Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on simulations of low-level machine models. By contrast, we develop a more structural approach. We show how high-level functional programs can be mapped compositionally (i.e. in a syntax-directed fashion) into a simple kind of automata which are immediately seen to be reversible. The size of the automaton is linear in the size of the functional term. In mathematical terms, we are building a concrete model of functional computation. This construction stems directly from ideas arising in Geometry of Interaction and Linear Logic---but can be understood without any knowledge of these topics. In fact, it serves as an excellent introduction to them. At the same time, an interesting logical delineation between reversible and irreversible forms of computation emerges from our analysis.
The formalization of process algebras usually starts with a minimal core of operators and rules for its transition system, and then relax the system to improve its usability and ease the proofs. In the calculus of communicating systems (CCS), the structural congruence plays this role by making e.g. parallel composition commutative and associative: without it, the system would be cumbersome to use and reason about, and it can be proven that this change is innocuous in a precise technical sense. For the two reversible calculi extending CCS, the situation is less clear: CCS with Communication Key…
Process algebra ACP based on the interleaving semantics can not be reversed. We design a reversible version of APTC called RAPTC. It has algebraic laws of reversible choice, sequence, parallelism, communication, silent step and abstraction, and also the soundness and completeness modulo strongly forward-reverse truly concurrent bisimulations and weakly forward-reverse truly concurrent bisimulations.
In a reversible language, any forward computation can be undone by a finite sequence of backward steps. Reversible computing has been studied in the context of different programming languages and formalisms, where it has been used for debugging and for enforcing fault-tolerance, among others. In this paper, we consider a subset of Erlang, a concurrent language based on the actor model. We formally introduce a reversible semantics for this language. To the best of our knowledge, this is the first attempt to define a reversible semantics for Erlang.
Our main models of computation (the Turing Machine and the RAM) make fundamental assumptions about which primitive operations are realizable. The consensus is that these include logical operations like conjunction, disjunction and negation, as well as reading and writing to memory locations. This perspective conforms to a macro-level view of physics and indeed these operations are realizable using macro-level devices involving thousands of electrons. This point of view is however incompatible with quantum mechanics, or even elementary thermodynamics, as both imply that information is a conserv…
Reversible computation is an unconventional form of computing where any executed sequence of operations can be executed in reverse at any point during computation. It has recently been attracting increasing attention in various research communities as on the one hand it promises low-power computation and on the other hand it is inherent or of interest in a variety of applications. In this paper, we propose a reversible approach to Petri nets by introducing machinery and associated operational semantics to tackle the challenges of the three main forms of reversibility, namely, backtracking, cau…
Reversible Primitive Permutations (RPP) are recursively defined functions designed to model Reversible Computation. We illustrate a proof, fully developed with the proof-assistant Lean, certifying that: "RPP can encode every Primitive Recursive Function". Our reworking of the original proof of that statement is conceptually simpler, fixes some bugs, suggests a new more primitive reversible iteration scheme for RPP, and, in order to keep formalization and semi-automatic proofs simple, led us to identify a single pattern that can generate some useful reversible algorithms in RPP: Cantor Pairing,…
In this work, we incorporate reversibility into structured communication-based programming, to allow parties of a session to automatically undo, in a rollback fashion, the effect of previously executed interactions. This permits taking different computation paths along the same session, as well as reverting the whole session and starting a new one. Our aim is to define a theoretical basis for examining the interplay in concurrent systems between reversible computation and session-based interaction. We thus enrich a session-based variant of pi-calculus with memory devices, dedicated to keep tra…
Reversible computing is a computational paradigm in which computations are deterministic in both the forward and backward direction, so that programs have well-defined forward and backward semantics. We investigate the formal semantics of the reversible functional programming language Rfun. For this purpose, we introduce join inverse rig categories, the natural marriage of join inverse categories and rig categories, which we show can be used to model the language Rfun, under reasonable assumptions. These categories turn out to be a particularly natural fit for reversible computing as a whole, …
Petri nets are a mathematical language for modeling and reasoning about distributed systems. In this paper we propose an approach to Petri nets for embedding reversibility, i.e., the ability of reversing an executed sequence of operations at any point during operation. Specifically, we introduce machinery and associated semantics to support the three main forms of reversibility namely, backtracking, causal reversing, and out-of-causal-order reversing in a variation of cyclic Petri nets where tokens are persistent and are distinguished from each other by an identity. Our formalism is influenced…
We generalise clones, which are sets of functions $f:A^n \rightarrow A$, to sets of mappings $f:A^n \rightarrow A^m$. We formalise this and develop language that we can use to speak about it. We then look at bijective mappings, which have connections to reversible computation, which is important for physical (e.g. quantum computation) as well as engineering (e.g. heat dissipation) reasons. We generalise Toffoli's seminal work on reversible computation to arbitrary arity logics. In particular, we show that some restrictions he found for reversible computation on alphabets of order 2 do not appl…
A Reversible Perspective on Petri Nets and Event Structures
ICC - Universidad de Buenos Aires, Conicet（布宜诺斯艾利斯大学计算机研究所（CONICET））；Dipartimento di Scienze Pure e Applicate, Università di Urbino（乌尔比诺大学纯科学与应用科学系）；Dipartimento di Matematica e Informatica, Università di Cagliari（卡利亚里大学数学与信息科学系）
Reversible computation is an unconventional form of computing that extends the standard forward-only mode of computation with the ability to execute a sequence of operations in reverse at any point during computation. As such, in this thesis we propose a reversible approach to Petri nets by introducing machinery and associated operational semantics to tackle the challenges of the main forms of reversibility. Our proposal concerns a variation of cyclic Petri nets, called Reversing Petri Nets (RPNs) where tokens are persistent and distinguished from each other by an identity. An immediate extens…
One of the well-known results in concurrency theory concerns the relationship between event structures and occurrence nets: an occurrence net can be associated with a prime event structure, and vice versa. More generally, the relationships between various forms of event structures and suitable forms of nets have been long established. Good examples are the close relationship between inhibitor event structures and inhibitor occurrence nets, or between asymmetric event structures and asymmetric occurrence nets. Several forms of event structures suited for the modelling of reversible computation …
