For a l m o s t as l o n g as a t t e m p t s a t p r o v i n g theorems by mach ines have been made, a c r i t i c a l p r o b l e m has been w e l l known: E q u a t i o n a l a x i o m s , i f l e f t w i t h o u t p r e c a u t i o n s i n t he d a t a base o f a n a u t o m a t i c t heo rem p r o v e r (ATP) , w i l l f o r c e the ATP t o g o a s t r a y . Four approaches t o cope w i t ...

A short proof of the characterization of idempotent subreducts of semimodules over commutative semirings is presented. It says that an idempotent algebra embeds into a semimodule over a commutative semiring, if and only if it belongs to the variety of Szendrei modes.

New algorithm for finding longest increasing subsequence is discussed. This algorithm is based on the ideas of idempotent mathematic and uses Max-Plus idempotent semiring. Problem of finding longest increasing subsequence is reformulated in a matrix form and solved with linear algebra.

The CPS (continuation-passing style) transformation on-terms has an interpretation both in programming languages, type theory, proof theory, and logic. Programming intuition suggests that it is idempotent, but this does not directly hold for all existing CPS transformations (Plotkin, Reynolds, Fischer, etc.). We rephrase it to make it syntactically idempotent, modulo-reduction of the newly intr...

This paper deals with aggregation operators. A new class of aggregation operators, called asymptotically idempotent, is introduced. A generalization of the basic notion of aggregation operator is provided, with an in-depth discussion of the notion of idempotency. Some general contruction methods of commutative, asymptotically idempotent aggregation operators admitting a neutral element are illu...

We develop some new topological tools to study maximal subgroups of free idempotent generated semigroups. As an application, we show that the rank 1 component of the free idempotent generated semigroup of the biordered set of a full matrix monoid of size n×n,n > 2 over a division ring Q has maximal subgroup isomorphic to the multiplicative subgroup of Q.

Viewing the elements of R as images f with pixels i∈ S of grey-scale value f(i) motivates the study of certain nonlinear operators :R → R . For translation invariant (called stack #lters in the signal processing literature) we derive the #rst necessary and su1cient condition for idempotency which can be tested in polynomial time. Various related properties can be tested in polynomial time as we...