Concurrent computation can be given an abstract mathematical treatment very similar to that provided for sequential computation by domain theory and denotational semantics of Scott and Strachey. A simple domain theory for concurrency is presented. Based on a categorical model of linear logic and associated comonads, it highlights the role of linearity in concurrent computation. Two choices of c...

We find the algebraic laws for true concurrency. Eventually, we establish a whole axiomatization for true concurrency called APTC (Algebra for Parallelism in True Concurrency). The theory APTC has four modules: BATC (Basic Algebra for True Concurrency), APTC (Algebra for Parallelism in True Concurrency), recursion and abstraction. And also, we show the applications and extensions of APTC.

Dozens of articles have been published describing "new" concurrency control algorithms for distributed database systems. All of these algorithms can be derived and understood using a few basic concepts. We show how to decompose the concurrency control problem into several subproblems, each of which has iust a few known solutions. By appropriately combining known solutions to the subproblems, we...

Teaching courses that rely on sound mathematical principles is nowadays a challenging task at many universities. On the one hand there is an increased demand for educating students in these areas, on the other hand there are more and more students being accepted with less adequate skills in mathematics. We report here on our experiences in teaching concurrency theory over the last twenty years ...

This work investigates the axiomatic concurrency theory proposed by Carl Adam Petri as a basis of general net theory starting with physically motivated axioms. A formulation in terms of partially ordered sets is intensionally not adopted here, in order to deal with this theory in a more general setting, viewing causality and concurrency as pure similarity relations. Concurrency structures, whic...

This paper investigates a methodology of using FM (FraenkelMostowski) sets, and the ideas of nominal set theory, to adjoin name generation to a semantic theory. By developing a domain theory for concurrency within FM sets the domain theory inherits types and operations for name generation, essentially without disturbing its original higherorder features. The original domain theory had a metalan...

Conventional transaction management in shared databases is traditionally viewed as a combination of two orthogonal problems. One is to guarantee correctness when several transactions are executed concurrently. This is ensured by the concurrency control component of a transaction processing system. The other is to ensure the correctness of the database in spite of transaction aborts and system f...