Program Algebra over an Algebra

Program Algebra over an Algebra1

We introduce an algebra with free variables, an algebra with undefined values, a program algebra over a term algebra, an algebra with integers, and an algebra with arrays. Program algebra is defined as universal algebra with assignments. Programs depend on the set of generators with supporting variables and supporting terms which determine the value of free variables in the next state. The exec...

Program Algebra and Thread Algebra

On Some Properties of the Max Algebra System Over Tensors

Recently we generalized the max algebra system to the class of nonnegative  tensors. In this paper we give some basic properties for the left (right) inverse, under the new system. The existence of order 2 left (right) inverse of tensors is characterized. Also we generalize the direct product of matrices to the direct product of tensors (of the same order, but may be different dimensions) and i...

Coherence in amalgamated algebra along an ideal

Let $f: Arightarrow B$ be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we investigate the transfer of the property of coherence to the amalgamation $Abowtie^{f}J$. We provide necessary and sufficient conditions for $Abowtie^{f}J$ to be a coherent ring.

An Introduction to Program and Thread Algebra

We provide an introduction to Program Algebra (PGA, an algebraic approach to the modeling of sequential programming) and to Thread Algebra (TA). PGA is used as a basis for several lowand higher-level programming languages. As an example we consider a simple language with goto’s. Threads in TA model the execution of programs. Threads may be composed with services which model (part of) the execut...