype automated real number theorem prover is presented, demonstrating a novel application of function interval arithmetic in the context of subdivision-based numerical theorem proving. The prototype is tested on correctness theorems for two simple yet nontrivial programs, proving exception freedom and tight accuracy guarantees automatically. The prover demonstrates a novel application of function interval arithmetic in the context of subdivision-based numerical theorem proving. The experiments show how function intervals can be used to combat the information loss problems that limit the applicability of traditional interval arithmetic in the context of hard real number theorem proving

Lattices related to conway's construction

Em 2002 e 2012 foram provados alguns resultados sobre a estrutura de reticulado associada à construção de Conway. Foi também mostrado que o conjunto dos jogos nascidos até ao dia n é um reticulado distributivo completo e que essa estrutura é mantida considerando um conjunto inicial não vazio, desde que seja auto-gerado. Neste trabalho é aprofundada a condição suficiente de distributividade e é dado o primeiro exemplo conhecido de reticulado modular não distributivo proveniente de uma construção tipo Conway. O principal resultado é o Teorema de Representação com Jogos que estabelece que reticulados completos, finitos e infinitos, podem emergir no primeiro dia de uma construção de Conway para certo conjunto inicial. Finalmente, é analisada a construção transfinita: é provado um Teorema de Convergência para a construção de Conway, e é apresentada uma condição que estabelece se o conjunto dos jogos nascidos em dias anteriores a um certo ordinal é um reticulado; ABSTRACT: In 2002 and 2012 some results on the lattice structure associated with Conway’s construction were proved. It was also shown that the set of games born by day n is a complete distributive lattice and that this structure is maintained with a not-empty initial set, provided that it is self-generated. This work deepens the sufficient condition for distributivity. The first known example of non-distributive modular lattice from a Conway’s construction is given. The main result is the Representation Theorem with Games, which states that complete lattices, finite and infinite, can emerge on the first day of a Conway’s construction for some initial set. Finally, the transfinite construction is analyzed: a Convergence Theorem for Conway’s construction is proved, and a condition that establishes whether the class of games born in the days before a certain ordinal is a lattice is presented

Topological and Computational Models for Fuzzy Metric Spaces via Domain Theory

This doctoral thesis is devoted to investigate the problem of establishing connections between Domain Theory and the theory of fuzzy metric spaces, in the sense of Kramosil and Michalek, by means of the notion of a formal ball, and then constructing topological and computational models for (complete) fuzzy metric spaces. The antecedents of this research are mainly the well-known articles of A. Edalat and R. Heckmann [A computational model for metric spaces, Theoret- ical Computer Science 193 (1998), 53-73], and R. Heckmann [Approximation of metric spaces by partial metric spaces, Applied Categorical Structures 7 (1999), 71-83], where the authors obtained nice and direct links between Do- main Theory and the theory of metric spaces - two crucial tools in the study of denotational semantics - by using formal balls. Since every metric induces a fuzzy metric (the so-called standard fuzzy metric), the problem of extending Edalat and Heckmann's works to the fuzzy framework arises in a natural way. In our study we essentially propose two di erent approaches. For the rst one, valid for those fuzzy metric spaces whose continuous t-norm is the minimum, we introduce a new notion of fuzzy metric completeness (the so-called standard completeness) that allows us to construct a (topological) model that includes the classical theory as a special case. The second one, valid for those fuzzy metric spaces whose continuous t-norm is greater or equal than the Lukasiewicz t-norm, allows us to construct, among other satisfactory results, a fuzzy quasi-metric on the continuous domain of formal balls whose restriction to the set of maximal elements is isometric to the given fuzzy metric. Thus we obtain a computational model for complete fuzzy metric spaces. We also prove some new xed point theorems in complete fuzzy metric spaces with versions to the intuitionistic case and the ordered case, respec- tively. Finally, we discuss the problem of extending the obtained results to the asymmetric framework.Ricarte Moreno, L. (2013). Topological and Computational Models for Fuzzy Metric Spaces via Domain Theory [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/34670TESI

Doctor of Philosophy

dissertationToday's smartphones house private and confidential data ubiquitously. Mobile apps running on the devices can leak sensitive information by accident or intentionally. To understand application behaviors before running a program, we need to statically analyze it, tracking what data are accessed, where sensitive data ow, and what operations are performed with the data. However, automated identification of malicious behaviors in Android apps is challenging: First, there is a primary challenge in analyzing object-oriented programs precisely, soundly and efficiently, especially in the presence of exceptions. Second, there is an Android-specific challenge|asynchronous execution of multiple entry points. Third, the maliciousness of any given behavior is application-dependent and subject to human judgment. In this work, I develop a generic, highly precise static analysis of object-oriented code with multiple entry points, on which I construct an eective malware identification system with a human in the loop. Specically, I develop a new analysis-pushdown exception-ow analysis, to generalize the analysis of normal control flows and exceptional flows in object-oriented programs. To rene points-to information, I generalize abstract garbage collection to object-oriented programs and enhance it with liveness analysis for even better precision. To tackle Android-specic challenges, I develop multientry point saturation to approximate the eect of arbitrary asynchronous events. To apply the analysis techniques to security, I develop a static taint- ow analysis to track and propagate tainted sensitive data in the push-down exception-flow framework. To accelerate the speed of static analysis, I develop a compact and ecient encoding scheme, called G odel hashes, and integrate it into the analysis framework. All the techniques are realized and evaluated in a system, named AnaDroid. AnaDroid is designed with a human in the loop to specify analysis conguration, properties of interest and then to make the nal judgment and identify where the maliciousness is, based on analysis results. The analysis results include control- ow graphs highlighting suspiciousness, permission and risk-ranking reports. The experiments show that AnaDroid can lead to precise and fast identication of common classes of Android malware

Blockchain-Free Cryptocurrencies: A Framework for Truly Decentralised Fast Transactions

The blockchain distributed ledger pioneered by Bitcoin is effective at preventing double-spending, but inherently attracts (1) user cartels and (2) incompressible delays, as a result of linear verification and a winner-takes-all incentive lottery. We propose to forgo the blocks and chain entirely, and build a truly distributed ledger system based on a lean graph of cross-verifying transactions, which now become the main and only objects in the system. A fully distributed consensus mechanism, based on progressive proofs of work with predictable incentives, ensures rapid convergence even across a large network of unequal participants, who all get rewards working at their own pace. Graph-based affirmation fosters snappy response through automatic scaling, while application-agnostic design supports all modern cryptocurrency features such as multiple denominations, swaps, securitisation, scripting, smart contracts, etc. We prove theoretically, and experimentally verify, our proposal to show it achieves a crucial convergence property, meaning that any valid transaction entering the system will quickly become enshrined into the ancestry upon which all future transactions will rest