Associate Professor
Department of Computer Science
Faculty of Mathematics and Computer Science
University of Bucharest
Background
I have spent three decades building security software. In 1997 I joined SOFTWIN, where I
co-architected the antimalware engine behind AVX, rebranded as Bitdefender in 2001. I served
as Bitdefender's Chief Technology Officer from 2001 to 2024 and have been its Chief Scientist
since June 2024. I have also co-founded several software companies, some of them still
active.
I hold an MSc in Mathematics and Computer Science and a PhD in Natural Language
Processing, both from the University of Bucharest, where I have taught since 2016.
What I teach
Theory of Computation(Limbaje Formale și Automate)
— year 1, BSc. Automata, grammars, and the languages they recognise.
Complexity Theory(Calculabilitate și Complexitate)
— year 3, BSc. Computability, tractability, and the complexity classes in between.
Computational Foundations of Transformers
— year 2, MSc in Natural Language Processing. Starts from computation graphs and
reverse-mode autodiff and builds up to a working decoder-only transformer.
In preparation: Quantum Computation: models, algorithms, and complexity,
an elective for final-year BSc and MSc students. It follows Aaronson and de Wolf in
treating quantum computation as a model of computation, so the course is about circuits,
algorithms and complexity classes rather than hardware or physics.
Research interests
My work is in combinatorics, done computationally. The problems are varied:
Ramsey-type questions, combinatorial geometry, graph labelings, combinatorial designs, and
now and then something from number theory or social choice. The method is the same each
time. I encode an open question so that a machine can search it, run the search as far as
the hardware allows, and try to turn what comes back into a proof. The tools are usually
SAT solvers, GPU search, exhaustive generation with structural reductions, and exact
rational arithmetic. Outside combinatorics, I keep returning to the separating words
problem.
I collaborate with undergraduates on hard problems, on our own time, outside the faculty
programme. Some of them start in their first year. I look for questions that are difficult but
have a computational way in, where someone can start writing code right away and get to real
mathematics fast. The aim is a paper with their name on it, not a report.
Work
2026
Alternating Extremes in
Graceful Labelings of Full Binary Trees and Spider Trees— with Mihai Nacu.
A pinned form of graceful labeling: can a deepest root-to-leaf path of a full binary tree
carry the alternating extreme pattern 0, n−1, 1, n−2, …? We prove this for comb full binary
trees and verify it computationally through order 23. For spider trees we prove a packing
theorem for self-matched legs, which yields graceful labelings for mixed-length spiders with
enough leaves.
Notes on Costas Array Search and Local
Signature Transport— with Cristian Budala. Manuscript.
The paper covers an order-28 search using prefix decomposition, symmetry reduction and
forward checking, and a CUDA split-and-conquer implementation for order 30 whose throughput
projects to 7.97 single-GPU years for a full search. Local difference patterns from smaller
arrays, used to restrict larger searches, returned 5,512 valid arrays across 63 order
pairs.
In progress
Numerical verification of the Erdős–Gyárfás conjecture — whether every finite
graph with minimum degree at least three contains a cycle whose length is a power of two.
I have been working on this on and off for three years. A note advancing the verification
on three fronts (general, bipartite and cubic graphs) is in preparation.
Condorcet probabilities under Impartial Anonymous Culture —
exact values are known through five candidates; six was out of reach because of the
dimension. Work on the six-candidate case is in preparation.
The 33-point Erdős–Szekeres problem — continuing from
the 2025 note below. A second version is in
preparation, with improved encodings aimed at the runtime variability that dominated the
first round. The results so far are good, but still partial.
No three in line — with the student group, searching for a new
solution at n = 72, possibly 74.
Ramsey numbers — R(5,5) is a problem I have been returning to
for years. I have partial results and intend to write them up.
2025
Notes on the Finiteness of
Powers of Two with All Even Digits
Which powers of two have only even decimal digits? Only n = 1, 2, 3, 6 and 11 are known, and
a search to 1015 turns up no others. A dynamical Borel–Cantelli argument shows the
set of initial phases generating infinitely many such powers has Lebesgue measure zero. That
is evidence for finiteness, not a proof.
A Sharper Upper Bound for the
Separating Words Problem
I posted an upper bound of O(log² n) states and then withdrew it — the proof of Theorem 1 had
an error, and the corrected argument does not improve on known bounds. This is the problem I
expect to keep working on for a long time.
Two-colorings of finite grids:
variations on a theorem of Tibor Gallai— with Mihai Prunescu.
Gallai's theorem guarantees a threshold beyond which no colouring of a grid can avoid a
monochromatic homothetic copy of a given finite set, but it is non-effective. We find or
confirm that threshold for triangles, squares and rectangles, and extend the question from
homothety to general similarity. Solved with SAT and symmetry breaking, with new lower
bounds for hexagons on the triangular lattice and cubes in Z³.
Notes on the 33-point
Erdős–Szekeres problem
ES(7) is the first open case of the planar Erdős–Szekeres problem, with the conjecture
predicting ES(7) = 33. A SAT encoding built on triple-orientation variables, a 4-set convexity
criterion and convex-layer anchoring, yielding UNSAT certificates for a collection of anchored
subfamilies. Runtime variability is heavy-tailed and currently dominates the effort.
