Profinite equations are an indispensable tool for the algebraic classification of formal languages. Reiterman’s theorem states that they precisely specify pseudovarieties, i.e., classes finite algebras closed under products, subalgebras and quotients. In this article, is generalized to Eilenberg-Moore a monad T on category D: we prove class -algebras pseudovariety iff it presentable by profinit...

in this paper, we find explicit solution to the operator equation$txs^* -sx^*t^*=a$ in the general setting of the adjointable operators between hilbert $c^*$-modules, when$t,s$ have closed ranges and $s$ is a self adjoint operator.

Abstract. A well–known property of an irreducible non–singular M–matrix is that its inverse is non–negative. However, when the matrix is an irreducible and singular M–matrix it is known that it has a generalized inverse which is non–negative, but this is not always true for any generalized inverse. We focus here in characterizing when the Moore–Penrose inverse of a symmetric, singular, irreduci...

This paper describes, by means of an example, how one may mechanically verify delay insensitive circuits on an automated theorem prover. It presents the verification of both the safety and liveness properties of an n-node delay insensitive fifo circuit [12]. The proof system used is a mechanized implementation of Unity [3] on the Boyer-Moore prover [1], described in [6, 7, 8]. This paper descri...

The method for reduction of the number of programmable array logic macrocells in a microprogrammed Moore finite state machine circuit is proposed. It is based on representation of the state code as a concatenation of a code for the class of pseudoequivalent states and a code of states inside this class. Such an approach allows eliminating the dependence between states and microoperations. The s...