Universally finitary symbolic extensions

Finitary Galois Extensions over Noncommutative Bases

We study Galois extensions M (co-)H ⊂ M for H-(co)module algebras M if H is a Frobenius Hopf algebroid. The relation between the action and coaction pictures is analogous to that found in Hopf-Galois theory for finite dimensional Hopf algebras over fields. So we obtain generalizations of various classical theorems of Kreimer-Takeuchi, Doi-Takeuchi and Cohen-FischmanMontgomery. We find that the ...

Symbolic extensions

Universally measurable sets in generic extensions

A subset of a topological space is said to be universally measurable if it is measured by the completion of each countably additive σ-finite Borel measure on the space, and universally null if it has measure zero for each such atomless measure. In 1908, Hausdorff proved that there exist universally null sets of real numbers of cardinality א1, and thus that there exist at least 2א1 such sets. La...

Algebraic Extensions for Symbolic Summation

The main result of this thesis is an effective method to extend Karr’s symbolic summation framework to algebraic extensions. These arise, for example, when working with expressions involving (−1)n. An implementation of this method, including a modernised version of Karr’s algorithm is also presented. Karr’s algorithm is the summation analogue of the Risch algorithm for indefinite integration. I...

Universally Composable Symbolic Analysis of Diffie-Hellman based Key Exchange

Canetti and Herzog (TCC’06) show how to efficiently perform fully automated, computationally sound security analysis of key exchange protocols with an unbounded number of sessions. A key tool in their analysis is composability, which allows deducing security of the multi-session case from the security of a single session. However, their framework only captures protocols that use public key encr...