Intersection Types and (Positive) Almost-Sure Termination

Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of obtaining any given result, rather than the possibility or the necessity of obtaining it, like in (non)deterministic computation. Termination, arguably the simplest kind of reachability problem, can be spelled out in at least two ways, depending on whether it talks about the probability of convergence or about the expected evaluation time, the second one providing a stronger guarantee. In this paper, we show that intersection types are capable of precisely characterizing both notions of termination inside a single system of types: the probability of convergence of any lambda-term can be underapproximated by its type, while the underlying derivation's weight gives a lower bound to the term's expected number of steps to normal form. Noticeably, both approximations are tight -- not only soundness but also completeness holds. The crucial ingredient is non-idempotency, without which it would be impossible to reason on the expected number of reduction steps which are necessary to completely evaluate any term. Besides, the kind of approximation we obtain is proved to be optimal recursion theoretically: no recursively enumerable formal system can do better than that

Complexity Hierarchies and Higher-Order Cons-Free Rewriting

Constructor rewriting systems are said to be cons-free if, roughly, constructor terms in the right-hand sides of rules are subterms of constructor terms in the left-hand side; the computational intuition is that rules cannot build new data structures. It is well-known that cons-free programming languages can be used to characterize computational complexity classes, and that cons-free first-order term rewriting can be used to characterize the set of polynomial-time decidable sets. We investigate cons-free higher-order term rewriting systems, the complexity classes they characterize, and how these depend on the order of the types used in the systems. We prove that, for every k $\geq$ 1, left-linear cons-free systems with type order k characterize E$^k$TIME if arbitrary evaluation is used (i.e., the system does not have a fixed reduction strategy). The main difference with prior work in implicit complexity is that (i) our results hold for non-orthogonal term rewriting systems with possible rule overlaps with no assumptions about reduction strategy, (ii) results for such term rewriting systems have previously only been obtained for k = 1, and with additional syntactic restrictions on top of cons-freeness and left-linearity. Our results are apparently among the first implicit characterizations of the hierarchy E = E$^1$TIME $\subseteq$ E$^2$TIME $\subseteq$ .... Our work confirms prior results that having full non-determinism (via overlaps of rules) does not directly allow characterization of non-deterministic complexity classes like NE. We also show that non-determinism makes the classes characterized highly sensitive to minor syntactic changes such as admitting product types or non-left-linear rules.Comment: Extended version (with appendices) of a paper published in FSCD 201

Intersection types and (positive) almost-sure termination

Randomized higher-order computation can be seen as being captured by a λ-calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of obtaining any given result, rather than the possibility or the necessity of obtaining it, like in (non)deterministic computation. Termination, arguably the simplest kind of reachability problem, can be spelled out in at least two ways, depending on whether it talks about the probability of convergence or about the expected evaluation time, the second one providing a stronger guarantee. In this paper, we show that intersection types are capable of precisely characterizing both notions of termination inside a single system of types: the probability of convergence of any λ-term can be underapproximated by its type, while the underlying derivation's weight gives a lower bound to the term's expected number of steps to normal form. Noticeably, both approximations are tight-not only soundness but also completeness holds. The crucial ingredient is non-idempotency, without which it would be impossible to reason on the expected number of reduction steps which are necessary to completely evaluate any term. Besides, the kind of approximation we obtain is proved to be optimal recursion theoretically: no recursively enumerable formal system can do better than that

