UH Biocomputation Group - Olga Tveretinahttp://biocomputation.herts.ac.uk/2024-04-14T17:42:53+01:00Complexity of Reachability and Mortality for Low-dimensional Dynamical Systems2024-04-14T17:42:53+01:002024-04-14T17:42:53+01:00Olga Tveretinatag:biocomputation.herts.ac.uk,2024-04-14:/2024/04/14/complexity-of-reachability-and-mortality-for-low-dimensional-dynamical-systems.html<p class="first last">Olga Tveretina's Journal Club session where she will talk about "Complexity of Reachability and Mortality for Low-dimensional Dynamical Systems".</p>
<p>On this week's Journal Club session, Olga Tveretina will talk about her work in the presentation entitled "Complexity of Reachability and Mortality for Low-dimensional Dynamical Systems".</p>
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<p>Theory of dynamical systems provides a powerful framework for understanding complex
dynamics, and its applications span a wide range of fields, including biological systems.</p>
<p>The reachability problem involves determining whether a given state or configuration of a
system can be reached from another state through a sequence of transitions or actions. It
is a fundamental question in computer science and has numerous applications across various
domains. Thus, reachability analysis applied in systems biology helps to model and analyze
biological networks such as gene regulatory networks, protein interaction networks, and
metabolic pathways.</p>
<p>The mortality problem can be stated as follows: given a dynamical
system, is it the case that all trajectories of the system are mortal? The mortality
problem is relevant to the field of program termination, and it has been studied in
different contexts and in different variants.</p>
<p>In this talk, I will present my current work
on the computational complexity of reachability and mortality for specific classes of low-
dimensional dynamical systems. Areas where variations of such systems arise include, among
others, biological systems (gene regulatory networks), robotics (the configuration space
of a robotic arm), and learning algorithms (finding a low-dimensional parameterization of
high-dimensional data).</p>
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<p>Papers:</p>
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<li>M. Oliveira, Oliveira, O. Tveretina, <a class="reference external" href="https://doi.org/10.1145/3501710.3519529">"Mortality and Edge-to-Edge Reachability are Decidable on Surfaces"</a>, 2022, Hybrid Systems: Computation and Control, 1--10</li>
<li>P. Bell, S. Chen, L. Jackson, <a class="reference external" href="https://doi.org/10.1016/j.tcs.2016.09.003">"On the decidability and complexity of problems for restricted hierarchical hybrid systems"</a>, 2016, Theoretical Computer Science, 652, 47--63</li>
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<p><strong>Date:</strong> 2024/04/19 <br />
<strong>Time:</strong> 14:00 <br />
<strong>Location</strong>: C258 & online</p>
Complexity of the Reachability and Mortality Problems for Hybrid Dynamical Systems2022-03-09T10:10:59+00:002022-03-09T10:10:59+00:00Olga Tveretinatag:biocomputation.herts.ac.uk,2022-03-09:/2022/03/09/complexity-of-the-reachability-and-mortality-problems-for-hybrid-dynamical-systems.html<p class="first last">Olga Tveretina's Journal Club session where she will talk about her work on "Complexity of the Reachability and Mortality Problems for Hybrid Dynamical Systems",</p>
<p>This week on Journal Club session Olga Tveretina will talk about her work on "Complexity of the Reachability and Mortality Problems for Hybrid Dynamical Systems",</p>
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<p>The mortality problem for a given dynamical system S consists of determining
whether every trajectory of S eventually halts. The mortality problem is
relevant to the field of program termination, and it has been studied in
different contexts and in different variants. Closely related to mortality is
the reachability problem: does exist a trajectory starting at a given initial
state which evolves to reach a given final state. Both problems are undecidable
in general, and they are only decidable for a limited number of classes of
hybrid dynamical systems.</p>
<p>My recent related work includes results on decidability of mortality and
reachability for some hybrid dynamical systems on manifolds [1, 2]. The
complexity of these problems has received less attention of the community than
the fundamental issue of their decidability. Studying the computational
complexity of the algorithms for deciding reachability and mortality problems
presented in [1, 2] is one of my current research focuses.</p>
<p>In my talk I will discuss the computational complexity of reachability and
mortality for the closely related systems, so-called Restricted Hierarchical
Hybrid Systems. These models have been studied by P. Bell, Sh. Chen, and L.
Jackson [3], and they are a useful tool for exploring the complexity of such
problems for other kinds of systems.</p>
<p>While the current aims are to improve understanding the boundary between
decidable and undecidable systems and their computational complexity, it is
worth mentioning that hybrid dynamical systems on manifolds have important
practical applications. Areas where surfaces arise include among others
biological systems (modelling processes on cell membranes), robotics (the
configuration space of a robotic arm) and learning algorithms (finding a
low-dimensional parameterization of high-dimensional data).</p>
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<p>Papers:</p>
<ul class="simple">
<li>M. de Oliveira Oliveira, O. Tveretina, "Mortality and Edge-to-Edge Reachability are Decidable on Surfaces, Hybrid Systems: Computation and Control",
2022</li>
<li>A. Sandler, O. Tveretina, <a class="reference external" href="http://link.springer.com/10.1007/978-3-030-30806-3_14">"Deciding Reachability for Piecewise Constant Derivative Systems on Orientable Manifolds, Reachability Problems"</a>, 2019</li>
<li>P. Bell, Sh. Chen, and L. Jackson, <a class="reference external" href="https://linkinghub.elsevier.com/retrieve/pii/S0304397516304674">"On the Decidability and Complexity of Problems for Restricted Hierarchical Hybrid Systems"</a>, Theoretical Computer Science, 2016</li>
</ul>
<p><strong>Date:</strong> 2022/03/11 <br />
<strong>Time:</strong> 14:00 <br />
<strong>Location</strong>: online</p>