Local matching indicators for transport problems with concave costs

In this paper, we introduce a class of indicators that enable to compute efficiently optimal transport plans associated to arbitrary distributions of N demands and M supplies in R in the case where the cost function is concave. The computational cost of these indicators is small and independent of N. A hierarchical use of them enables to obtain an efficient algorithm

Remarks on the Generalized Chaplygin Gas

We have developed an action formulation for the Generalized Chaplygin Gas (GCG). The most general form for the nonrelativistic GCG action is derived consistent with the equation of state. We have also discussed a relativistic formulation for GCG by providing a detailed analysis of the Poincare algebra.Comment: References addede

How unprovable is Rabin's decidability theorem?

We study the strength of set-theoretic axioms needed to prove Rabin's theorem on the decidability of the MSO theory of the infinite binary tree. We first show that the complementation theorem for tree automata, which forms the technical core of typical proofs of Rabin's theorem, is equivalent over the moderately strong second-order arithmetic theory $\mathsf{ACA}_0$ to a determinacy principle implied by the positional determinacy of all parity games and implying the determinacy of all Gale-Stewart games given by boolean combinations of ${\bf \Sigma^0_2}$ sets. It follows that complementation for tree automata is provable from $\Pi^1_3$- but not $\Delta^1_3$-comprehension. We then use results due to MedSalem-Tanaka, M\"ollerfeld and Heinatsch-M\"ollerfeld to prove that over $\Pi^1_2$-comprehension, the complementation theorem for tree automata, decidability of the MSO theory of the infinite binary tree, positional determinacy of parity games and determinacy of $\mathrm{Bool}({\bf \Sigma^0_2})$ Gale-Stewart games are all equivalent. Moreover, these statements are equivalent to the $\Pi^1_3$-reflection principle for $\Pi^1_2$-comprehension. It follows in particular that Rabin's decidability theorem is not provable in $\Delta^1_3$-comprehension.Comment: 21 page

Practical End-to-End Verifiable Voting via Split-Value Representations and Randomized Partial Checking

We describe how to use Rabin's "split-value" representations, originally developed for use in secure auctions, to efficiently implement end-to-end verifiable voting. We propose a simple and very elegant combination of split-value representations with "randomized partial checking" (due to Jakobsson et al. [16])

Practical Provably Correct Voter Privacy Protecting End-to-End Voting Employing Multiparty Computations and Split Value Representations of Votes

Continuing the work of Rabin and Rivest we present another simple and fast method for conducting end to end voting and allowing public verification of correctness of the announced vote tallying results. This method was referred to in as the SV/VCP method. In the present note voter privacy protection is achieved by use of a simple form of Multi Party Computations (MPC). At the end of vote tallying process, random permutations of the cast votes are publicly posted in the clear, without identification of voters or ballot ids. Thus vote counting and assurance of correct form of cast votes are directly available. Also, a proof of the claim that the revealed votes are a permutation of the concealed cast votes is publicly posted and verifiable by any interested party. Advantages of this method are: Easy understandability by non-­‐cryptographers, implementers and ease of use by voters and election officials. Direct handling of complicated ballot forms. Independence from any specialized primitives. Speed of vote-­‐tallying and correctness proving: elections involving a million voters can be tallied and proof of correctness of results posted within a few minutes

Aspects of Diffeomorphism and Conformal invariance in classical Liouville theory

The interplay between the diffeomorphism and conformal symmetries (a feature common in quantum field theories) is shown to be exhibited for the case of black holes in two dimensional classical Liouville theory. We show that although the theory is conformally invariant in the near horizon limit, there is a breaking of the diffeomorphism symmetry at the classical level. On the other hand, in the region away from the horizon, the conformal symmetry of the theory gets broken with the diffeomorphism symmetry remaining intact.Comment: Accepted in Euro. Phys. Letters., Title changed, abstract modified, major modifications made in the pape

Verifiable Random Functions

We efficiently combine unpredictability and verifiability by extending the Goldreich-Goldwasser-Micali notion of pseudorandom functions $f_s$ from a secret seed s, so that knowledge of $s$ not only enables one to evaluate $f_s$ at any point x, but also to provide an NP-proof that the value $f{_s}(x)$ is indeed correct without compromising the unpredictability of $f_s$ at any other point for which no such a proof was provided.Engineering and Applied Science

Deciding Quantifier-Free Presburger Formulas Using Parameterized Solution Bounds

Given a formula in quantifier-free Presburger arithmetic, if it has a satisfying solution, there is one whose size, measured in bits, is polynomially bounded in the size of the formula. In this paper, we consider a special class of quantifier-free Presburger formulas in which most linear constraints are difference (separation) constraints, and the non-difference constraints are sparse. This class has been observed to commonly occur in software verification. We derive a new solution bound in terms of parameters characterizing the sparseness of linear constraints and the number of non-difference constraints, in addition to traditional measures of formula size. In particular, we show that the number of bits needed per integer variable is linear in the number of non-difference constraints and logarithmic in the number and size of non-zero coefficients in them, but is otherwise independent of the total number of linear constraints in the formula. The derived bound can be used in a decision procedure based on instantiating integer variables over a finite domain and translating the input quantifier-free Presburger formula to an equi-satisfiable Boolean formula, which is then checked using a Boolean satisfiability solver. In addition to our main theoretical result, we discuss several optimizations for deriving tighter bounds in practice. Empirical evidence indicates that our decision procedure can greatly outperform other decision procedures.Comment: 26 page