Jarkko Kari achieved a significant reduction in the complexity of aperiodic Wang tile sets, trimming the required number from over 20,000 to just 14. This work centers on unit squares with colored edges used to tessellate planes, a challenge where determining the validity of the tiling is proven to be computationally undecidable.
Academic Foundation
Born in Lahti, Finland, in 1964, Kari pursued his higher education at the University of Turku. He completed his foundational studies in 1986 and went on to earn his Doctor of Philosophy in 1990. His doctoral research was supervised by Arto Salomaa, establishing an academic trajectory within the Department of Mathematics at the University of Turku, where he currently serves as a professor.
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Kari focuses on the theoretical properties of Wang tiles, which require matching edge colors for valid plane tessellation. By utilizing Mealy machines to simulate Beatty sequences, he demonstrated that aperiodic sets could be constructed with significantly fewer tiles than previously established by Robert Berger. His investigations extend into the hyperbolic plane, where he verified the persistence of undecidability in these tiling problems.
Cellular Automata Contributions
Beyond tiling, his work addresses algorithmic problems within the theory of cellular automata. Kari established that determining the reversibility of a cellular automaton rule remains undecidable for systems in two or more dimensions. For one-dimensional systems, he identified tight bounds regarding the neighborhood size required to simulate the reverse dynamics of these machines.
Professional Recognition
His sustained contributions to applied mathematics and computer science were acknowledged in 2006 when he received the Väisälä Prize. He remains active in his field, continuing his professional commitments at the University of Turku in Finland.
Fast facts
- Born: 1964, Lahti, Finland
- Citizenship: Finland
- Current Occupation: Professor, University of Turku
- Doctoral Year: 1990, University of Turku
- Award: Väisälä Prize (2006)
- Primary Fields: Applied Mathematics, Computer Science
Questions readers ask
What specific improvement did Jarkko Kari make to Wang tile sets?
He reduced the required number of tiles for an aperiodic set from over 20,000 to 14.
Is the reversibility of cellular automata decidable?
It is decidable for one-dimensional cellular automata, but Kari proved it is undecidable for systems in two or more dimensions.
Achievements
- Väisälä Prize — 2006
- Held posts at University of Turku
