arXiv subjects

Sara Riva

Publications and source records attributed to Sara Riva.

9 recordsLinked to original sources

arXiv2026

Abstract Simulation of Reaction Networks

Reaction networks model reactions between a finite set of species. These networks can be associated with different semantics, depending on the type of analysis and the phenomena under study. The standard continuous semantics is given by a system of differential equations based on the kinetic expressions of the reactions. To simulate a network under this semantics, the full knowledge of the kinetic laws of each reaction and the initial concentrations of each species is necessary. Since in empirical settings the quantitative information about the reactions can be partially or totally unknown, the challenge is to introduce new semantics that can still be applied. In this direction, a recent approach in the state of the art concerning Reaction Networks proposes a qualitative abstraction that is too coarse to properly capture the time-course continuous behaviour. Starting from the ideas of this approach, in this paper we first introduce the causal continuous semantics for Reaction Networks to capture their continuous-time dynamics, preserving the causality hidden inside each transition. Later, we introduce the differential sign semantics to abstract in a qualitative way the behaviour of a system under the causal continuous semantics. We show that our new method, based on abstract interpretation, yields appropriate Boolean transition graphs that refine those provided by the previous approach.

cs.DM↗

arXiv2025

On solving basic equations over the semiring of functional digraphs

Endowing the set of functional graphs (FGs) with the sum (disjoint union of graphs) and product (standard direct product on graphs) operations induces on FGs a structure of a commutative semiring R. The operations on R can be naturally extended to the set of univariate polynomials R[X] over R. This paper provides a polynomial time algorithm for deciding if equations of the type AX=B have solutions when A is just a single cycle and B a set of cycles of identical size. We also prove a similar complexity result for some variants of the previous equation.

cs.DM↗

arXiv2025

Roots in the semiring of finite deterministic dynamical systems

Finite discrete-time dynamical systems (FDDS) model phenomena that evolve deterministically in discrete time. It is possible to define sum and product operations on these systems (disjoint union and direct product, respectively) giving a commutative semiring. This algebraic structure led to several works employing polynomial equations to model hypotheses on phenomena modelled using FDDS. To solve these equations, algorithms for performing the division and computing $k$-th roots are needed. In this paper, we propose two polynomial algorithms for these tasks, under the condition that the result is a connected FDDS. This ultimately leads to an efficient solution to equations of the type $AX^k=B$ for connected $X$. These results are some of the important final steps for solving more general polynomial equations on FDDS.

cs.DM↗

arXiv2024

Decomposition and factorisation of transients in Functional Graphs

Functional graphs (FGs) model the graph structures used to analyse the behaviour of functions from a discrete set to itself. In turn, such functions are used to study real complex phenomena evolving in time. As the systems involved can be quite large, it is interesting to decompose and factorise them into several subgraphs acting together. Polynomial equations over functional graphs provide a formal way to represent this decomposition and factorisation mechanism, and solving them validates or invalidates hypotheses on their decomposability. The current solution method breaks down a single equation into a series of basic equations of the form AxX = B (with A, X, and B being FGs) to identify the possible solutions. However, it is able to consider just FGs made of cycles only. This work proposes an algorithm for solving these basic equations for general connected FGs. By exploiting a connection with the cancellation problem, we prove that the upper bound to the number of solutions is closely related to the size of the cycle in the coefficient A of the equation. The cancellation problem is also involved in the main algorithms provided by the paper. We introduce a polynomial-time semi-decision algorithm able to provide constraints that a potential solution will have to satisfy if it exists. Then, exploiting the ideas introduced in the first algorithm, we introduce a second exponential-time algorithm capable of finding all solutions by integrating several 'hacks' that try to keep the exponential as tight as possible.

math.DS↗

arXiv2024

Bringing memory to Boolean networks: a unifying framework

Boolean networks are extensively applied as models of complex dynamical systems, aiming at capturing essential features related to causality and synchronicity of the state changes of components along time. Dynamics of Boolean networks result from the application of their Boolean map according to a so-called update mode, specifying the possible transitions between network configurations. In this paper, we explore update modes that possess a memory on past configurations, and provide a generic framework to define them. We show that recently introduced modes such as the most permissive and interval modes can be naturally expressed in this framework, and we propose novel update modes, the history-based, trapping, and subcube-based modes. Building on the unified definitions, we provide a comprehensive comparison of memory-based update modes, resulting in their hierarchy by simulation and weak simulation. Finally, we highlight consequences of introducing memory on the notions of trajectory and attractors.

