Rate Equations for Graphs

In this paper, we combine ideas from two different scientific traditions: 1) graph transformation systems (GTSs) stemming from the theory of formal languages and concurrency, and 2) mean field approximations (MFAs), a collection of approximation techniques ubiquitous in the study of complex dynamics. Using existing tools from algebraic graph rewriting, as well as new ones, we build a framework which generates rate equations for stochastic GTSs and from which one can derive MFAs of any order (no longer limited to the humanly computable). The procedure for deriving rate equations and their approximations can be automated. An implementation and example models are available online at https://rhz.github.io/fragger. We apply our techniques and tools to derive an expression for the mean velocity of a two-legged walker protein on DNA.Comment: to be presented at the 18th International Conference on Computational Methods in Systems Biology (CMSB 2020

CRIL: A Concurrent Reversible Intermediate Language

We present a reversible intermediate language with concurrency for translating a high-level concurrent programming language to another lower-level concurrent programming language, keeping reversibility. Intermediate languages are commonly used in compiling a source program to an object code program closer to the machine code, where an intermediate language enables behavioral analysis and optimization to be decomposed in steps. We propose CRIL (Concurrent Reversible Intermediate Language) as an extension of RIL used by Mogensen for a functional reversible language, incorporating a multi-thread process invocation and the synchronization primitives based on the P-V operations. We show that the operational semantics of CRIL enjoy the properties of reversibility, including the causal safety and causal liveness proposed by Lanese et al., checking the axiomatic properties. The operational semantics is defined by composing the bidirectional control flow with the dependency information on updating the memory, called annotation DAG. We show a simple example of `airline ticketing' to illustrate how CRIL preserves the causality for reversibility in imperative programs with concurrency.Comment: In Proceedings EXPRESS/SOS2023, arXiv:2309.0578

Static versus dynamic reversibility in CCS

The notion of reversible computing is attracting interest because of its applications in diverse fields, in particular the study of programming abstractions for fault tolerant systems. Most computational models are not naturally reversible since computation causes loss of information, and history information must be stored to enable reversibility. In the literature, two approaches to reverse the CCS process calculus exist, differing on how history information is kept. Reversible CCS (RCCS), proposed by Danos and Krivine, exploits dedicated stacks of memories attached to each thread. CCS with Keys (CCSK), proposed by Phillips and Ulidowski, makes CCS operators static so that computation does not cause information loss. In this paper we show that RCCS and CCSK are equivalent in terms of LTS isomorphism

Moment Semantics for Reversible Rule-Based Systems

International audienceWe develop a notion of stochastic rewriting over marked graphs – i.e. directed multigraphs with degree constraints. The approach is based on double-pushout (DPO) graph rewriting. Marked graphs are expressive enough to internalize the 'no-dangling-edge' condition inherent in DPO rewriting. Our main result is that the linear span of marked graph occurrence-counting functions – or motif functions – form an algebra which is closed under the infinitesimal generator of (the Markov chain associated with) any such rewriting system. This gives a general procedure to derive the moment semantics of any such rewriting system, as a countable (and recursively enumerable) system of differential equations indexed by motif functions. The differential system describes the time evolution of moments (of any order) of these motif functions under the rewriting system. We illustrate the semantics using the example of preferential attachment networks; a well-studied complex system, which meshes well with our notion of marked graph rewriting. We show how in this case our procedure obtains a finite description of all moments of degree counts for a fixed degree

Rate Equations for Graphs

International audienceIn this paper, we combine ideas from two different scientifictraditions: 1) graph transformation systems (GTSs) stemming from thetheory of formal languages and concurrency, and 2) mean field approx-imations (MFAs), a collection of approximation techniques ubiquitousin the study of complex dynamics. Using existing tools from algebraicgraph rewriting, as well as new ones, we build a framework which gener-ates rate equations for stochastic GTSs and from which one can deriveMFAs of any order (no longer limited to the humanly computable). Theprocedure for deriving rate equations and their approximations can beautomated. An implementation and example models are available onlineat https://rhz.github.io/fragger. We apply our techniques and tools toderive an expression for the mean velocity of a two-legged walker proteinon DNA

Static versus Dynamic Reversibility in CCS

International audienceThe notion of reversible computing is attracting interest because of its applications in diverse fields, in particular the study of programming abstractions for fault tolerant systems. Most computational models are not naturally reversible since computation causes loss of information, and history information must be stored to enable reversibility. In the literature, two approaches to reverse the CCS process calculus exist, differing on how history information is kept. Reversible CCS (RCCS), proposed by Danos and Krivine, exploits dedicated stacks of memories attached to each thread. CCS with Keys (CCSK), proposed by Phillips and Ulidowski, makes CCS operators static so that computation does not cause information loss. In this paper we show that RCCS and CCSK are equivalent in terms of LTS isomorphism