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Researcher profile

Udi Boker

Udi Boker contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Formal Languages and Automata TheoryLogic in Computer ScienceMachine Learning

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Published work

5 published item(s)

preprint2026arXiv

Woodelf++: A Fast and Unified Partial Dependence Plot Algorithm for Decision Tree Ensembles

Partial Dependence Plots (PDPs) visualize how changes in a single feature affect the average model prediction. They are widely used in practice to interpret decision tree ensembles and other machine learning models. Joint-PDPs extend this idea to pairs of features, revealing their combined effect. Partial Dependence Interaction Values (PDIVs) measure feature interactions. The Any-Order-PDIVs task computes these interactions for every feature subset across all rows of the dataset. We introduce Woodelf++, a unified and efficient approach for computing all these useful explainability tools on decision tree ensembles, building on Woodelf, an algorithm for efficient SHAP computation. By deriving suitable metrics over pseudo-Boolean functions, Woodelf++ can compute PDPs (exact and approximate), Joint-PDPs, and Any-Order-PDIVs in a unified framework. Our method delivers substantial complexity improvements over the state of the art, including an exponential gain for Any-Order-PDIVs. Additionally, we introduce and efficiently compute Full PDPs, which leverage the model's split thresholds to faithfully capture its behavior across all possible feature values. Woodelf++ is implemented in pure Python and supports GPU acceleration. On a dataset with 400,000 rows, Woodelf++ computes PDP and Joint-PDP up to 6x faster than the state of the art and up to five orders of magnitude faster than scikit-learn. For Any-Order-PDIVs, the gap is even larger: Woodelf++ computes all interaction values in 5 minutes, while the state of the art is estimated to require over 1,000,000 years.

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preprint2022arXiv

On the Translation of Automata to Linear Temporal Logic

While the complexity of translating future linear temporal logic (LTL) into automata on infinite words is well-understood, the size increase involved in turning automata back to LTL is not. In particular, there is no known elementary bound on the complexity of translating deterministic $ω$-regular automata to LTL. Our first contribution consists of tight bounds for LTL over a unary alphabet: alternating, nondeterministic and deterministic automata can be exactly exponentially, quadratically and linearly more succinct, respectively, than any equivalent LTL formula. Our main contribution consists of a translation of general counter-free deterministic $ω$-regular automata into LTL formulas of double exponential temporal-nesting depth and triple exponential length, using an intermediate Krohn-Rhodes cascade decomposition of the automaton. To our knowledge, this is the first elementary bound on this translation. Furthermore, our translation preserves the acceptance condition of the automaton in the sense that it turns a looping, weak, Büchi, coBüchi or Muller automaton into a formula that belongs to the matching class of the syntactic future hierarchy. In particular, it can be used to translate an LTL formula recognising a safety language to a formula belonging to the safety fragment of LTL (over both finite and infinite words).

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preprint2020arXiv

On Succinctness and Recognisability of Alternating Good-for-Games Automata

We study alternating good-for-games (GFG) automata, i.e., alternating automata where both conjunctive and disjunctive choices can be resolved in an online manner, without knowledge of the suffix of the input word still to be read. We show that they can be exponentially more succinct than both their nondeterministic and universal counterparts. Furthermore, we lift many results from nondeterministic parity GFG automata to alternating ones: a single exponential determinisation procedure, an Exptime upper bound to the GFGness problem, a PTime algorithm for the GFGness problem of weak automata, and a reduction from a positive solution to the $G_2$ conjecture to a PTime algorithm for the GFGness problem of parity automata with a fixed index. The $G_2$ conjecture states that a nondeterministic parity automaton A is GFG if and only if a token game, known as the $G_2$ game, played on A is won by the first player. So far, it had only been proved for Büchi automata; we provide further evidence for it by proving it for coBüchi automata. We also study the complexity of deciding "half-GFGness", a property specific to alternating automata that only requires nondeterministic choices to be resolved in an online manner. We show that this problem is strictly more difficult than GFGness check, already for alternating automata on finite words.

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preprint2020arXiv

Parametrized Universality Problems for One-Counter Nets

We study the language universality problem for One-Counter Nets, also known as 1-dimensional Vector Addition Systems with States (1-VASS), parameterized either with an initial counter value, or with an upper bound on the allowed counter value during runs. The language accepted by an OCN (defined by reaching a final control state) is monotone in both parameters. This yields two natural questions: 1) Does there exist an initial counter value that makes the language universal? 2) Does there exist a sufficiently high ceiling so that the bounded language is universal? Although the ordinary universality problem is decidable (and Ackermann-complete) and these parameterized problems seem to reduce to checking basic structural properties of the underlying automaton, we show that in fact both problems are undecidable. We also look into the complexities of the problems for several decidable subclasses, namely for unambiguous, and deterministic systems, and for those over a single-letter alphabet.

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preprint2005arXiv

Comparing Computational Power

It is common practice to compare the computational power of different models of computation. For example, the recursive functions are strictly more powerful than the primitive recursive functions, because the latter are a proper subset of the former (which includes Ackermann's function). Side-by-side with this "containment" method of measuring power, it is standard to use an approach based on "simulation". For example, one says that the (untyped) lambda calculus is as powerful--computationally speaking--as the partial recursive functions, because the lambda calculus can simulate all partial recursive functions by encoding the natural numbers as Church numerals. The problem is that unbridled use of these two ways of comparing power allows one to show that some computational models are strictly stronger than themselves! We argue that a better definition is that model A is strictly stronger than B if A can simulate B via some encoding, whereas B cannot simulate A under any encoding. We then show that the recursive functions are strictly stronger in this sense than the primitive recursive. We also prove that the recursive functions, partial recursive functions, and Turing machines are "complete", in the sense that no injective encoding can make them equivalent to any "hypercomputational" model.

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