We classify a certain collection of bialgebras that are generated by a single element over a finite field , giving a parameterization using positive integers. We then put necessary and sufficient conditions on this pair so that the bialgebra lifts uniquely to the ring () of Witt vectors with...

Communication-induced checkpointing protocols constitute an interesting approach to the on-line determination of checkpoint and communication patterns enjoying desirable properties such as domino-effect freedom. They do not add control messages to the computation, but instead may attach control...

We describe algebraic obstruction theories for realizing an abstract (co)algebra over the mod Steenrod algebra as the (co)homology of a topological space, and for distinguishing between the -homotopy types of different realizations. The theories are expressed in terms of the Quillen cohomology of

When a computer system is expensive to use or is not often available, one may want to tune software for it via analytical models that run on more common, less costly machines. In contrast, if the host system is readily available, the attraction of analytical models is far less. One instead...

The product of the first primes (2..) has neighbours ± 1 with all prime divisors beyond , implying there are infinitely many primes [Euclid]. All primes between and are in the group of units in semigroup of multiplication mod . Squarefree modulus yields as disjoint union of 2 groups, with as...

In this paper we address the problem of preventive maintenance of operational software systems, an approach recently proposed to counteract the phenomenon of software “aging”. We consider the so-called “software rejuvenation” technique [11], which consists in periodically stopping the...

This note shows that a semi-Markov process with Borel state space is under a fairly weak condition on the or and assuming that the embedded Markov chain satisfies either one of the following conditions: (a) it is ; (b) it is and the “recurrent part” of the state space is reached with...