Digital Bifurcation Analysis

Student: Samuel Pastva

Supervisor: Luboš Brim

Mgr. in Informatics with honours, Parallel and Distributed Systems specialisation

Samuel Pastva

Member of the Sybila (systems biology) laboratory since 2015

co-author of 10 international publications

Google Scholar h-index 4

Luboš Brim

Google Scholar h-index 31

Active in the area of formal verification since 1980

Founder and head of Sybila since 2009

David Šafránek

Google Scholar h-index 12

Coordinator of The National Infrastructure for Systems Biology and CyanoTeam group

GAČR project: Techniques for analysis of complex dynamical systems

Bifurcation analysis is a well studied problem in continuous dynamical systems.

Physical reality is becoming increasingly digital.

Digital systems also exhibit bifurcation*

Local stability and Hopf bifurcation analysis of a Rate Control Protocol with two delays

Abuthahir and Gaurav Raina, 2015

*

Bifurcation: A smooth parameter change leads to a qualitative change in behaviour.

To design safe and robust digital systems, we need to understand their behaviour with respect to parameters.

  • Define bifurcation in terms of appropriate qualitative behavioural equivalence.
  • Study techniques for expressing behavioural patterns.
  • Design techniques and algorithms for computing digital bifurcation analysis.
  • Evaluate these techniques using a suitable implementation.

Research question:

What is bifurcation in digital reactive systems?

Qualitative equivalence of reactive systems

  • Topological vs. simulation perspective (bisimulation, etc.)
  • Continuity on parameter space

Behavioural patterns

  • Temporal logics with hybrid operators

Algorithms based on formal verification

  • Model checking
  • Abstraction, state-space reduction, parallel computation

Evaluation (case studies)

  • Abstractions of continuous systems (ODE)
  • Discrete models (Boolean Networks, TLA+)
  • Hybrid systems

Preliminary results:

In [1] and [2], we have shown that temporal logics with parameter synthesis can be used to detect behavioural patterns.

[1] High-performance discrete bifurcation analysis for piecewise-affine dynamical systems

L. Brim, M. Demko, S. Pastva, D. Šafránek, HSB 2015

[2] A Model Checking Approach to Discrete Bifurcation Analysis

N. Beneš, L. Brim, M. Demko, S. Pastva, D. Šafránek, FM 2016

In [3] and [4], we have introduced a semi-symbolic parameter synthesis technique and a tool PITHYA.

Preliminary results:

[3] Parallel SMT-based parameter synthesis with application to piecewise multi-affine systems

N. Beneš, L. Brim, M. Demko, S. Pastva, D. Šafránek, ATVA 2015

[4] Pithya: A Parallel Tool for Parameter Synthesis of Piecewise Multi-affine Dynamical Systems

N. Beneš, L. Brim, M. Demko, S. Pastva, D. Šafránek, CAV 2017

In [5] and [6], we present case studies of aforementioned techniques based on collaboration with Faculty of Science and Faculty of Medicine.

Preliminary results:

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

M. Demko, N. Beneš, L. Brim, S. Pastva, D. Šafránek, CMSB 2016

[6] Toward Modelling and Analysis of Transient and Sustained Behaviour of Signalling Pathways

M. Hajnal, D. Šafránek, M. Demko, S. Pastva, P. Krejčí, L. Brim, HSB 2016