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The proliferation of agentic systems has thrust the reasoning capabilities of AI into the forefront of contemporary machine learning. While it is known that there \emph{exist} neural networks which can reason through any Boolean task…
We display an application of the notions of kernelization and data reduction from parameterized complexity to proof complexity: Specifically, we show that the existence of data reduction rules for a parameterized problem having (a). a…
We present a recursive formulation of the Horn algorithm for deciding the satisfiability of propositional clauses. The usual presentations in imperative pseudo-code are informal and not suitable for simple proofs of its main properties. By…
It is shown that a class of optical physical unclonable functions (PUFs) can be learned to arbitrary precision with arbitrarily high probability, even in the presence of noise, given access to polynomially many challenge-response pairs and…
We study from the proof complexity perspective the (informal) proof search problem: Is there an optimal way to search for propositional proofs? We note that for any fixed proof system there exists a time-optimal proof search algorithm.…
We present Proof-of-Perception (PoP), a tool-using framework that casts multimodal reasoning as an executable graph with explicit reliability guarantees. Each perception or logic node outputs a conformal set, yielding calibrated, stepwise…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
The progress of deep learning (DL), especially the recent development of automatic design of networks, has brought unprecedented performance gains at heavy computational cost. On the other hand, blockchain systems routinely perform a huge…
Proof-of-Learning (PoL) proposes that a model owner logs training checkpoints to establish a proof of having expended the computation necessary for training. The authors of PoL forego cryptographic approaches and trade rigorous security…
New proof assistant developments often involve concepts similar to already formalized ones. When proving their properties, a human can often take inspiration from the existing formalized proofs available in other provers or libraries. In…
We consider the proof complexity of the minimal complete fragment, KS, of standard deep inference systems for propositional logic. To examine the size of proofs we employ atomic flows, diagrams that trace structural changes through a proof…
We consider the probability hierarchy for Popperian FINite learning and study the general properties of this hierarchy. We prove that the probability hierarchy is decidable, i.e. there exists an algorithm that receives p_1 and p_2 and…
A hypothesis testing algorithm is replicable if, when run on two different samples from the same distribution, it produces the same output with high probability. This notion, defined by by Impagliazzo, Lei, Pitassi, and Sorell [STOC'22],…
In this paper we give an optimization for active learning algorithms, applicable to learning Moore machines where the output comprises several observables. These machines can be decomposed themselves by projecting on each observable,…
We present FOLD-SE, an efficient, explainable machine learning algorithm for classification tasks given tabular data containing numerical and categorical values. FOLD-SE generates a set of default rules-essentially a stratified normal logic…
We distinguish finitarily between algorithmic verifiability, and algorithmic computability, to show that Goedel's 'formally' unprovable, but 'numeral-wise' provable, arithmetical proposition [(Ax)R(x)] can be finitarily evidenced as:…
Partially ordered automata are automata where the transition relation induces a partial order on states. The expressive power of partially ordered automata is closely related to the expressivity of fragments of first-order logic on finite…
We give an efficient algorithm for learning a binary function in a given class C of bounded VC dimension, with training data distributed according to P and test data according to Q, where P and Q may be arbitrary distributions over X. This…
We present an approach for testing student learning outcomes in a course on automated reasoning using the Isabelle proof assistant. The approach allows us to test both general understanding of formal proofs in various logical proof systems…
The need for formal definition of the very basis of mathematics arose in the last century. The scale and complexity of mathematics, along with discovered paradoxes, revealed the danger of accumulating errors across theories. Although,…