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This work investigates the algorithmic complexity of non-classical logics, focusing on superintuitionistic and modal systems. It is shown that propositional logics are usually polynomial-time reducible to their fragments with at most two…
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there are definite programs and constraint logic programs that compute a solution as an answer substitution to a query…
Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a key method for improving Large Language Models' reasoning capabilities, yet recent evidence suggests it may paradoxically shrink the reasoning boundary rather than…
We start the study of the enumeration complexity of different satisfiability problems in first-order team logics. Since many of our problems go beyond DelP, we use a framework for hard enumeration analogous to the polynomial hierarchy,…
We develop and study the complexity of propositional proof systems of varying strength extending resolution by allowing it to operate with disjunctions of linear equations instead of clauses. We demonstrate polynomial-size refutations for…
We investigate the satisfiability and finite satisfiability problem for probabilistic computation-tree logic (PCTL) where operators are not restricted by any step bounds. We establish decidability for several fragments containing…
Following the idea of Subexponential Linear Logic and Stratified Bounded Linear Logic, we propose a new parameterized version of Linear Logic which subsumes other systems like ELL, LLL or SLL, by including variants of the exponential rules.…
Although Deep Neural Networks (DNNs) have shown incredible performance in perceptive and control tasks, several trustworthy issues are still open. One of the most discussed topics is the existence of adversarial perturbations, which has…
With the rapid progress of Large Language Models (LLMs), it becomes increasingly important to understand their abilities and limitations. In two experiments, we investigate the causal and compositional reasoning abilities of LLMs and humans…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
Conditional lower bounds based on $P\neq NP$, the Exponential-Time Hypothesis (ETH), or similar complexity assumptions can provide very useful information about what type of algorithms are likely to be possible. Ideally, such lower bounds…
Why are classifiers in high dimension vulnerable to "adversarial" perturbations? We show that it is likely not due to information theoretic limitations, but rather it could be due to computational constraints. First we prove that, for a…
Partial label learning (PLL) is an important problem that allows each training example to be labeled with a coarse candidate set, which well suits many real-world data annotation scenarios with label ambiguity. Despite the promise, the…
We consider the problem of designing an adaptive sequence of questions that optimally classify a candidate's ability into one of several categories or discriminative grades. A candidate's ability is modeled as an unknown parameter, which,…
We survey recent progress in the proof complexity of strong proof systems and its connection to algebraic circuit complexity, showing how the synergy between the two gives rise to new approaches to fundamental open questions, solutions to…
Recent years have seen tremendous growth in the amount of verified software. Proofs for complex properties can now be achieved using higher-order theories and calculi. Complex properties lead to an ever-growing number of definitions and…
One method to determine whether or not a system of partial differential equations is consistent is to attempt to construct a solution using merely the "algebraic data" associated to the system. In technical terms, this translates to the…
The satisfiability problem of the branching time logic CTL is studied in terms of computational complexity. Tight upper and lower bounds are provided for each temporal operator fragment. In parallel, the minimal model size is studied with a…
We show that satisfiability for CTL* with equality-, order-, and modulo-constraints over Z is decidable. Previously, decidability was only known for certain fragments of CTL*, e.g., the existential and positive fragments and EF.
Despite large language models' (LLMs) recent advancements, their bias and hallucination issues persist, and their ability to offer consistent preferential rankings remains underexplored. This study investigates the capacity of LLMs to…