Jarkko Kari A N Kirillov and Tero Laihonen at University of Turku 20190404

Jarkko J. Kari is a

Finnish Finnish may refer to: * Something or someone from, or related to Finland * Culture of Finland * Finnish people or Finns, the primary ethnic group in Finland * Finnish language, the national language of the Finnish people * Finnish cuisine See also ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

and

computer scientist A computer scientist is a person who is trained in the academic study of computer science. Computer scientists typically work on the theoretical side of computation, as opposed to the hardware side on which computer engineers mainly focus (al ...

, known for his contributions to the theory of

Wang tile Wang tiles (or Wang dominoes), first proposed by mathematician, logician, and philosopher Hao Wang in 1961, are a class of formal systems. They are modelled visually by square tiles with a color on each side. A set of such tiles is selected, an ...

s and

cellular automata A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessel ...

. Kari is currently a professor at the Department of Mathematics,

University of Turku sv, Åbo universitet , latin_name = Universitas Aboensis , image_name = University of Turku.svg , motto = ''Vapaan kansan lahja vapaalle tieteelle'' , established = 1920 , type ...

Biography

Kari received his Ph.D. in 1990 from the University of Turku; his dissertation, supervised by

Arto Salomaa Arto K. Salomaa (born 6 June 1934) is a Finnish mathematician and computer scientist. His research career, which spans over forty years, is focused on formal languages and automata theory. Early life and education Salomaa was born in Turku, Finl ...

. He married

Lila Kari Lila Kari (née Sântean) is a Romanian and Canadian computer scientist, professor in the David R. Cheriton School of Computer Science at the University of Waterloo, Canada. Biography Professor Kari earned a master's degree at the University of ...

, a later mathematics student at Turku; they divorced, and afterwards Lila Kari became a professor of

computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...

at the

University of Western Ontario The University of Western Ontario (UWO), also known as Western University or Western, is a Public university, public research university in London, Ontario, London, Ontario, Canada. The main campus is located on of land, surrounded by resident ...

Canada Canada is a country in North America. Its ten provinces and three territories extend from the Atlantic Ocean to the Pacific Ocean and northward into the Arctic Ocean, covering over , making it the world's second-largest country by tot ...

Research

s are

unit square In mathematics, a unit square is a square whose sides have length . Often, ''the'' unit square refers specifically to the square in the Cartesian plane with corners at the four points ), , , and . Cartesian coordinates In a Cartesian coordinate ...

s with colored markings on each side; they may be used to

tesselate A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of ge ...

the plane, but only with tiles that have matching colors on adjoining edges. The problem of determining whether a set of Wang tiles forms a valid tessellation is undecidable, and its undecidability rests on finding sets of Wang tiles that can only tesselate the plane aperiodically, in such a way that no translation of the plane is a symmetry of the tiling. The first set of aperiodic Wang tiles found, by Robert Berger, had over 20,000 different tiles in it. Kari reduced the size of this set to only 14, by finding a set of tiles that (when used to tile the plane) simulates the construction of a

Beatty sequence In mathematics, a Beatty sequence (or homogeneous Beatty sequence) is the sequence of integers found by taking the floor of the positive multiples of a positive irrational number. Beatty sequences are named after Samuel Beatty, who wrote about th ...

Mealy machine In the theory of computation, a Mealy machine is a finite-state machine whose output values are determined both by its current state and the current inputs. This is in contrast to a Moore machine, whose output values are determined solely by its cu ...

s. The same approach was later shown to lead to aperiodic sets of 13 tiles, the minimum known. Kari has also shown that the Wang tiling problem remains undecidable in the

hyperbolic plane In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai– Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: :For any given line ''R'' and point ''P'' ...

, and has discovered sets of Wang tiles with additional mathematical properties. Kari has also used the Wang tiling problem as the basis of proofs that several algorithmic problems in the theory of

are undecidable. In particular, in his thesis research, he showed that it is undecidable to determine whether a given cellular automaton rule in two or more dimensions is reversible. For one-dimensional cellular automata, reversibility is known to be decidable, and Kari has provided tight bounds on the size of the neighborhood needed to simulate the reverse dynamics of reversible one-dimensional automata..

References

External links

Jarkko Kari's personal homepage
Cellular automatists Finnish computer scientists Finnish mathematicians Living people Year of birth missing (living people) Vaisala Prize Laureates {{europe-mathematician-stub