Combinatorial Variations on Cantor's Diagonal

We discuss counting problems linked to finite versions of Cantor's diagonal of infinite tableaux. We extend previous results of [2] by refining an equivalence relation that reduces significantly the exhaustive generation. New enumerative results follow and allow to look at the sub-class of the so- called bi-Cantorian tableaux. We conclude with a correspondence between Cantorian-type tableaux and coloring of hypergraphs having a square number of vertices

Pattern Matching for Superpositional Graphs

Käesolev magistritöö esitab algoritmi mustrite leidmiseks superpositsioonigraafides. Algoritm leiab mustrite arvu ajaga O(kn), kus n on teksti pikkus ja k mustri pikkus. Samasugune ajaline keerukus kehtib ka mustrite leidmisel lahutatavates permutatsioonides.This master's thesis presents a pattern matching algorithm for superpositional graphs which counts a number of matches with time complexity O(kn), where n is a length of a text and k is a length of a pattern. Consequently, the same time complexity is achieved for the case, when both text and pattern are separable permutations

Proving Coercion-Resistance of Scantegrity II

By now, many voting protocols have been proposed that, among others, are designed to achieve coercion-resistance, i.e., resistance to vote buying and voter coercion. Scantegrity II is among the most prominent and successful such protocols in that it has been used in several elections. However, almost none of the modern voting protocols used in practice, including Scantegrity II, has undergone a rigorous cryptographic analysis. In this paper, we prove that Scantegrity II enjoys an optimal level of coercion-resistance, i.e., the same level of coercion-resistance as an ideal voting protocol (which merely reveals the outcome of the election), except for so-called forced abstention attacks. This result is obtained under the (necessary) assumption that the workstation used in the protocol is honest. Our analysis is based on a rigorous cryptographic definition of coercion-resistance we recently proposed. We argue that this definition is in fact the only existing cryptographic definition of coercion-resistance suitable for analyzing Scantegrity II. Our case study should encourage and facilitate rigorous cryptographic analysis of coercion-resistance also for other voting protocols used in practice

Pushing the frontier of minimality

The Minimal Constraint Satisfaction Problem, or Minimal CSP for short, arises in a number of real-world applications, most notably in constraint-based product configuration. It is composed of the set of CSP problems where every allowed tuple can be extended to a solution. Despite the very restrictive structure, computing a solution to a Minimal CSP instance is NP-hard in the general case. In this paper, we look at three independent ways to add further restrictions to the problem. First, we bound the size of the domains. Second, we define the arity as a function on the number of variables. Finally we study the complexity of computing a solution to a Minimal CSP instance when not just every allowed tuple, but every partial solution smaller than a given size, can be extended to a solution. In all three cases, we show that finding a solution remains NP-hard. All these results reveal that the hardness of minimality is very robust