Continuous valuations of temporal logic specifications with applications to parameter optimization and robustness measures

International audienceFinding mathematical models satisfying a specification built from the formalization of biological experiments, is a common task of the modeler that techniques like model-checking help solving, in the qualitative but also in the quantitative case. In this article we go one step further by defining a continuous degree of satisfaction of temporal logic formulae with constraints. We show how such a satisfaction measure can be used as a fitness function with state-of-the-art evolutionary optimization methods in order to find biochemical kinetic parameter values satisfying a set of biological properties formalized in temporal logic. We also show how it can be used to define a measure of robustness of a biological model with respect to some temporal specification. These methods are evaluated on models of the cell cycle and of the MAPK signalling cascade

Formal Verification of Safety Critical Autonomous Systems via Bayesian Optimization

As control systems become increasingly more complex, there exists a pressing need to find systematic ways of verifying them. To address this concern, there has been significant work in developing test generation schemes for black-box control architectures. These schemes test a black-box control architecture's ability to satisfy its control objectives, when these objectives are expressed as operational specifications through temporal logic formulae. Our work extends these prior, model based results by lower bounding the probability by which the black-box system will satisfy its operational specification, when subject to a pre-specified set of environmental phenomena. We do so by systematically generating tests to minimize a Lipschitz continuous robustness measure for the operational specification. We demonstrate our method with experimental results, wherein we show that our framework can reasonably lower bound the probability of specification satisfaction

Formal methods paradigms for estimation and machine learning in dynamical systems

Formal methods are widely used in engineering to determine whether a system exhibits a certain property (verification) or to design controllers that are guaranteed to drive the system to achieve a certain property (synthesis). Most existing techniques require a large amount of accurate information about the system in order to be successful. The methods presented in this work can operate with significantly less prior information. In the domain of formal synthesis for robotics, the assumptions of perfect sensing and perfect knowledge of system dynamics are unrealistic. To address this issue, we present control algorithms that use active estimation and reinforcement learning to mitigate the effects of uncertainty. In the domain of cyber-physical system analysis, we relax the assumption that the system model is known and identify system properties automatically from execution data. First, we address the problem of planning the path of a robot under temporal logic constraints (e.g. "avoid obstacles and periodically visit a recharging station") while simultaneously minimizing the uncertainty about the state of an unknown feature of the environment (e.g. locations of fires after a natural disaster). We present synthesis algorithms and evaluate them via simulation and experiments with aerial robots. Second, we develop a new specification language for tasks that require gathering information about and interacting with a partially observable environment, e.g. "Maintain localization error below a certain level while also avoiding obstacles.'' Third, we consider learning temporal logic properties of a dynamical system from a finite set of system outputs. For example, given maritime surveillance data we wish to find the specification that corresponds only to those vessels that are deemed law-abiding. Algorithms for performing off-line supervised and unsupervised learning and on-line supervised learning are presented. Finally, we consider the case in which we want to steer a system with unknown dynamics to satisfy a given temporal logic specification. We present a novel reinforcement learning paradigm to solve this problem. Our procedure gives "partial credit'' for executions that almost satisfy the specification, which can lead to faster convergence rates and produce better solutions when the specification is not satisfiable

Mapping behavioral specifications to model parameters in synthetic biology

With recent improvements of protocols for the assembly of transcriptional parts, synthetic biological devices can now more reliably be assembled according to a given design. The standardization of parts open up the way for in silico design tools that improve the construct and optimize devices with respect to given formal design specifications. The simplest such optimization is the selection of kinetic parameters and protein abundances such that the specified design constraints are robustly satisfied. In this work we address the problem of determining parameter values that fulfill specifications expressed in terms of a functional on the trajectories of a dynamical model. We solve this inverse problem by linearizing the forward operator that maps parameter sets to specifications, and then inverting it locally. This approach has two advantages over brute-force random sampling. First, the linearization approach allows us to map back intervals instead of points and second, every obtained value in the parameter region is satisfying the specifications by construction. The method is general and can hence be incorporated in a pipeline for the rational forward design of arbitrary devices in synthetic biology

Mapping behavioral specifications to model parameters in synthetic biology

With recent improvements of protocols for the assembly of transcriptional parts, synthetic biological devices can now more reliably be assembled according to a given design. The standardization of parts open up the way for in silico design tools that improve the construct and optimize devices with respect to given formal design specifications. The simplest such optimization is the selection of kinetic parameters and protein abundances such that the specified design constraints are robustly satisfied. In this work we address the problem of determining parameter values that fulfill specifications expressed in terms of a functional on the trajectories of a dynamical model. We solve this inverse problem by linearizing the forward operator that maps parameter sets to specifications, and then inverting it locally. This approach has two advantages over brute-force random sampling. First, the linearization approach allows us to map back intervals instead of points and second, every obtained value in the parameter region is satisfying the specifications by construction. The method is general and can hence be incorporated in a pipeline for the rational forward design of arbitrary devices in synthetic biology

Robustness Analysis for Value-Freezing Signal Temporal Logic

In our previous work we have introduced the logic STL*, an extension of Signal Temporal Logic (STL) that allows value freezing. In this paper, we define robustness measures for STL* by adapting the robustness measures previously introduced for Metric Temporal Logic (MTL). Furthermore, we present an algorithm for STL* robustness computation, which is implemented in the tool Parasim. Application of STL* robustness analysis is demonstrated on case studies.Comment: In Proceedings HSB 2013, arXiv:1308.572