Tolerance distributive and tolerance modular varieties of commutative semigroups

Varieties of Commutative Semigroups

In this paper, we describe all equational theories of commutative semigroups in terms of certain well-quasi-orderings on the set of finite sequences of nonnegative integers. This description yields many old and new results on varieties of commutative semigroups. In particular, we obtain also a description of the lattice of varieties of commutative semigroups, and we give an explicit uniform sol...

Salt tolerance of sunflower varieties during germination

Finitely Based Modular Congruence Varieties Are Distributive

R. Dedekind introduced the modular law, a lattice equation true in most of the lattices associated with classical algebraic systems, see [4]. Although this law is one of the most important tools for working with these lattices, it does not fully describe the equational properties of these lattices. This was made clear in [8] where B. Jónsson and the author showed that if any modular congruence ...

Free Partially Commutative Semigroups in Band Varieties 3

Byzantine Fault-Tolerance with Commutative Commands

State machine replication is a popular approach to increasing the availability of computer services. While it has been largely studied in the presence of crash-stop failures and malicious failures, all existing state machine replication protocols that provide byzantine faulttolerance implement some variant of atomic broadcast. In this context, this paper makes two contributions. First, it prese...