CMS Special Colloquium with Peter Gacs
Before coming to BU, Peter studied in Budapest, worked at the Hungarian Academy of Science with trips to Moscow, obtained a PhD in Frankfurt, did postdoc work at Stanford, and taught in Rochester. Professor Gacs has worked on problems derived from information theory (classical, and algorithmic) and reliable computation. With Ahlswede and Körner wrote some of the earliest papers of multi-user information theory. In algorithmic information theory (Kolmogorov complexity), Gacs also had some part in developing the fundamental results (earlier with Levin, later with Vitányi and others). In reliable computation, his main contributions are to the probabilistic cellular automaton model: in some sense the most natural one, but mathematically difficult. He has been the principal investigator of several NSF grants, and is an external member of the Hungarian Academy of Sciences.
We consider a computation model that is like a 1-tape Turing machine. It has an
internal state (from a fixed finite set), and a head scanning a tape with cells
having content from some finite alphabet. In each step the head can move at
most one step, and the state and the content of the scanned cell can change.
This change is dictated by a fixed transition function in most cases. But in
difference from a standard Turing machine, with some small probability and
independently in each time step, the change can be something else (it still must
be local!).
The result (joint work with Ilir Çapuni) is that there is a machine of this kind that,
that for some positive noise bound, performs arbitrarily large computations.
(We will spell out the precise input-output conventions.)
The construction and the proof are complex, similar to the hierarchical one used
for reliable cellular automata, but we don't know of any easy reduction from one
result to the other.
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