In this preliminary work, I provide the outline of an argument (leaving the full proof to a future publication) that there exists a valid renormalization group blocking transformation which converts the continuum fermion action into a Ginsparg-Wilson lattice action. I construct the blocking for the massless overlap operator as a specific example, indicating how other Ginsparg-Wilson lattice Dir...

This work is a natural companion of [10], where the dynamics of cocycles of isometries of R over a minimal dynamics (semigroup action) is studied. While [10] is mostly devoted to the case in which the orbits of the fibered (skew) dynamics are bounded (a condition that turns out to be equivalent to the existence of a continuous invariant section), here we concentrate on the opposite (i.e. non-re...

We consider a version of the notion of F -inverse semigroup (studied in the algebraic theory of inverse semigroups). We point out that an action of such an inverse semigroup on a locally compact space has associated a natural groupoid construction, very similar to the one of a transformation group. We discuss examples related to Toeplitz algebras on subsemigroups of discrete groups, to Cuntz-Kr...

We study the idempotent-generated subsemigroup of the partition monoid. In the finite case this subsemigroup consists of the identity and all the singular partitions. In the infinite case, the subsemigroup is described in terms of certain parameters that measure how far a partition is from being a permutation. As one of several corollaries, we deduce Howie’s description from 1966 of the semigro...

This paper describes algorithms for computing the structure of finite transformation semigroups. The algorithms depend crucially on a new data structure for an R-class in terms of a group and an action. They provide for local computations, concerning a single R-class, without computing the whole semigroup, as well as for computing the global structure of the semigroup. The algorithms have been ...

In this paper we investigate the semigroup structure of the syntactic monoid Syn(C+) of C+, the semigroup generated by a maximal prefix code C for which C+ is a single class of the syntactic congruence. In particular we prove that for such a prefix code C, either Syn(C+) is a group or it is isomorphic to a special type of submonoid of G× T (R) where G is a group and T (R) is the full transforma...

Let Xn = {1, 2, . . . , n}. On a partial transformation α : Domα ⊆ Xn → Im α ⊆ Xn of Xn the following parameters are defined: the breadth or width of α is | Dom α |, the height of α is | Im α |, and the right (resp., left) waist of α is max(Im α) (resp., min(Im α)). We compute the cardinalities of some equivalences defined by equalities of these parameters on OPn, the semigroup of orientation-p...

The variant of a semigroup S with respect to an element a ∈ S, denoted S, is the semigroup with underlying set S and operation ? defined by x ? y = xay for x, y ∈ S. In this article, we study variants T a X of the full transformation semigroup TX on a finite set X. We explore the structure of T a X as well as its subsemigroups Reg(T a X) (consisting of all regular elements) and E X (consisting ...

The purpose of this paper is towards the algebraic study of rough finite state machines, i.e., to introduce the concept of homomorphisms between two rough finite state machines, to associate a rough transformation semigroup with a rough finite state machine and to introduce the concept of coverings of rough finite state machines as well as rough transformation semigroups.