Jonathan Hayman

Graphs, Rewriting and Pathway Reconstruction for Rule-Based Models

In this paper, we introduce a novel way of constructing concise causal histories (pathways) to represent how specified structures are formed during simulation of systems represented by rule-based models. This is founded on a new, clean, graph-based semantics introduced in the first part of this paper for Kappa, a rule-based modelling language that has emerged as a natural description of protein-protein interactions in molecular biology [Bachman 2011]. The semantics is capable of capturing the whole of Kappa, including subtle side-effects on deletion of structure, and its structured presentation provides the basis for the translation of techniques to other models. In particular, we give a notion of trajectory compression, which restricts a trace culminating in the production of a given structure to the actions necessary for the structure to occur. This is central to the reconstruction of biochemical pathways due to the failure of traditional techniques to provide adequately concise causal histories, and we expect it to be applicable in a range of other modelling situations.

Independence and Concurrent Separation Logic

A compositional Petri net based semantics is given to a simple pointer-manipulating language. The model is then applied to give a notion of validity to the judgements made by concurrent separation logic that emphasizes the process-environment duality inherent in such rely-guarantee reasoning. Soundness of the rules of concurrent separation logic with respect to this definition of validity is shown. The independence information retained by the Petri net model is then exploited to characterize the independence of parallel processes enforced by the logic. This is shown to permit a refinement operation capable of changing the granularity of atomic actions

The unfolding of general Petri nets

The unfolding of (1-)safe Petri nets to occurrence nets is well understood. There is a universal characterization of the unfolding of a safe net which is part and parcel of a coreflection from the category of occurrence nets to the category of safe nets. The unfolding of general Petri nets, nets with multiplicities on arcs whose markings are multisets of places, does not possess a directly analogous universal characterization, essentially because there is an implicit symmetry in the multiplicities of general nets, and that symmetry is not expressed in their traditional occurrence net unfoldings. In the present paper, we show how to recover a universal characterization by representing the symmetry in the behaviour of the occurrence net unfoldings of general Petri nets. We show that this is part of a coreflection between enriched categories of general Petri nets with symmetry and occurrence nets with symmetry.

Context-Sensitive Flow Analyses: A Hierarchy of Model Reductions

Rule-based modelling allows very compact descriptions of protein-protein interaction networks. However, combinatorial complexity increases again when one attempts to describe formally the behaviour of the networks, which motivates the use of abstractions to make these models more coarse-grained. Context-insensitive abstractions of the intrinsic flow of information among the sites of chemical complexes through the rules have been proposed to infer sound coarse-graining, providing an efficient way to find macro-variables and the corresponding reduced models. In this paper, we propose a framework to allow the tuning of the context-sensitivity of the information flow analyses and show how these finer analyses can be used to find fewer macro-variables and smaller reduced differential models.

On Pushouts of Partial Maps

The paper gives a sufficient condition for the existence of all pushouts in an arbitrary category of partial maps \(\mathbb{C}_{*\mathcal{M}}\) that is necessary whenever the category of total maps \(\mathbb{C} \subseteq \mathbb{C}_{*\mathcal{M}}\) has cocones of spans; the latter is the case in all slice categories of ℂ and thus the condition is necessary locally. The main theorem is that, given an admissible class of monos \(\mathcal{M}\) in a category ℂ that has cocones of spans, the category of partial maps \(\mathbb{C}_{*\mathcal{M}}\) has pushouts if and only if the category of total maps ℂ has hereditary pushouts and right adjoints to inverse image functors (where both properties are w.r.t. \(\mathcal{M}\)). This result clarifies previous work by Kennaway on graph rewriting in categories of partial maps that implicitly assumed existence of cocones of spans in the category of total maps.

Granularity and concurrent separation logic

When defining the semantics of shared-memory concurrent programming languages, one conventionally has to make assumptions about the atomicity of actions such as assignments. Running on physical hardware, these assumptions can fail to hold in practice, which puts in question reasoning about their concurrent execution. We address an observation, due to John Reynolds, that processes proved sound in concurrent separation logic are separated to an extent that these assumptions can be disregarded, so judgements remain sound even if the assumptions on atomicity fail to hold. We make use of a Petri-net based semantics for concurrent separation logic with explicit representations of the key notions of ownership and interference. A new characterization of the separation of processes is given and is shown to be stronger than existing race-freedom results for the logic. Exploiting this, sufficient criteria are then established for an operation of refinement of processes capable of changing the atomicity of assignments.

Containment in Rule-Based Models

Recently, there has been substantial interest in using rule-based modelling approaches, such as the Kappa modelling language, to attack the combinatorial intractability of many biochemical systems. These approaches have allowed several novel static analyses to be developed, which motivates broadening their expressivity. In this paper, we build upon prior work giving Kappa an SPO-rewriting semantics to add containment structure, to model the various ways in which biological mixtures are partitioned and enclosed by membranes.

Independence and concurrent separation logic

A compositional Petri net based semantics is given to a simple pointer-manipulating language. The model is then applied to give a notion of validity to the judgements made by concurrent separation logic that emphasizes the process-environment duality inherent in such rely-guarantee reasoning. Soundness of the rules of concurrent separation logic with respect to this definition of validity is shown. The independence information retained by the Petri net model is then exploited to characterize the independence of parallel processes enforced by the logic. This is shown to permit a refinement operation capable of changing the granularity of atomic actions

Non-angelic Concurrent Game Semantics.

The hiding operation, crucial in the compositional aspect of game semantics, removes computation paths not leading to observable results. Accordingly, games models are usually biased towards angelic non-determinism: diverging branches are forgotten.

Interaction and Causality in Digital Signature Exchange Protocols

Causal reasoning is a powerful tool in analysing security protocols, as seen in the popularity of the strand space model. However, for protocols that branch, more subtle models are called for to capture the ways in which they can interact with a possibly malign environment. We study a model for security protocols encompassing causal reasoning and interaction, developing a semantics for a simple security protocol language based on concurrent games played on event structures. We show how it supports causal reasoning about a protocol for secure digital signature exchange. The semantics paves the way for the application of more sophisticated forms of concurrent game, for example including symmetry and probability, to the analysis of security protocols.