Quantitative Analysis of Concurrent Reversible Computations

Reversible computing is a paradigm of computation that extends the standard forward-only programming to reversible programming, so that programs can be executed both in the standard, forward direction, and backward, going back to past states. In this paper we present novel quantitative stochastic model for concurrent and cooperating computations. More precisely, we introduce the class of ρ-reversible stochastic automata and define a semantics for the synchronization ensuring that this class of models is closed under composition. For this class of automata we give an efficient way of deriving the equilibrium distribution. Moreover, we prove that the equilibrium distribution of the composition of reversible automata can be derived as the product of the equilibrium distributions of each automaton in isolation

Formal executable descriptions of biological systems

The similarities between systems of living entities and systems of concurrent processes may support biological experiments in silico. Process calculi offer a formal framework to describe biological systems, as well as to analyse their behaviour, both from a qualitative and a quantitative point of view. A couple of little examples help us in showing how this can be done. We mainly focus our attention on the qualitative and quantitative aspects of the considered biological systems, and briefly illustrate which kinds of analysis are possible. We use a known stochastic calculus for the first example. We then present some statistics collected by repeatedly running the specification, that turn out to agree with those obtained by experiments in vivo. Our second example motivates a richer calculus. Its stochastic extension requires a non trivial machinery to faithfully reflect the real dynamic behaviour of biological systems

Bridging Causal Reversibility and Time Reversibility: A Stochastic Process Algebraic Approach

Causal reversibility blends reversibility and causality for concurrent systems. It indicates that an action can be undone provided that all of its consequences have been undone already, thus making it possible to bring the system back to a past consistent state. Time reversibility is instead considered in the field of stochastic processes, mostly for efficient analysis purposes. A performance model based on a continuous-time Markov chain is time reversible if its stochastic behavior remains the same when the direction of time is reversed. We bridge these two theories of reversibility by showing the conditions under which causal reversibility and time reversibility are both ensured by construction. This is done in the setting of a stochastic process calculus, which is then equipped with a variant of stochastic bisimilarity accounting for both forward and backward directions

Flux Analysis in Process Models via Causality

We present an approach for flux analysis in process algebra models of biological systems. We perceive flux as the flow of resources in stochastic simulations. We resort to an established correspondence between event structures, a broadly recognised model of concurrency, and state transitions of process models, seen as Petri nets. We show that we can this way extract the causal resource dependencies in simulations between individual state transitions as partial orders of events. We propose transformations on the partial orders that provide means for further analysis, and introduce a software tool, which implements these ideas. By means of an example of a published model of the Rho GTP-binding proteins, we argue that this approach can provide the substitute for flux analysis techniques on ordinary differential equation models within the stochastic setting of process algebras

Analysis of signalling pathways using continuous time Markov chains

We describe a quantitative modelling and analysis approach for signal transduction networks. We illustrate the approach with an example, the RKIP inhibited ERK pathway [CSK+03]. Our models are high level descriptions of continuous time Markov chains: proteins are modelled by synchronous processes and reactions by transitions. Concentrations are modelled by discrete, abstract quantities. The main advantage of our approach is that using a (continuous time) stochastic logic and the PRISM model checker, we can perform quantitative analysis such as what is the probability that if a concentration reaches a certain level, it will remain at that level thereafter? or how does varying a given reaction rate affect that probability? We also perform standard simulations and compare our results with a traditional ordinary differential equation model. An interesting result is that for the example pathway, only a small number of discrete data values is required to render the simulations practically indistinguishable

Comparative Transition System Semantics for Cause-Respecting Reversible Prime Event Structures

Reversible computing is a new paradigm that has emerged recently and extends the traditional forwards-only computing mode with the ability to execute in backwards, so that computation can run in reverse as easily as in forward. Two approaches to developing transition system (automaton-like) semantics for event structure models are distinguished in the literature. In the first case, states are considered as configurations (sets of already executed events), and transitions between states are built by starting from the initial configuration and repeatedly adding executable events. In the second approach, states are understood as residuals (model fragments that have not yet been executed), and transitions are constructed by starting from the given event structure as the initial state and deleting already executed (and conflicting) parts thereof during execution. The present paper focuses on an investigation of how the two approaches are interrelated for the model of prime event structures extended with cause-respecting reversibility. The bisimilarity of the resulting transition systems is proved, taking into account step semantics of the model under consideration.Comment: In Proceedings AFL 2023, arXiv:2309.0112

On functional module detection in metabolic networks

Functional modules of metabolic networks are essential for understanding the metabolism of an organism as a whole. With the vast amount of experimental data and the construction of complex and large-scale, often genome-wide, models, the computer-aided identification of functional modules becomes more and more important. Since steady states play a key role in biology, many methods have been developed in that context, for example, elementary flux modes, extreme pathways, transition invariants and place invariants. Metabolic networks can be studied also from the point of view of graph theory, and algorithms for graph decomposition have been applied for the identification of functional modules. A prominent and currently intensively discussed field of methods in graph theory addresses the Q-modularity. In this paper, we recall known concepts of module detection based on the steady-state assumption, focusing on transition-invariants (elementary modes) and their computation as minimal solutions of systems of Diophantine equations. We present the Fourier-Motzkin algorithm in detail. Afterwards, we introduce the Q-modularity as an example for a useful non-steady-state method and its application to metabolic networks. To illustrate and discuss the concepts of invariants and Q-modularity, we apply a part of the central carbon metabolism in potato tubers (Solanum tuberosum) as running example. The intention of the paper is to give a compact presentation of known steady-state concepts from a graph-theoretical viewpoint in the context of network decomposition and reduction and to introduce the application of Q-modularity to metabolic Petri net models

A Truly Concurrent Semantics for Reversible CCS

Reversible CCS (RCCS) is a well-established, formal model for reversible communicating systems, which has been built on top of the classical Calculus of Communicating Systems (CCS). In its original formulation, each CCS process is equipped with a memory that records its performed actions, which is then used to reverse computations. More recently, abstract models for RCCS have been proposed in the literature, basically, by directly associating RCCS processes with (reversible versions of) event structures. In this paper we propose a different abstract model: starting from one of the well-known encoding of CCS into Petri nets we apply a recently proposed approach to incorporate causally-consistent reversibility to Petri nets, obtaining as result the (reversible) net counterpart of every RCCS term