Simulating reversible computation with reaction systems (original) (raw)

Reversibility in Chemical Reactions

Reversible Computation: Extending Horizons of Computing

In this chapter we give an overview of techniques for the modelling and reasoning about reversibility of systems, including outof-causal-order reversibility, as it appears in chemical reactions. We consider the autoprotolysis of water reaction, and model it with the Calculus of Covalent Bonding, the Bonding Calculus, and Reversing Petri Nets. This exercise demonstrates that the formalisms, developed for expressing advanced forms of reversibility, are able to model autoprotolysis of water very accurately. Characteristics and expressiveness of the three formalisms are discussed and illustrated. Keywords: Reversible computation • Reaction modelling • Calculus of Covalent Bonding • Bonding Calculus • Reversing Petri Nets The authors acknowledge partial support of COST Action IC1405 on Reversible Computation-Extending Horizons of Computing.

About reversibility in sP colonies and reaction systems

Natural Computing

In this paper, we study reversibility in sP colonies and in reaction systems. sP colony is a bio-inspired computational model formed from an environment and a finite set of agents. The current state of the environment is represented by a finite set of objects and the current state of the agent is given by a finite multiset of objects. By execution of a program from a set of programs associated with the agent, the agent can change the objects in its own state and possibly in the environment, too. Reaction systems are a bio-inspired computational model where reactants are transformed into products only if some inhibitors are not present. We define sP colonies without input influence and prove that to any reversible sP colony of such type an inverse sP colony can be constructed that performs inverse computation. In the second part of the paper, we show that the concept of a reversible reaction system and the notion of an inverse reaction system can be defined in a similar way, and pa...

A structural approach to reversible computation

2005

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 (ie in a syntax-directed fashion) into a simple kind of automata which are immediately seen to be reversible.

Molecular computation models: unconventional approaches

Biology has long inspired unconventional models of computations to computer scientists. In this paper, we will focus on a model inspired by biological development both at the molecular and cellular levels. Such biological processes are particularly interesting for computer science because the dynamic organization emerges from many decentralized and local interactions that occur concurrently at several time and space scales. Thus, they provide a source of inspiration to solve various problems related to mobility, distributed systems, open systems, etc.

A Design-based model of reversible computation

2006

Abstract. We investigate, within the UTP framework of designs, the effect of seeing computation as an essentially reversible process. We describe the theoretical link between reversibility and the minimum power requirements of a computation, and we review Zuliani’s work on Reversible pGCL which brings reversible computing within the scope of formal software development. We propose an alternative formalisation of reversible computing which exploits reversibility to provide backtracking. To obtain a basic backtracking language able to search for a single result we exploit the already recognised properties of non-deterministic choice, using it as provisional choice rather than implementor’s choice. We add a “prospective values ” formalism which can describe programs that return all the possible results of a search, and we show how to formally describe the premature termination of such a search, a mechanism analogous to the “cut ” of Prolog. An appendix describes some aspects of the wp ...

Programmability of chemical reaction networks

2009

Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a well-stirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and Boolean Logic Circuits, Vector Addition Systems, Petri nets, Gate Implementability, Primitive Recursive Functions, Register Machines, Fractran, and Turing Machines. A theme to these investigations is the thin line between decidable and undecidable questions about SCRN behavior. M. Cook ( )

Reversible simulation of irreversible computation

Physica D: Nonlinear Phenomena, 1998

Reversible simulation of irreversible algorithms is analyzed in the stylized form of a 'reversible' pebble game. The reacheable reversible simulation instantaneous descriptions (pebble configurations) are characterized completely. As a corollary we obtain the reversible simulation by Bennett and that among all simulations that can be modelled by the pebble game, Bennett's simulation is optimal in that it uses the least auxiliary space for the greatest number of simulated steps. One can reduce the auxiliary storage overhead incurred by the reversible simulation at the cost of allowing limited erasing leading to an irreversibility-space tradeoff. We show that in this resource-bounded setting the limited erasing needs to be performed at precise instants during the simulation. We show that the reversible simulation can be modified so that it is applicable also when the simulated computation time is unknown.

Reversible Computation in Petri Nets

Reversible Computation

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, causal reversing and out-of-causal-order reversing. Our proposal concerns a variation of Petri nets where tokens are persistent and are distinguished from each other by an identity which allows for transitions to be reversed spontaneously in or out of causal order. Our design decisions are influenced by applications in biochemistry but the methodology can be applied to a wide range of problems that feature reversibility. In particular, to demonstrate the applicability of our approach we use an example of a biochemical system and an example of a transaction-processing system both of which naturally embed reversible behaviour.

Towards bridging two cell-inspired models: P systems and R systems

Theoretical Computer Science, 2012

We examine, from the point of view of membrane computing, the two basic assumptions of reaction systems, the "threshold" and "no permanence" ones. In certain circumstances (e.g., defining the successful computations by local halting), the second assumption can be incorporated in a transition P system or in a symport/antiport P system without losing the universality. The case of the first postulate remains open: the reaction systems deal, deterministically, with finite sets of symbols, which is not of much interest for computing; three ways to introduce nondeterminism are suggested and left as research topics.

Transition Graphs of Reversible Reaction Systems

Membrane Computing, 2021

We study the transition graphs, and thus, the possible computational paths of reaction systems which are reversible according to different notions of reversibility. We show that systems which are reversible in the sense of our earlier work produce very simple types of transition graphs. A somewhat more complicated, but still quite simple class of transition graphs is obtained if we consider so called initialized reversible systems. Finally we introduce the notion of reversibility with lookbehind, and show that systems which are reversible in this sense produce the same transition graphs (and thus, the same computations) as the state transition diagrams of reversible finite transition systems.