Reversible computation allows computation to proceed not only in the standard, forward direction, but also backward, recovering past states. While reversible computation has attracted interest for its multiple applications, covering areas as different as low-power computing, simulation, robotics and debugging, such applications need to be supported by a clear understanding of the foundations of reversible computation. We report below on many threads of research in the area of foundations of reversible computing, giving particular emphasis to the results obtained in the framework of the European COST Action IC1405, entitled “Reversible Computation - Extending Horizons of Computing”, which took place in the years 2015–2019.

We investigate the enhanced mobile membranes, a new class of mobile membrane system in which new rules are introduced. The contextual evolution rules describe how an object from a membrane can evolve only in some context. The other rules describe the objective endocytosis and exocytosis. We use the class of enhanced mobile membrane system to model some evolutions in the immune system.

We modify the most used evolution strategy in membrane systems (namely that of maximal parallelism) by imposing a synchronization between rules. A synchronization over a set of rules can be applied only if each rule of the set can be applied at least once. For membrane systems working in the accepting mode, this synchronization is powerful enough to provide the computational completeness without any other ingredient (no catalysts, promoters, inhibitors, etc). The modeling power of synchronization is described by simulating the basic arithmetic operations (addition, subtraction, multiplication and division).