Toghrul is a PhD Student at the MPI-SWS since 2019, working with Joël Ouaknine. Before that, he completed his undergraduate studies at Oxford University.

SWS   Info

AG Audience

English

60 Minutes

Saarbrücken

Linear dynamical systems (LDS) are mathematical models widely used in engineering and science to describe systems that evolve over time. In this thesis, we study algorithms for various decision problems of discrete-time linear dynamical systems. Our main focus is the Model-Checking Problem, which is to decide, given a linear dynamical system and an ω-regular specification, whether the trajectory of the LDS satisfies the specification. Using tools from various mathematical disciplines, most notably algebraic number theory, Diophantine approximation, automata theory, and combinatorics on words, we prove decidability of the Model-Checking Problem for large classes of linear dynamical systems and ω regular properties. We further exploit deep connections between linear dynamical systems and contemporary number theory to show that improving any of our decidability results would amount to major mathematical breakthroughs. Our results delineate the boundaries of decision problems of linear dynamical systems that, at the present time, can be solved algorithmically.

Lena Schneider

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