We use security in the Universal Composition framework as a means to study the “cryptographic complexity” of 2-party secure computation tasks (functionalities). We say that a functionality F reduces to another functionality G if there is a UC-secure protocol for F using ideal access to G. This reduction is a natural and fine-grained way to compare the relative complexities of cryptographic task...

Consider the following probabilistic one-player game: The board is a graph with n vertices, which initially contains no edges. In each step, a new edge is drawn uniformly at random from all non-edges and is presented to the player, henceforth called Painter. Painter must assign one of r available colors to each edge immediately, where r ≥ 2 is a fixed integer. The game is over as soon as a mono...

Using the transfer matrix method, we give the exact solution of a deterministic sandpile model for arbitrary N , where N is the size of a single toppling. The oneand two-point functions are given in term of the eigenvalues of an N × N transfer matrix. All the n-point functions can be found in the same way. Application of this method to a more general class of models is discussed. We also presen...

Deterministic one-way Turing machines with sublinear space bounds are systematically studied. We distinguish among the notions of strong, weak, and restricted space bounds. The latter is motivated by the study of P automata. The space available on the work tape depends on the number of input symbols read so far, instead of the entire input. The class of functions space constructible by such mac...

An algebraic representation of the Turing machines is given, where the configurations of Turing machines are represented by 4 order tensors, and the transition functions by 8 order tensors. Two types of tensor product are defined, one is to model the evolution of the Turing machines, and the other is to model the compositions of transition functions. It is shown that the two types of tensor pro...

Deterministic replay of parallel execution and communication operations is required both by HPC debuggers and resilience mechanisms. Despite its potential performance advantages, the inherent nondeterminism present in one-sided communication makes replaying difficult. The essential problem is that the readers of updated shared data do not have any information on which remote threads produced th...

In physics, engineering and other settings, it is important to understand the macroscopic behaviour of systems whose evolution is determined by microscale effects. It seems natural to consider these microscale effects to be random in nature (and, therefore, beyond the scope of classical averaging and homogenization theory) and to constitute some perturbation of a well-understood smooth structur...