Computational Geometry Column 42

A compendium of thirty previously published open problems in computational geometry is presented.Comment: 7 pages; 72 reference

On the Complexity of Nonrecursive XQuery and Functional Query Languages on Complex Values

This paper studies the complexity of evaluating functional query languages for complex values such as monad algebra and the recursion-free fragment of XQuery. We show that monad algebra with equality restricted to atomic values is complete for the class TA[2^{O(n)}, O(n)] of problems solvable in linear exponential time with a linear number of alternations. The monotone fragment of monad algebra with atomic value equality but without negation is complete for nondeterministic exponential time. For monad algebra with deep equality, we establish TA[2^{O(n)}, O(n)] lower and exponential-space upper bounds. Then we study a fragment of XQuery, Core XQuery, that seems to incorporate all the features of a query language on complex values that are traditionally deemed essential. A close connection between monad algebra on lists and Core XQuery (with ``child'' as the only axis) is exhibited, and it is shown that these languages are expressively equivalent up to representation issues. We show that Core XQuery is just as hard as monad algebra w.r.t. combined complexity, and that it is in TC0 if the query is assumed fixed.Comment: Long version of PODS 2005 pape

Composable Security in the Bounded-Quantum-Storage Model

We present a simplified framework for proving sequential composability in the quantum setting. In particular, we give a new, simulation-based, definition for security in the bounded-quantum-storage model, and show that this definition allows for sequential composition of protocols. Damgard et al. (FOCS '05, CRYPTO '07) showed how to securely implement bit commitment and oblivious transfer in the bounded-quantum-storage model, where the adversary is only allowed to store a limited number of qubits. However, their security definitions did only apply to the standalone setting, and it was not clear if their protocols could be composed. Indeed, we first give a simple attack that shows that these protocols are not composable without a small refinement of the model. Finally, we prove the security of their randomized oblivious transfer protocol in our refined model. Secure implementations of oblivious transfer and bit commitment then follow easily by a (classical) reduction to randomized oblivious transfer.Comment: 21 page