� noto che i linguaggi regolari ? o di tipo 3 ? sono equivalenti agli automi a stati finiti. Tuttavia, in letteratura sono presenti altre caratterizzazioni di questa classe di linguaggi, in termini di modelli riconoscitori e grammatiche. Per esempio, limitando le risorse computazionali di modelli pi� generali, quali grammatiche context-free, automi a pila e macchine di Turing, che caratterizzano classi di linguaggi pi� ampie, � possibile ottenere modelli che generano o riconoscono solamente i linguaggi regolari. I dispositivi risultanti forniscono delle rappresentazioni alternative dei linguaggi di tipo 3, che, in alcuni casi, risultano significativamente pi� compatte rispetto a quelle dei modelli che caratterizzano la stessa classe di linguaggi. Il presente lavoro ha l?obiettivo di studiare questi modelli formali dal punto di vista della complessit� descrizionale, o, in altre parole, di analizzare le relazioni tra le loro dimensioni, ossia il numero di simboli utilizzati per specificare la loro descrizione. Sono presentati, inoltre, alcuni risultati connessi allo studio della famosa domanda tuttora aperta posta da Sakoda e Sipser nel 1978, inerente al costo, in termini di numero di stati, per l?eliminazione del nondeterminismo dagli automi stati finiti sfruttando la capacit� degli automi two-way deterministici di muovere la testina avanti e indietro sul nastro di input.

In the first part of this dissertation, we study the fundamental problem of sampling from a discrete probability distribution. Specifically, given non-negative numbers p1, . . . , pn the task is to draw i with probability proportional to pi. We extend the classic solution to this problem, Walker’s alias method, in various directions: 1. We improve upon its space requirements by presenting optimal succinct sampling data structures. 2. We present improved trade-offs between preprocessing and query time for sorted inputs, and generalize this from proportional sampling to sampling subsets. 3. For Bernoulli, geometric, and binomial random variates we present optimal sampling algorithms on a bounded precision machine. 4. As an application, we speed up sampling of internal diffusion limited aggregation. The second part of this dissertation belongs to the area of computational geometry and deals with algorithms for the Frechet distance, which is a popular measure of similarity of two curves and can be computed in quadratic time (ignoring logarithmic factors). We provide the first conditional lower bound for this problem: No polynomial factor improvement over the quadratic running time is possible unless the Strong Exponential Time Hypothesis fails. Our various extensions of this main result include conditional lower bounds under realistic input assumptions, which do not match the known algorithms. We close this gap by presenting an improved approximation algorithm for the Frechet distance.

Secure computation enables many parties to jointly compute a function of their private inputs. The security requirement is that the input privacy of any honest party is preserved even if other parties participating in the protocol collude or deviate from the protocol. In concurrent and physical adversarial parties try to break the privacy of honest parties by exploiting the network connection or physical weaknesses of the honest parties’ machine. This article provides an overview of the results for achieving secure computation in presence of concurrent and physical attacks contained in the phD thesis:”Secure Computation under concurrent and physical attacks, with emphasis to the relation of such results with the state of the art.

The Boolean Satisfiability (SAT) decision problem can be deservedly declared a success story of computer science. Although SAT was the first problem to be proved NP-complete, the last decade and a half have seen dramatic improvements in the performance of SAT solvers on many practical problem instances. These performance improvements enabled a wide range of real-world applications, several of which have key industrial significance. This article surveys the organization of modern conflict-driven clause learning (CDCL) SAT solvers, focusing on the principal techniques that have contributed to this impressive performance. The article also empirically evaluates these techniques on a comprehensive suite of problem instances taken from a range of representative applications, allowing for a better understanding of their relative contribution.

There exist many different Petri net formalisms. In this paper, we present the Petri Net Cube which helps to structure and classify the variety of Petri net formalisms. We show, that three basic aspects are sufficient for describing most classical Patri net formalisms. Since these aspects are independent of each other, we call them the three Dimensions of Petri Nets.

The aim of this paper is to emphasize the fact that for all finitely-many-valued logics there is a completely systematic relation between sequent calculi and tableau systems. More importantly, we show that for both of these systems there are always two dual proof systems (not just only two ways to interpret the calculi). This phenomenon may easily escape one's attention since in the classical (two-valued) case the two systems coincide. (In two-valued logic the assignment of a truth value and the exclusion of the opposite truth value describe the same situation.