Yuri Matiyasevich is Head of the Laboratory of Mathematical Logic, Steklov Institute of Mathematics, Russian Academy of Sciences, Saint Petersburg.At the 1900 International Congress of Mathematicians, held that year in Paris, the German mathematician David Hilbert put forth a list of 23 unsolved problems that he saw as being the greatest challenges for twentieth-century mathematics.Expand

We prove decidability results for fragments of monadic simultaneous rigid E-unification and show the connections between this notion and some algorithmic problems of logic and computer science.Expand

We show that the accessibility problem, common descendant problem, the termination problem and the uniform termination problem are undecidable for 3-rules semi-Thue systems.Expand

For several decision problems about semi-Thue systems, we try to locate the frontier between the decidable and the undecidable from the point of view of the number of rules.Expand

The notion of word, considered as an element of a free monoid, has been long ago generalized to the notion of a trace, an elements of a partially commutative monoId.Expand

We are searching for subsequences in a text which is compressed using Lempel-Ziv-like compression algorithms, without decompressing the text, and we would like our algorithms to be almost optimal.Expand

We generalize the Knuth–Morris–Pratt (KMP) pattern matching algorithm; we define a non-conventional kind of RAM, the MP-RAMs which model more closely the microprocessor operations.Expand

We give another proof that the question whether an equation over a trace monoid has a solution or not is decidable using lexicographical normal forms.Expand