On Expressing and Monitoring Oscillatory Dynamics

  title={On Expressing and Monitoring Oscillatory Dynamics},
  author={Petr Dluhos and Lubo{\vs} Brim and David {\vS}afr{\'a}nek},
To express temporal properties of dense-time real-valued signals, the Signal Temporal Logic (STL) has been defined by Maler et al. The work presented a monitoring algorithm deciding the satisfiability of STL formulae on finite discrete samples of continuous signals. The logic has been used to express and analyse biological systems, but it is not expressive enough to sufficiently distinguish oscillatory properties important in biology. In this paper we define the extended logic STL* in which STL… 

Mixed-Time Signal Temporal Logic

STL-mx has the expressive power of STL supplemented with an implicit T-periodic clock signal, and an algorithm for monitoring STL-mx formulas is developed and implemented, illustrating the approach using a mixed-signal example.

Monitoring and Measuring Hybrid Behaviors A Tutorial

This tutorial provides an overview of methods for checking whether a hybrid behavior is correct and robust with respect to its specification; and measuring of quantitative characteristics of a hybrid system by property-driven extraction of relevant data from its behaviors.

Spatio-temporal logic for the analysis of biochemical models

A spatio-temporal logic, the Logic of Behaviour in Context (LBC), is developed for the analysis of biochemical models and it is shown that a number of interesting and useful properties can be expressed in LBC and that it is possible to express highly useful properties of real models in the biochemistry domain, with practical application.

Robustness Analysis for Value-Freezing Signal Temporal Logic

This paper defines robustness Measures for STL* by adapting the robustness measures previously introduced for Metric Temporal Logic (MTL), and presents an algorithm for STL*, robustness computation, which is implemented in the tool Parasim.

Analysis of a Post-translational Oscillator Using Process Algebra and Spatio-Temporal Logic

This work describes the modelling of a post-translational oscillator using a process algebra and the specification of complex properties of its dynamics using a spatio-temporal logic, and shows that the theoretical model behaves in a manner in keeping with known properties of biological circadian oscillators.

Falsifying Oscillation Properties of Parametric Biological Models

This work proposes an approach to falsification of oscillation properties of parametric biological models, based on the recently developed techniques for testing continuous and hybrid systems, which can be specified using a hybrid automaton.

Abnormal Data Classification Using Time-Frequency Temporal Logic

A technique to investigate abnormal behaviors of signals in both time and frequency domains using an extension of time-frequency logic that uses the continuous wavelet transform and a parameter synthesis approach that can be used to classify hunting behavior are presented.

Formal Methods for Dynamical Systems

Preface. This volume presents a set of papers accompanying the lectures of the 13th International School on Formal Methods for the Design of Computer, Communication, and Software Systems (SFM). This

Timed Pattern Matching

The set of all matches of a timed regular expression by a signal of finite variability and duration can be written as a finite union of zones.



Monitoring Temporal Properties of Continuous Signals

A variant of temporal logic tailored for specifying desired properties of continuous signals, based on a bounded subset of the real-time logic mitl, augmented with a static mapping from continuous domains into propositions is introduced.

Robust Satisfaction of Temporal Logic over Real-Valued Signals

We consider temporal logic formulae specifying constraints in continuous time and space on the behaviors of continuous and hybrid dynamical system admitting uncertain parameters. We present several

On Temporal Logic and Signal Processing

Time-Frequency Logic is a new specification formalism for real-valued signals that combines temporal logic properties in the time domain with frequency-domain properties and is a contribution to a unified systems theory for hybrid systems.

On a Continuous Degree of Satisfaction of Temporal Logic Formulae with Applications to Systems Biology

This article defines a continuous degree of satisfaction of a temporal logic formula with constraints and shows how such a satisfaction measure can be used as a fitness function with state-of-the-art search methods in order to find biochemical kinetic parameter values satisfying a set of biological properties formalized in temporal logic.

AMT: A Property-Based Monitoring Tool for Analog Systems

STL/PSL, a specification formalism based on the industrial standard language PSL and the real-time temporal logic MITL, extended with constructs that allow describing behaviors of real-valued variables is introduced.

Machine Learning Biochemical Networks from Temporal Logic Properties

This paper describes two algorithms for inferring reaction rules and kinetic parameter values from a temporal specification formalizing the biological data and illustrates how these machine learning techniques may be useful to the modeler.

High-performance analysis of biological systems dynamics with the DiVinE model checker

In this review, a brief description of the tool DiVinE adapted for automatized analysis of biological systems dynamics is provided, which employs high-performance computing techniques to enable analysis of large models.

Detecting synchronisation of biological oscillators by model checking