Implementation of Web Query Languages Reconsidered

Visions of the next generation Web such as the "Semantic Web" or the "Web 2.0" have triggered the emergence of a multitude of data formats. These formats have different characteristics as far as the shape of data is concerned (for example tree- vs. graph-shaped). They are accompanied by a puzzlingly large number of query languages each limited to one data format. Thus, a key feature of the Web, namely to make it possible to access anything published by anyone, is compromised. This thesis is devoted to versatile query languages capable of accessing data in a variety of Web formats. The issue is addressed from three angles: language design, common, yet uniform semantics, and common, yet uniform evaluation. % Thus it is divided in three parts: First, we consider the query language Xcerpt as an example of the advocated class of versatile Web query languages. Using this concrete exemplar allows us to clarify and discuss the vision of versatility in detail. Second, a number of query languages, XPath, XQuery, SPARQL, and Xcerpt, are translated into a common intermediary language, CIQLog. This language has a purely logical semantics, which makes it easily amenable to optimizations. As a side effect, this provides the, to the best of our knowledge, first logical semantics for XQuery and SPARQL. It is a very useful tool for understanding the commonalities and differences of the considered languages. Third, the intermediate logical language is translated into a query algebra, CIQCAG. The core feature of CIQCAG is that it scales from tree- to graph-shaped data and queries without efficiency losses when tree-data and -queries are considered: it is shown that, in these cases, optimal complexities are achieved. CIQCAG is also shown to evaluate each of the aforementioned query languages with a complexity at least as good as the best known evaluation methods so far. For example, navigational XPath is evaluated with space complexity O(q d) and time complexity O(q n) where q is the query size, n the data size, and d the depth of the (tree-shaped) data. CIQCAG is further shown to provide linear time and space evaluation of tree-shaped queries for a larger class of graph-shaped data than any method previously proposed. This larger class of graph-shaped data, called continuous-image graphs, short CIGs, is introduced for the first time in this thesis. A (directed) graph is a CIG if its nodes can be totally ordered in such a manner that, for this order, the children of any node form a continuous interval. CIQCAG achieves these properties by employing a novel data structure, called sequence map, that allows an efficient evaluation of tree-shaped queries, or of tree-shaped cores of graph-shaped queries on any graph-shaped data. While being ideally suited to trees and CIGs, the data structure gracefully degrades to unrestricted graphs. It yields a remarkably efficient evaluation on graph-shaped data that only a few edges prevent from being trees or CIGs

Nanoindentation of thin organic films and self-assembled monolayers

textIt has been established for some time now that interfaces between polymers and stiff substrates contain an interphase region (10 nm thick) where the properties of the polymer differ from those of the bulk. It has also been observed that interfacial cracks actually grow in these interphase regions. Thus it is important to understand the mechanical behavior of materials in such thin materials. Self-assembled monolayers (SAMs) provide well-controlled models for such studies. They are also important materials in MEMS devices where they are used for reducing friction and stiction. The SAM considered in this study was octadecyltrichlorosilane (OTS), which has a chain length of 2.6 nm. The OTS was probed with an interfacial force microscope (IFM). This relatively new device provides unambiguous force-displacement profiles in tension (adhesion) and compression (indentation). The IFM was also used to probe thicker films of (3-aminopropyl)triethoxysilane (γ-APS) so that a range of thickness could be considered. Thin γ-APS films and self-assembled OTS monolayers were deposited on Si(100) surfaces and characterized. A new approach for making OTS monolayers with nano-scale uniformity was developed. Some guidelines for the analysis of IFM experiments were drawn from a parametric study of layer and substrate interactions. Its high resolution in both force and displacement allows the IFM to be used to determine both the elastic mechanical and adhesive properties of thin films. Due to the different molecular structure of thin γ-APS films and selfassembled OTS monolayers, different analytical approaches were required. Combined experimental and continuum analyses of IFM nanoindentation of thin films, which accounted for the layer/substrate and adhesive interactions, were developed. A continuum analysis was used for γ-APS films, while a hybrid continuum-molecular analysis was required for OTS monolayers.Mechanical Engineerin

