Related papers: L is different from NP
Nomadic applications create replicas of shared objects that evolve independently while they are disconnected. When reconnecting, the system has to reconcile the divergent replicas. In the log-based approach to reconciliation, such as in the…
We construct in ZFC an L topological vector space -- a topological vector space that is an L space -- and an L field -- a topological field that is an L space. This generalizes results in [5] and [8].
In this paper, we develop a quantified propositional proof systems that corresponds to logarithmic-space reasoning. We begin by defining a class SigmaCNF(2) of quantified formulas that can be evaluated in log space. Then our new proof…
We present one of the preliminary NLP works under the challenging setup of Learning from Label Proportions (LLP), where the data is provided in an aggregate form called bags and only the proportion of samples in each class as the ground…
A new class UF of problems is introduced, strictly included in the class NP, which arises in the analysis of the time verifying the intermediate results of computations. The implications of the introduction of this class are considered.…
In this article, I focus on the resiliency of the P=?NP problem. The main point to deal with is the change of the underlying logic from first to second-order logic. In this manner, after developing the initial steps of this change, I can…
Local operations with classical communication (LOCC) and separable operations are two classes of quantum operations that play key roles in the study of quantum entanglement. Separable operations are strictly more powerful than LOCC, but no…
We give a novel descriptive-complexity theoretic characterization of L and NL computable queries over finite structures using traversal invariance. We summarize this as (N)L = FO + (breadth-first) traversal-invariance.
We consider a number of graph kernels and proximity measures including commute time kernel, regularized Laplacian kernel, heat kernel, exponential diffusion kernel (also called "communicability"), etc., and the corresponding distances as…
In this paper, we examine Lin's "On NP versus coNP and Frege Systems" [Lin25]. Lin claims to prove that $\text{NP} \neq \text{coNP}$ by constructing a language $L_d$ such that $L_d \in \text{NP}$ but $L_d \notin \text{coNP}$. We present a…
Limited Discrepancy Search (LDS) is a popular algorithm to search a state space with a heuristic to order the possible actions. Nested Search (NS) is another algorithm to search a state space with the same heuristic. NS spends more time on…
Log parsing serves as an essential prerequisite for various log analysis tasks. Recent advancements in this field have improved parsing accuracy by leveraging the semantics in logs through fine-tuning large language models (LLMs) or…
Let gamma be a (not necessarily finite) structure with a finite relational signature. We prove that deciding whether a given existential positive sentence holds in gamma is in Logspace or complete for the class CSP(gamma)_NP under…
We present a direct proof of the fact that the weak-$L^1$ and weak-$\ell^1$ spaces do not have type $1$.
We present the MEoP problem that decides the existence of solutions to certain modular equations over prime numbers and show how this separates the complexity class NP from its subclass P
In this expository note we show that the learning parities with noise (LPN) assumption is robust to weak dependencies in the noise distribution of small batches of samples. This provides a partial converse to the linearization technique of…
The subject logic in computer science should entail proof theoretic applications. So the question arises whether open problems in computational complexity can be solved by advanced proof theoretic techniques. In particular, consider the…
In order to prove that the P of problems is different to the NP class, we consider the satisfability problem of propositional calculus formulae, which is an NP-complete problem. It is shown that, for every search algorithm A, there is a set…
We prove that if $1 \leq p, q \leq \infty$, then the spaces $L_p +L_q$ and $L_p \cap L_q$ are isomorphic if and only if $p = q$. In particular, $L_2 +L_{\infty}$ and $L_2 \cap L_{\infty}$ are not isomorphic which is an answer to a question…
We present an algebraic view on logic programming, related to proof theory and more specifically linear logic and geometry of interaction. Within this construction, a characterization of logspace (deterministic and non-deterministic)…