Slice Nondeterminism

This paper studies a technique for describing and formalising nondeterministic functions, using slice categories. Results of a nondeterministic function are modelled by an object of the slice category over the codomain of the function, which is an indexed family over the codomain. Two such families denote the same set of results if slice morphisms exist between them in both directions. We formulate the category of nondeterministic functions by expressing a set of possible results as an equivalence class of objects. If we allow families to use any indexing set, this category will be equivalent to the category of relations. When we limit ourselves to a smaller universe of indexing sets, we get a subcategory which more closely resembles nondeterministic programs. We compare this category with other representations of the category of relations, and see how many properties can be carried over, such as its product, coproduct and other monoidal structures. We can describe inductive nondeterministic structures by lifting free monads from the category of sets. Moreover, due to the intensional nature of the slice representation, nondeterministic processes are easily represented, such as interleaving concurrency and labelled transition systems. This paper has been formalised in Agda

Reversible Computation: Extending Horizons of Computing

This open access State-of-the-Art Survey presents the main recent scientific outcomes in the area of reversible computation, focusing on those that have emerged during COST Action IC1405 "Reversible Computation - Extending Horizons of Computing", a European research network that operated from May 2015 to April 2019. Reversible computation is a new paradigm that extends the traditional forwards-only mode of computation with the ability to execute in reverse, so that computation can run backwards as easily and naturally as forwards. It aims to deliver novel computing devices and software, and to enhance existing systems by equipping them with reversibility. There are many potential applications of reversible computation, including languages and software tools for reliable and recovery-oriented distributed systems and revolutionary reversible logic gates and circuits, but they can only be realized and have lasting effect if conceptual and firm theoretical foundations are established first

Reversible Computation: Extending Horizons of Computing

This open access State-of-the-Art Survey presents the main recent scientific outcomes in the area of reversible computation, focusing on those that have emerged during COST Action IC1405 "Reversible Computation - Extending Horizons of Computing", a European research network that operated from May 2015 to April 2019. Reversible computation is a new paradigm that extends the traditional forwards-only mode of computation with the ability to execute in reverse, so that computation can run backwards as easily and naturally as forwards. It aims to deliver novel computing devices and software, and to enhance existing systems by equipping them with reversibility. There are many potential applications of reversible computation, including languages and software tools for reliable and recovery-oriented distributed systems and revolutionary reversible logic gates and circuits, but they can only be realized and have lasting effect if conceptual and firm theoretical foundations are established first