A Novel User Oriented Network Forensic Analysis Tool

In the event of a cybercrime, it is necessary to examine the suspect’s digital device(s) in a forensic fashion so that the culprit can be presented in court along with the extracted evidence(s). But, factors such as existence and availability of anti-forensic tools/techniques and increasing replacement of hard disk drives with solid state disks have the ability to eradicate critical evidences and/or ruin their integrity. Therefore, having an alternative source of evidence with a lesser chance of being tampered with can be beneficial for the investigation. The organisational network traffic can fit into this role as it is an independent source of evidence and will contain a copy of all online user activities. Limitations of prevailing network traffic analysis techniques – packet based and flow based – are reflected as certain challenges in the investigation. The enormous volume and increasing encrypted nature of traffic, the dynamic nature of IP addresses of users’ devices, and the difficulty in extracting meaningful information from raw traffic are among those challenges. Furthermore, current network forensic tools, unlike the sophisticated computer forensic tools, are limited in their capability to exhibit functionalities such as collaborative working, visualisation, reporting and extracting meaningful user-level information. These factors increase the complexity of the analysis, and the time and effort required from the investigator. The research goal was set to design a system that can assist in the investigation by minimising the effects of the aforementioned challenges, thereby reducing the cognitive load on the investigator, which, the researcher thinks, can take the investigator one step closer to the culprit. The novelty of this system comes from a newly proposed interaction based analysis approach, which will extract online user activities from raw network metadata. Practicality of the novel interaction-based approach was tested by designing an experimental methodology, which involved an initial phase of the researcher looking to identify unique signatures for activities performed on popular Internet applications (BBC, Dropbox, Facebook, Hotmail, Google Docs, Google Search, Skype, Twitter, Wikipedia, and YouTube) from the researcher’s own network metadata. With signatures obtained, the project moved towards the second phase of the experiment in which a much larger dataset (network traffic collected from 27 users for over 2 months) was analysed. Results showed that it is possible to extract unique signature of online user activities from raw network metadata. However, due to the complexities of the applications, signatures were not found for some activities. The interaction-based approach was able to reduce the data volume by eliminating the noise (machine to machine communication packets) and to find a way around the encryption issue by using only the network metadata. A set of system requirements were generated, based on which a web based, client-server architecture for the proposed system (i.e. the User-Oriented Network Forensic Analysis Tool) was designed. The system functions in a case management premise while minimising the challenges that were identified earlier. The system architecture led to the development of a functional prototype. An evaluation of the system by academic experts from the field acted as a feedback mechanism. While the evaluators were satisfied with the system’s capability to assist in the investigation and meet the requirements, drawbacks such as inability to analyse real-time traffic and meeting the HCI standards were pointed out. The future work of the project will involve automated signature extraction, real-time processing and facilitation of integrated visualisation

A pattern language for evolution reuse in component-based software architectures

Context: Modern software systems are prone to a continuous evolution under frequently varying requirements and changes in operational environments. Architecture-Centric Software Evolution (ACSE) enables changes in a system’s structure and behaviour while maintaining a global view of the software to address evolution-centric trade-offs. Lehman’s law of continuing change demands for long-living and continuously evolving architectures to prolong the productive life and economic value of software. Also some industrial research shows that evolution reuse can save approximately 40% effort of change implementation in ACSE process. However, a systematic review of existing research suggests a lack of solution(s) to support a continuous integration of reuse knowledge in ACSE process to promote evolution-off-the-shelf in software architectures. Objectives: We aim to unify the concepts of software repository mining and software evolution to discover evolution-reuse knowledge that can be shared and reused to guide ACSE. Method: We exploit repository mining techniques (also architecture change mining) that investigates architecture change logs to discover change operationalisation and patterns. We apply software evolution concepts (also architecture change execution) to support pattern-driven reuse in ACSE. Architecture change patterns support composition and application of a pattern language that exploits patterns and their relations to express evolution-reuse knowledge. Pattern language composition is enabled with a continuous discovery of patterns from architecture change logs and formalising relations among discovered patterns. Pattern language application is supported with an incremental selection and application of patterns to achieve reuse in ACSE. The novelty of the research lies with a framework PatEvol that supports a round-trip approach for a continuous acquisition (mining) and application (execution) of reuse knowledge to enable ACSE. Prototype support enables customisation and (semi-) automation for the evolution process. Results: We evaluated the results based on the ISO/IEC 9126 - 1 quality model and a case study based validation of the architecture change mining and change execution processes. We observe consistency and reusability of change support with pattern-driven architecture evolution. Change patterns support efficiency for architecture evolution process but lack a fine-granular change implementation. A critical challenge lies with the selection of appropriate patterns to form a pattern language during evolution. Conclusions: The pattern language itself continuously evolves with an incremental discovery of new patterns from change logs over time. A systematic identification and resolution of change anti-patterns define the scope for future research