Related papers: Proof equivalence in MLL is PSPACE-complete
In a seminal paper from 1985, Sistla and Clarke showed that the model-checking problem for Linear Temporal Logic (LTL) is either NP-complete or PSPACE-complete, depending on the set of temporal operators used. If, in contrast, the set of…
Large Language Models (LLMs) have achieved human-level proficiency across diverse tasks, but their ability to perform rigorous mathematical problem solving remains an open challenge. In this work, we investigate a fundamental yet…
A distance-based inconsistency indicator, defined by the third author for the consistency-driven pairwise comparisons method, is extended to the incomplete case. The corresponding optimization problem is transformed into an equivalent…
Assessing the stability of a multiple testing procedure under dependence is important but very challenging. Even for multiple testing which among a set of Normal random variables have mean zero, which we refer to as the "Normal means…
In this paper we consider the problem of how to computationally test whether a matrix inequality is positive semidefinite on a semialgebraic set. We propose a family of sufficient conditions using the theory of matrix Positivstellensatz…
Proof nets are a syntax for linear logic proofs which gives a coarser notion of proof equivalence with respect to syntactic equality together with an intuitive geometrical representation of proofs. In this paper we give an alternative…
We introduce a new -as far as we know- problem, according to which we are asked to match sequences of two digits in matrices having entries among those two digits (but others too) and prove that this problem is NP-complete
Equivalence testing, a fundamental problem in the field of distribution testing, seeks to infer if two unknown distributions on $[n]$ are the same or far apart in the total variation distance. Conditional sampling has emerged as a powerful…
Boolean matching is an important problem in logic synthesis and verification. Despite being well-studied for conventional Boolean circuits, its treatment for reversible logic circuits remains largely, if not completely, missing. This work…
Linear logic (LL) is a resource-aware, abstract logic programming language that refines both classical and intuitionistic logic. Linear logic semantics is typically presented in one of two ways: by associating each formula with the set of…
Probabilistic systems are an important theme in AI domain. As the specification language, the logic PCTL is now the default logic for reasoning about probabilistic properties. In this paper, we present a natural and succinct probabilistic…
Pure, or type-free, Linear Logic proof nets are Turing complete once cut-elimination is considered as computation. We introduce modal impredicativity as a new form of impredicativity causing the complexity of cut-elimination to be…
Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to…
In this paper, we proposed an interesting problem that might be classified into enumerative combinatorics. Featuring a distinctive two-fold dependence upon the sequences' terms, our problem can be really difficult, which calls for novel…
Permutation Pattern Matching (or PPM) is a decision problem whose input is a pair of permutations $\pi$ and $\tau$, represented as sequences of integers, and the task is to determine whether $\tau$ contains a subsequence order-isomorphic to…
Maximum likelihood estimation problems are, in general, intractable optimization problems. As a result, it is common to approximate the maximum likelihood estimator (MLE) using convex relaxations. In some cases, the relaxation is tight: it…
We solve open problems concerning the Kleene star $L^*$ of a finite set $L$ of words over an alphabet $\Sigma$. The \emph{Frobenius monoid} problem is the question for a given finite set of words $L$, whether the language $L^*$ is cofinite.…
Proof assistants play a dual role as programming languages and logical systems. As programming languages, proof assistants offer standard modularity mechanisms such as first-class functions, type polymorphism and modules. As logical…
We show that (1) the Minimal False QCNF search-problem (MF-search) and the Minimal Unsatisfiable LTL formula search problem (MU-search) are FPSPACE complete because of the very expressive power of QBF/LTL, (2) we extend the PSPACE-hardness…
The POPLMARK Challenge comprises a set of problems intended to measure the strength of reasoning systems in the realm of mechanizing programming language meta-theory at the time the challenge was enunciated. Included in the collection is…