Local reversibility and the Calculus of Covalent Bonding

We introduce a process calculus with a new action prefixing operator that allows to model locally controlled reversibility. Since the observation of covalent bonding in chemical reactions is the starting point of our work we call the process calculus the Calculus of Covalent Bonding (CCB). The calculus is based on CCSK, but adds an operator of the form (s; b), where s is a sequence of actions. Action b can only be executed once all actions in s are done and executing it requires to undo one action in s. By this we achieve control over when reverse actions happen without the need of a global control or a memory. The calculus also allows spontaneous undoing and sequences of forward and reverse actions. We give a formal definition of the calculus using Structural Operational Semantics rules. We also show properties of the calculus, in particular we show that it can model out-of-causal order reversibility. In order to demonstrate the use of our calculus we model the hydration of formaldehyde in water into methanediol. We use a system of four molecules, where various paths are possible to produce the final result. These path include a range of chemical situations. Our calculus can model most of them. We also model Base Excision Repair (BER), a bio-chemical process, on a higher level. This show that our calculus is also useful to model more general situations than the chemical reactions it was derived from.