cs.LO↗

arXiv2023

Tackling Universal Properties of Minimal Trap Spaces of Boolean Networks

Minimal trap spaces (MTSs) capture subspaces in which the Boolean dynamics is trapped, whatever the update mode. They correspond to the attractors of the most permissive mode. Due to their versatility, the computation of MTSs has recently gained traction, essentially by focusing on their enumeration. In this paper, we address the logical reasoning on universal properties of MTSs in the scope of two problems: the reprogramming of Boolean networks for identifying the permanent freeze of Boolean variables that enforce a given property on all the MTSs, and the synthesis of Boolean networks from universal properties on their MTSs. Both problems reduce to solving the satisfiability of quantified propositional logic formula with 3 levels of quantifiers ($\exists\forall\exists$). In this paper, we introduce a Counter-Example Guided Refinement Abstraction (CEGAR) to efficiently solve these problems by coupling the resolution of two simpler formulas. We provide a prototype relying on Answer-Set Programming for each formula and show its tractability on a wide range of Boolean models of biological networks.

cs.LO↗

arXiv2022

An Algorithmic Pipeline for Solving Equations over Discrete Dynamical Systems Modelling Hypothesis on Real Phenomena

This paper provides an algorithmic pipeline for studying the intrinsic structure of a finite discrete dynamical system (DDS) modelling an evolving phenomenon. Here, by intrinsic structure we mean, regarding the dynamics of the DDS under observation, the feature of resulting from the "cooperation" of the dynamics of two or more smaller DDS. The intrinsic structure is described by an equation over DDS which represents a hypothesis over the phenomenon under observation. The pipeline allows solving such an equation, i.e., validating the hypothesis over the phenomenon, as far the asymptotic behavior and the number of states of the DDS under observation are concerned. The results are about the soundness and completeness of the pipeline and they are obtained by exploiting the algebraic setting for DDS introduced in [10].

math.DS↗

arXiv2020

Non-maximal sensitivity to synchronism in periodic elementary cellular automata: exact asymptotic measures

In [11] and [13] the authors showed that elementary cellular automata rules 0, 3, 8, 12, 15, 28, 32, 34, 44, 51, 60, 128, 136, 140, 160, 162, 170, 200 and 204 (and their conjugation, reflection, reflected-conjugation) are not maximum sensitive to synchronism, i.e. they do not have a different dynamics for each (non-equivalent) block-sequential update schedule (defined as ordered partitions of cell positions). In this work we present exact measurements of the sensitivity to synchronism for these rules, as functions of the size. These exhibit a surprising variety of values and associated proof methods, such as the special pairs of rule 128, and the connection to the bissection of Lucas numbers of rule 8.

cs.FL↗

arXiv2019

Solving Equations on Discrete Dynamical Systems (Extended version)

Boolean automata networks, genetic regulation networks, and metabolic networks are just a few examples of biological modelling by discrete dynamical systems (DDS). A major issue in modelling is the verification of the model against the experimental data or inducing the model under uncertainties in the data. Equipping finite discrete dynamical systems with an algebraic structure of commutative semiring provides a suitable context for hypothesis verification on the dynamics of DDS. Indeed, hypothesis on the systems can be translated into polynomial equations over DDS. Solutions to these equations provide the validation to the initial hypothesis. Unfortunately, finding solutions to general equations over DDS is undecidable. In this article, we want to push the envelope further by proposing a practical approach for some decidable cases in a suitable configuration that we call the Hypothesis Checking. We demonstrate that for many decidable equations all boils down to a "simpler" equation. However, the problem is not to decide if the simple equation has a solution, but to enumerate all the solutions in order to verify the hypothesis on the real and undecidable systems. We evaluate experimentally our approach and show that it has good scalability properties.

math.DS↗