Concurrent Knowledge-Extraction in the Public-Key Model

Knowledge extraction is a fundamental notion, modelling machine possession of values (witnesses) in a computational complexity sense. The notion provides an essential tool for cryptographic protocol design and analysis, enabling one to argue about the internal state of protocol players without ever looking at this supposedly secret state. However, when transactions are concurrent (e.g., over the Internet) with players possessing public-keys (as is common in cryptography), assuring that entities ``know'' what they claim to know, where adversaries may be well coordinated across different transactions, turns out to be much more subtle and in need of re-examination. Here, we investigate how to formally treat knowledge possession by parties (with registered public-keys) interacting over the Internet. Stated more technically, we look into the relative power of the notion of ``concurrent knowledge-extraction'' (CKE) in the concurrent zero-knowledge (CZK) bare public-key (BPK) model.Comment: 38 pages, 4 figure

Times series averaging from a probabilistic interpretation of time-elastic kernel

At the light of regularized dynamic time warping kernels, this paper reconsider the concept of time elastic centroid (TEC) for a set of time series. From this perspective, we show first how TEC can easily be addressed as a preimage problem. Unfortunately this preimage problem is ill-posed, may suffer from over-fitting especially for long time series and getting a sub-optimal solution involves heavy computational costs. We then derive two new algorithms based on a probabilistic interpretation of kernel alignment matrices that expresses in terms of probabilistic distributions over sets of alignment paths. The first algorithm is an iterative agglomerative heuristics inspired from the state of the art DTW barycenter averaging (DBA) algorithm proposed specifically for the Dynamic Time Warping measure. The second proposed algorithm achieves a classical averaging of the aligned samples but also implements an averaging of the time of occurrences of the aligned samples. It exploits a straightforward progressive agglomerative heuristics. An experimentation that compares for 45 time series datasets classification error rates obtained by first near neighbors classifiers exploiting a single medoid or centroid estimate to represent each categories show that: i) centroids based approaches significantly outperform medoids based approaches, ii) on the considered experience, the two proposed algorithms outperform the state of the art DBA algorithm, and iii) the second proposed algorithm that implements an averaging jointly in the sample space and along the time axes emerges as the most significantly robust time elastic averaging heuristic with an interesting noise reduction capability. Index Terms-Time series averaging Time elastic kernel Dynamic Time Warping Time series clustering and classification

Fuzzy Natural Logic in IFSA-EUSFLAT 2021

The present book contains five papers accepted and published in the Special Issue, “Fuzzy Natural Logic in IFSA-EUSFLAT 2021”, of the journal Mathematics (MDPI). These papers are extended versions of the contributions presented in the conference “The 19th World Congress of the International Fuzzy Systems Association and the 12th Conference of the European Society for Fuzzy Logic and Technology jointly with the AGOP, IJCRS, and FQAS conferences”, which took place in Bratislava (Slovakia) from September 19 to September 24, 2021. Fuzzy Natural Logic (FNL) is a system of mathematical fuzzy logic theories that enables us to model natural language terms and rules while accounting for their inherent vagueness and allows us to reason and argue using the tools developed in them. FNL includes, among others, the theory of evaluative linguistic expressions (e.g., small, very large, etc.), the theory of fuzzy and intermediate quantifiers (e.g., most, few, many, etc.), and the theory of fuzzy/linguistic IF–THEN rules and logical inference. The papers in this Special Issue use the various aspects and concepts of FNL mentioned above and apply them to a wide range of problems both theoretically and practically oriented. This book will be of interest for researchers working in the areas of fuzzy logic, applied linguistics, generalized quantifiers, and their applications