Subshifts, MSO Logic, and Collapsing Hierarchies

We use monadic second-order logic to define two-dimensional subshifts, or sets of colorings of the infinite plane. We present a natural family of quantifier alternation hierarchies, and show that they all collapse to the third level. In particular, this solves an open problem of [Jeandel & Theyssier 2013]. The results are in stark contrast with picture languages, where such hierarchies are usually infinite.Comment: 12 pages, 5 figures. To appear in conference proceedings of TCS 2014, published by Springe

Interpretations of Presburger Arithmetic in Itself

Presburger arithmetic PrA is the true theory of natural numbers with addition. We study interpretations of PrA in itself. We prove that all one-dimensional self-interpretations are definably isomorphic to the identity self-interpretation. In order to prove the results we show that all linear orders that are interpretable in (N,+) are scattered orders with the finite Hausdorff rank and that the ranks are bounded in terms of the dimension of the respective interpretations. From our result about self-interpretations of PrA it follows that PrA isn't one-dimensionally interpretable in any of its finite subtheories. We note that the latter was conjectured by A. Visser.Comment: Published in proceedings of LFCS 201

Authentication with Weaker Trust Assumptions for Voting Systems

Some voting systems are reliant on external authentication services. Others use cryptography to implement their own. We combine digital signatures and non-interactive proofs to derive a generic construction for voting systems with their own authentication mechanisms, from systems that rely on external authentication services. We prove that our construction produces systems satisfying ballot secrecy and election verifiability, assuming the underlying voting system does. Moreover, we observe that works based on similar ideas provide neither ballot secrecy nor election verifiability. Finally, we demonstrate applicability of our results by applying our construction to the Helios voting system

Languages ordered by the subword order

We consider a language together with the subword relation, the cover relation, and regular predicates. For such structures, we consider the extension of first-order logic by threshold- and modulo-counting quantifiers. Depending on the language, the used predicates, and the fragment of the logic, we determine four new combinations that yield decidable theories. These results extend earlier ones where only the language of all words without the cover relation and fragments of first-order logic were considered

Verifiability of Helios Mixnet

We study game-based definitions of individual and universal verifiability by Smyth, Frink & Clarkson. We prove that building voting systems from El Gamal coupled with proofs of correct key generation suffices for individual verifiability. We also prove that it suffices for an aspect of universal verifiability. Thereby eliminating the expense of individual-verifiability proofs and simplifying universal-verifiability proofs for a class of encryption-based voting systems. We use the definitions of individual and universal verifiability to analyse the mixnet variant of Helios. Our analysis reveals that universal verifiability is not satisfied by implementations using the weak Fiat-Shamir transformation. Moreover, we prove that individual and universal verifiability are satisfied when statements are included in hashes (i.e., when using the Fiat-Shamir transformation, rather than the weak Fiat-Shamir transformation)

C-Terminus Glycans with Critical Functional Role in the Maturation of Secretory Glycoproteins

The N-glycans of membrane glycoproteins are mainly exposed to the extracellular space. Human tyrosinase is a transmembrane glycoprotein with six or seven bulky N-glycans exposed towards the lumen of subcellular organelles. The central active site region of human tyrosinase is modeled here within less than 2.5 Å accuracy starting from Streptomyces castaneoglobisporus tyrosinase. The model accounts for the last five C-terminus glycosylation sites of which four are occupied and indicates that these cluster in two pairs - one in close vicinity to the active site and the other on the opposite side. We have analyzed and compared the roles of all tyrosinase N-glycans during tyrosinase processing with a special focus on the proximal to the active site N-glycans, s6:N337 and s7:N371, versus s3:N161 and s4:N230 which decorate the opposite side of the domain. To this end, we have constructed mutants of human tyrosinase in which its seven N-glycosylation sites were deleted. Ablation of the s6:N337 and s7:N371 sites arrests the post-translational productive folding process resulting in terminally misfolded mutants subjected to degradation through the mannosidase driven ERAD pathway. In contrast, single mutants of the other five N-glycans located either opposite to the active site or into the N-terminus Cys1 extension of tyrosinase are temperature-sensitive mutants and recover enzymatic activity at the permissive temperature of 31°C. Sites s3 and s4 display selective calreticulin binding properties. The C-terminus sites s7 and s6 are critical for the endoplasmic reticulum retention and intracellular disposal. Results herein suggest that individual N-glycan location is critical for the stability, regional folding control and secretion of human tyrosinase and explains some tyrosinase gene missense mutations associated with oculocutaneous albinism type I