Samuel Pastva

Parameter Synthesis by Parallel Coloured CTL Model Checking

We propose a new distributed-memory parallel algorithm for parameter synthesis from CTL hypotheses. The algorithm colours the state space transitions by different parameterisations and extends CTL model checking to identify the maximal set of parameters that guarantee the satisfaction of the given CTL property. We experimentally confirm good scalability of our approach and demonstrate its applicability in the case study of a genetic switch controlling decisions in the cell cycle.

High-Performance Discrete Bifurcation Analysis for Piecewise-Affine Dynamical Systems

Analysis of equilibria, their stability and instability, is an unavoidable ingredient of model analysis in systems biology. In particular, bifurcation analysis which focuses on behaviour of phase portraits under variations of parameters is of great importance. We propose a novel method for bifurcation analysis that employs coloured model checking to analyse phase portraits bifurcation in rectangular abstractions of piecewise-affine systems. The algorithm works on clusters of workstations and multi-core computers to allow scalability. We demonstrate the method on a repressilator genetic regulatory network.

Extended dependency graphs and efficient distributed fixed-point computation

Equivalence and model checking problems can be encoded into computing fixed points on dependency graphs. Dependency graphs represent causal dependencies among the nodes of the graph by means of hyper-edges. We suggest to extend the model of dependency graphs with so-called negation edges in order to increase their applicability. The graphs (as well as the verification problems) suffer from the state space explosion problem. To combat this issue, we design an on-the-fly algorithm for efficiently computing fixed points on extended dependency graphs. Our algorithm supplements previous approaches with the possibility to back-propagate, in certain scenarios, the domain value 0, in addition to the standard back-propagation of the value 1. Finally, we design a distributed version of the algorithm, implement it in an open-source tool, and demonstrate the efficiency of our general approach on the benchmark of Petri net models and CTL queries from the Model Checking Contest 2016.

Parallel SMT-Based Parameter Synthesis with Application to Piecewise Multi-affine Systems

We propose a novel scalable parallel algorithm for synthesis of interdependent parameters from CTL specifications for non-linear dynamical systems. The method employs a symbolic representation of sets of parameter valuations in terms of the first-order theory of the reals. To demonstrate its practicability, we apply the method to a class of piecewise multi-affine dynamical systems representing dynamics of biological systems with complex non-linear behaviour.

A Model Checking Approach to Discrete Bifurcation Analysis

Bifurcation analysis is a central task of the analysis of parameterised high-dimensional dynamical systems that undergo transitions as parameters are changed. The classical numerical and analytical methods are typically limited to a small number of system parameters. In this paper we propose a novel approach to bifurcation analysis that is based on a suitable discrete abstraction of the system and employs model checking for discovering critical parameter values, referred to as bifurcation points, for which various kinds of behaviour (equilibrium, cycling) appear or disappear. To describe such behaviour patterns, called phase portraits, we use a hybrid version of a CTL logic augmented with direction formulae. We demonstrate the method on a case study taken from systems biology.

High-Performance Symbolic Parameter Synthesis of Biological Models: A Case Study

Complex behaviour arising in biological systems is described by highly parameterised dynamical models. Most of the parameters are mutually dependent and therefore it is hard and computationally demanding to find admissible parameter values with respect to hypothesised constraints and wet-lab measurements. Recently, we have developed several high-performance techniques for parameter synthesis that are based on parallel coloured model checking. These methods allow to obtain parameter values that guarantee satisfaction of a given set of dynamical properties and parameter constraints. In this paper, we review the applicability of our techniques in the context of biological systems. In particular, we provide an extended analysis of a genetic switch controlling the regulation in mammalian cell cycle phase transition and a synthetic pathway for biodegradation of a toxic pollutant in E. coli.

Toward Modelling and Analysis of Transient and Sustained Behaviour of Signalling Pathways

Signalling pathways provide a complex cellular information processing machinery that evaluates particular input stimuli and transfers them into the genome by means of regulation of specific genes expression. In this short paper, we provide a preliminary study targeting minimal models representing the topology of main signalling mechanisms. A special emphasis is given to distinguishing between monotonous (sustained) and non-monotonous (transient) time-course behaviour. A set of minimal parametrised ODE models is formulated and analysed in a workflow based on formal methods.

Pithya: A Parallel Tool for Parameter Synthesis of Piecewise Multi-Affine Dynamical Systems

We present a novel tool for parameter synthesis of piecewise multi-affine dynamical systems from specifications expressed in a hybrid branching-time temporal logic. The tool is based on the algorithm of parallel semi-symbolic coloured model checking that extends standard model checking methods to cope with parametrised Kripke structures. The tool implements state-of-the-art techniques developed in our previous research and is primarily intended to be used for the analysis of dynamical systems with uncertain parameters that frequently arise in computational systems biology. However, it can be employed for any dynamical system where the non-linear equations can be sufficiently well approximated by piecewise multi-affine equations.

Detecting Attractors in Biological Models with Uncertain Parameters

Complex behaviour arising in biological systems is typically characterised by various kinds of attractors. An important problem in this area is to determine these attractors. Biological systems are usually described by highly parametrised dynamical models that can be represented as parametrised graphs typically constructed as discrete abstractions of continuous-time models. In such models, attractors are observed in the form of terminal strongly connected components (tSCCs). In this paper, we introduce a novel method for detecting tSCCs in parametrised graphs. The method is supplied with a parallel algorithm and evaluated on discrete abstractions of several non-linear biological models.