Parallel parameter synthesis from hybrid logic HUCTL formulas

Samuel Pastva

advisor: Luboš Brim

Physical reality is becoming increasingly digital.

physical (continuous) components

digital (discrete) components

interactions

interactions

Cyber-physical systems

Cyber-physical systems are used at global scale in safety critical applications.

Wrong assumptions about a cyber-physical system can cost lives! (and millions of dollars)

Problem: System's behaviour can change with parameters.

Friction 

Wind speed

Traction control on/off

Turbocharger on/off

Emission avoiding on/off

Fuel efficiency

In continuous systems small (smooth) change in parameters usually produces a small change in behaviour.

Problem: Usually

Bifurcation: Big (qualitative) change of behaviour 

Behaviour patterns:

     Stability ➔ 

➔ Oscillation ➔ 

➔ Stability

HUCTL: Logic for behavioural pattern specification

Stable equilibrium

Cycle (oscillation)

Unstable equilibrium

General attractor

\textbf {bind \textrm{s}: AX \textrm{s}}
bind s: AX s\textbf {bind \textrm{s}: AX \textrm{s}}
\textbf{bind} \text{s}: \textbf{EX}\ \text{s}\ \land\ \neg\textbf{AX}\ s
binds:EX s ∧ ¬AX s\textbf{bind} \text{s}: \textbf{EX}\ \text{s}\ \land\ \neg\textbf{AX}\ s
\textbf{bind} \text{s}: \textbf{AF}\ \text{s}\ \land\ \neg\textbf{AX}\ s
binds:AF s ∧ ¬AX s\textbf{bind} \text{s}: \textbf{AF}\ \text{s}\ \land\ \neg\textbf{AX}\ s
\textbf{bind} \text{s}: \textbf{AG EF}\ \text{s}
binds:AG EF s\textbf{bind} \text{s}: \textbf{AG EF}\ \text{s}

Behavioural patterns
(HUCTL)

Parameter Synthesis

Pattern validity regions

Parameter Synthesis: given a family of systems, find the ones which satisfy given specification.

(If breaks are engaged, the car slows down.)

Semi-symbolic Parameter Synthesis Algorithm [1]

  • Explicit state space, symbolic parameters
  • Allows parallel and distributed computation
  • Parameter representation using SMT formulae
  • Works with both discrete systems and abstractions of continuous systems.

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

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

PITHYA: Parameter Investigation Tool [2]

  • Implementation with focus on dynamical systems used in systems biology.
  • Collaboration with Faculty of Sciences and Faculty of Medicine on case studies [3, 4].

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

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

[5] 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

[3] 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

Interested? Contact us at sybila.fi.muni.cz