Free Groups are, in a sense, the most generic kind of group. They are defined over a set of generators with no additional relations in between them. They play an important role in the definition of group presentations and in other fields. This theory provides the definition of Free Group as the set of fully canceled words in the generators. The universal property is proven, as well as some isom...

We present a symbolic definition of election verifiability for electronic voting protocols. Our definition is given in terms of reachability assertions in the applied pi calculus and is amenable to automated reasoning using the tool ProVerif. The definition distinguishes three aspects of verifiability, which we call individual, universal, and eligibility verifiability. It also allows us to dete...

We present a symbolic definition that captures some cases of election verifiability for electronic voting protocols. Our definition is given in terms of reachability assertions in the applied pi calculus and is amenable to automated reasoning using the software tool ProVerif. The definition distinguishes three aspects of verifiability, which we call individual, universal, and eligibility verifi...

The previously proposed cybernetic definition of a living (biological) individual and the cybernetic model of a psychical individual (a self endowed with subjective consciousness) are extended and compared, and their formal similarities are isolated and highlighted. It is argued that the emergence of the biological level of reality from the physical level and of the psychical level from the bio...

We recall some definitions and a claim proved in our previous lecture. These will be required to finish the proof for the Leftover Hash Lemma. Definition 1 H∞(X) = − log (maxx Pr [X = x]) ♦ Definition 2 A function Ext : U × S → V is a (k, ε) extractor if for all random variables X with H∞(X) ≥ k, we have: SD [(S,Ext(X,S)) , (S, V )] ≤ ε where S is uniformly distributed over S and V is uniformly...

1. Basic homological algebra 1 1.1. Chain complexes 2 1.2. Maps and homotopies of maps of chain complexes 2 1.3. Tensor products of chain complexes 3 1.4. Short and long exact sequences 3 1.5. Dual cochain complexes and Hom complexes 4 1.6. Relations between ⊗ and Hom 4 2. The universal coefficient and Künneth theorems 5 2.1. Universal coefficients in homology 5 2.2. The Künneth theorem 6 2.3. ...