Costrutti ed Applicazioni di Programmazione Generica in Linguaggi Object-Oriented

Generic programming is likely to become a new challenge for a critical mass of developers. Therefore, it is crucial to refine the support for generic programming in mainstream Object-Oriented languages — both at the design and at the implementation level — as well as to suggest novel ways to exploit the additional degree of expressiveness made available by genericity. This study is meant to provide a contribution towards bringing Java genericity to a more mature stage with respect to mainstream programming practice, by increasing the effectiveness of its implementation, and by revealing its full expressive power in real world scenario. With respect to the current research setting, the main contribution of the thesis is twofold. First, we propose a revised implementation for Java generics that greatly increases the expressiveness of the Java platform by adding reification support for generic types. Secondly, we show how Java genericity can be leveraged in a real world case-study in the context of the multi-paradigm language integration. Several approaches have been proposed in order to overcome the lack of reification of generic types in the Java programming language. Existing approaches tackle the problem of reification of generic types by defining new translation techniques which would allow for a runtime representation of generics and wildcards. Unfortunately most approaches suffer from several problems: heterogeneous translations are known to be problematic when considering reification of generic methods and wildcards. On the other hand, more sophisticated techniques requiring changes in the Java runtime, supports reified generics through a true language extension (where clauses) so that backward compatibility is compromised. In this thesis we develop a sophisticated type-passing technique for addressing the problem of reification of generic types in the Java programming language; this approach — first pioneered by the so called EGO translator — is here turned into a full-blown solution which reifies generic types inside the Java Virtual Machine (JVM) itself, thus overcoming both performance penalties and compatibility issues of the original EGO translator. Java-Prolog integration Integrating Object-Oriented and declarative programming has been the subject of several researches and corresponding technologies. Such proposals come in two flavours, either attempting at joining the two paradigms, or simply providing an interface library for accessing Prolog declarative features from a mainstream Object-Oriented languages such as Java. Both solutions have however drawbacks: in the case of hybrid languages featuring both Object-Oriented and logic traits, such resulting language is typically too complex, thus making mainstream application development an harder task; in the case of library-based integration approaches there is no true language integration, and some “boilerplate code” has to be implemented to fix the paradigm mismatch. In this thesis we develop a framework called PatJ which promotes seamless exploitation of Prolog programming in Java. A sophisticated usage of generics/wildcards allows to define a precise mapping between Object-Oriented and declarative features. PatJ defines a hierarchy of classes where the bidirectional semantics of Prolog terms is modelled directly at the level of the Java generic type-system.

Exact Algorithms for Different Classes of Vehicle Routing Problems

We deal with five problems arising in the field of logistics: the Asymmetric TSP (ATSP), the TSP with Time Windows (TSPTW), the VRP with Time Windows (VRPTW), the Multi-Trip VRP (MTVRP), and the Two-Echelon Capacitated VRP (2E-CVRP). The ATSP requires finding a lest-cost Hamiltonian tour in a digraph. We survey models and classical relaxations, and describe the most effective exact algorithms from the literature. A survey and analysis of the polynomial formulations is provided. The considered algorithms and formulations are experimentally compared on benchmark instances. The TSPTW requires finding, in a weighted digraph, a least-cost Hamiltonian tour visiting each vertex within a given time window. We propose a new exact method, based on new tour relaxations and dynamic programming. Computational results on benchmark instances show that the proposed algorithm outperforms the state-of-the-art exact methods. In the VRPTW, a fleet of identical capacitated vehicles located at a depot must be optimally routed to supply customers with known demands and time window constraints. Different column generation bounding procedures and an exact algorithm are developed. The new exact method closed four of the five open Solomon instances. The MTVRP is the problem of optimally routing capacitated vehicles located at a depot to supply customers without exceeding maximum driving time constraints. Two set-partitioning-like formulations of the problem are introduced. Lower bounds are derived and embedded into an exact solution method, that can solve benchmark instances with up to 120 customers. The 2E-CVRP requires designing the optimal routing plan to deliver goods from a depot to customers by using intermediate depots. The objective is to minimize the sum of routing and handling costs. A new mathematical formulation is introduced. Valid lower bounds and an exact method are derived. Computational results on benchmark instances show that the new exact algorithm outperforms the state-of-the-art exact methods.

Implicit computational complexity and probabilistic classes

The thesis applies the ICC tecniques to the probabilistic polinomial complexity classes in order to get an implicit characterization of them. The main contribution lays on the implicit characterization of PP (which stands for Probabilistic Polynomial Time) class, showing a syntactical characterisation of PP and a static complexity analyser able to recognise if an imperative program computes in Probabilistic Polynomial Time. The thesis is divided in two parts. The first part focuses on solving the problem by creating a prototype of functional language (a probabilistic variation of lambda calculus with bounded recursion) that is sound and complete respect to Probabilistic Prolynomial Time. The second part, instead, reverses the problem and develops a feasible way to verify if a program, written with a prototype of imperative programming language, is running in Probabilistic polynomial time or not. This thesis would characterise itself as one of the first step for Implicit Computational Complexity over probabilistic classes. There are still open hard problem to investigate and try to solve. There are a lot of theoretical aspects strongly connected with these topics and I expect that in the future there will be wide attention to ICC and probabilistic classes.

Permutation classes, sorting algorithms, and lattice paths

A permutation is said to avoid a pattern if it does not contain any subsequence which is order-isomorphic to it. Donald Knuth, in the first volume of his celebrated book "The art of Computer Programming", observed that the permutations that can be computed (or, equivalently, sorted) by some particular data structures can be characterized in terms of pattern avoidance. In more recent years, the topic was reopened several times, while often in terms of sortable permutations rather than computable ones. The idea to sort permutations by using one of Knuth’s devices suggests to look for a deterministic procedure that decides, in linear time, if there exists a sequence of operations which is able to convert a given permutation into the identical one. In this thesis we show that, for the stack and the restricted deques, there exists an unique way to implement such a procedure. Moreover, we use these sorting procedures to create new sorting algorithms, and we prove some unexpected commutation properties between these procedures and the base step of bubblesort. We also show that the permutations that can be sorted by a combination of the base steps of bubblesort and its dual can be expressed, once again, in terms of pattern avoidance. In the final chapter we give an alternative proof of some enumerative results, in particular for the classes of permutations that can be sorted by the two restricted deques. It is well-known that the permutations that can be sorted through a restricted deque are counted by the Schrӧder numbers. In the thesis, we show how the deterministic sorting procedures yield a bijection between sortable permutations and Schrӧder paths.