Related papers: The Almost Equivalence by Asymptotic Probabilities…
Large language models (LLMs) are known to struggle with complicated reasoning tasks such as math word problems (MWPs). In this paper, we present how analogy from similarly structured questions can improve LLMs' problem-solving capabilities…
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…
This paper proposes a notion of branching bisimilarity for non-deterministic probabilistic processes. In order to characterize the corresponding notion of rooted branching probabilistic bisimilarity, an equational theory is proposed for a…
We present a technique to study normalizing strategies when termination is asymptotic, that is, it appears as a limit, as opposite to reaching a normal form in a finite number of steps. Asymptotic termination occurs in several settings,…
We examine the computational complexity of testing and finding small plans in probabilistic planning domains with both flat and propositional representations. The complexity of plan evaluation and existence varies with the plan type sought;…
On the one hand, classical terminological knowledge representation excludes the possibility of handling uncertain concept descriptions involving, e.g., "usually true" concept properties, generalized quantifiers, or exceptions. On the other…
We consider the following problem: given a program, find tight asymptotic bounds on the values of some variables at the end of the computation (or at any given program point) in terms of its input values. We focus on the case 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…
Several application domains require formal but flexible approaches to the comparison problem. Different process models that cannot be related by behavioral equivalences should be compared via a quantitative notion of similarity, which is…
We study Krasnoselskii-Mann style iterative algorithms for approximating fixpoints of asymptotically weakly contractive mappings, with a focus on providing generalised convergence proofs along with explicit rates of convergence. More…
Logic programming under the answer-set semantics nowadays deals with numerous different notions of program equivalence. This is due to the fact that equivalence for substitution (known as strong equivalence) and ordinary equivalence are…
It is well known that sparse approximation problem is \textsf{NP}-hard under general dictionaries. Several algorithms have been devised and analyzed in the past decade under various assumptions on the \emph{coherence} $\mu$ of the…
Approximate Bayesian computation allows for statistical analysis in models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on…
We investigate regular realizability (RR) problems, which are the problems of verifying whether intersection of a regular language -- the input of the problem -- and fixed language called filter is non-empty. In this paper we focus on the…
We study approximate equivalence relations up to commensurability, in the presence of a definable measure. As a basic framework, we give a presentation of probability logic based on continuous logic. Hoover's normal form is valid here; if…
The $p$-curvature of a system of linear differential equations in positive characteristic $p$ is a matrix that measures how far the system is from having a basis of polynomial solutions. We show that the similarity class of the…
In this work we investigate the asymptotic behaviour of weighted partial sums of a particular class of random variables related to Oppenheim series expansions. More precisely, we verify convergence in probability as well as almost sure…
We propose an efficient algorithm for approximate computation of the profile maximum likelihood (PML), a variant of maximum likelihood maximizing the probability of observing a sufficient statistic rather than the empirical sample. The PML…
The efficient sparse coding and reconstruction of signal vectors via linear observations has received a tremendous amount of attention over the last decade. In this context, the automated learning of a suitable basis or overcomplete…
Probabilistic concurrent systems are foundational models for modern mobile computing. In this paper, a unifying approach to probabilistic testing equivalences is proposed. With the help of a new distribution-based semantics for…