Reversible computation opens up the possibility of overcoming some of the hardware's current physical limitations. It also offers theoretical insights, as it enriches multiple paradigms and models of computation, and sometimes retrospectively enlightens them. Concurrent reversible computation, for instance, offered interesting extensions to the Calculus of Communicating Systems, but was still lacking a natural and pertinent bisimulation to study processes equivalences. Our paper formulates an equivalence exploiting the two aspects of reversibility: backward moves and memory mechanisms. This bisimulation captures classical equivalences relations for denotational models of concurrency (History-and hereditary history-preserving bisimulation, (H)HPB), that were up to now only partially characterized by process algebras. This result gives an insight on the expressiveness of reversibility, as both backward moves and a memory mechanism-providing 'backward determinism'-are needed to capture HHPB.

Site-graph rewriting languages, such as Kappa or BNGL, offer parsimonious ways to describe highly combinatorial systems of mechanistic interactions among proteins. These systems may be then simulated efficiently. Yet, the modeling mechanisms that involve counting (a number of phosphorylated sites for instance) require an exponential number of rules in Kappa. In BNGL, updating the set of the potential applications of rules in the current state of the system comes down to the sub-graph isomorphism problem (which is NP-complete). In this paper, we extend Kappa to deal both parsimoniously and efficiently with counters. We propose a single push-out semantics for Kappa with counters. We show how to compile Kappa with counters into Kappa without counters (without requiring an exponential number of rules). We design a static analysis, based on affine relationships, to identify the meaning of counters and bound their ranges accordingly.

Motivation: We present an overview of the Kappa platform, an integrated suite of analysis and visualization techniques for building and interactively exploring rule-based models. The main components of the platform are the Kappa Simulator, the Kappa Static Analyzer and the Kappa Story Extractor. In addition to these components, we describe the Kappa User Interface, which includes a range of interactive visualization tools for rule-based models needed to make sense of the complexity of biological systems. We argue that, in this approach, modeling is akin to programming and can likewise benefit from an integrated development environment. Our platform is a step in this direction. Results: We discuss details about the computation and rendering of static, dynamic, and causal views of a model, which include the contact map (CM), snaphots at different resolutions, the dynamic influence network (DIN) and causal compression. We provide use cases illustrating how these concepts generate insight. Specifically, we show how the CM and snapshots provide information about systems capable of polymerization, such as Wnt signaling. A well-understood model of the KaiABC oscillator, translated into Kappa from the literature, is deployed to demonstrate the DIN and its use in understanding systems dynamics. Finally, we discuss how pathways might be discovered or recovered from a rule-based model by means of causal compression, as exemplified for early events in EGF signaling. Availability and implementation: The Kappa platform is available via the project website at kappalanguage.org. All components of the platform are open source and freely available through the authors' code repositories.

We present a type system to guarantee termination of π-calculus processes that exploits input/output capabilities and subtyping, as originally introduced by Pierce and Sangiorgi, in order to analyse the usage of channels. Our type system is based on Deng and Sangiorgi's level-based analysis of processes. We show that the addition of i/o-types makes it possible to typecheck processes where a form oflevel polymorphismis at work. We discuss to what extent this programming idiom can be treated by previously existing proposals. We demonstrate how our system can be extended to handle the encoding of the simply-typed λ-calculus, and discuss questions related to type inference.

We introduce a labelled transition semantics for the reversible π-calculus. It is the first account of a compositional definition of a reversible calculus, that has both concurrency primitives and name mobility. The notion of reversibility is strictly linked to the notion of causality. We discuss the notion of causality induced by our calculus, and we compare it with the existing notions in the literature, in particular for what concerns the syntactic feature of scope extrusion, typical of the π-calculus.