arXiv subjects
Publications and source records attributed to Matteo Palazzo.
We introduce an imperative, stack-based, and reversible computational model that characterizes Two-way Bijections both implicitly, concerning their computational complexity, and with zero-garbage.
This work examines approaches to making computational models reversible. Broadly speaking, transforming a computational model into a reversible one, i.e. reversibilizing it, means extending its operational semantics conservatively in a way that each term of the model is interpretable as a bijection. We recall that the most common strategy to reversibilize a computational model yields operational semantics that halts computations whenever a computational state cannot be uniquely determined from its successor state, thereby allowing terms to be interpreted as partial bijective functions. We are interested in reversible computational models whose terms can be interpreted as total bijective functions. This is essential for studying aspects of computational complexity related to reversible computational models. We introduce SCORE, a language designed for manipulating variables and stacks. Notably, common reversibilization strategies naturally lead to interpreting the functions for stack manipulation as partial bijections. According to our interests, we demonstrate how to interpret SCORE in a state space where, using a proof-assistant, we certify that stack operations are total bijections. It follows that all SCORE terms can be interpreted as total bijections.
Concerning classical computational models able to express all the Primitive Recursive Functions (PRF), there are interesting results regarding limits on their algorithmic expressiveness or, equivalently, efficiency, namely the ability to express algorithms with minimal computational cost. By introducing the reversible programming model Forest, at our knowledge, we provide a first study of analogous properties, adapted to the context of reversible computational models that can represent all the functions in PRF. Firstly, we show that Forest extends Matos' linear reversible computational model MSRL, the very extension being a guaranteed terminating iteration that can be halted by means of logical predicates. The consequence is that Forest is PRF complete, because MSRL is. Secondly, we show that Forest is strictly algorithmically more expressive than MSRL: it can encode a reversible algorithm for the minimum between two integers in optimal time, while MSRL cannot.