Related papers: On randomized counting versus randomised decision
Reward models (RMs) play a crucial role in aligning large language models (LLMs) with human preferences and enhancing reasoning quality. Traditionally, RMs are trained to rank candidate outputs based on their correctness and coherence.…
The minmax regret problem for combinatorial optimization under uncertainty can be viewed as a zero-sum game played between an optimizing player and an adversary, where the optimizing player selects a solution and the adversary selects costs…
The performance of coverage-based fault localization greatly depends on the quality of test cases being executed. These test cases execute some lines of the given program and determine whether the underlying tests are passed or failed. In…
Given data y(n) and p(n)covariates x(n) one problem in linear regression is to decide which if any of the covariates to include. There are many articles on this problem but all are based on a stochastic model for the data. This paper gives…
In this paper, we consider termination of probabilistic programs with real-valued variables. The questions concerned are: 1. qualitative ones that ask (i) whether the program terminates with probability 1 (almost-sure termination) and (ii)…
Abstraction and realization are bilateral processes that are key in deriving intelligence and creativity. In many domains, the two processes are approached through rules: high-level principles that reveal invariances within similar yet…
Given a linear recurrence sequence (LRS) over the integers, the Positivity Problem} asks whether all terms of the sequence are positive. We show that, for simple LRS (those whose characteristic polynomial has no repeated roots) of order 9…
Test case prioritisation (TCP) is a critical task in regression testing to ensure quality as software evolves. Machine learning has become a common way to achieve it. In particular, learning-to-rank (LTR) algorithms provide an effective…
We study the complexity of various fundamental counting problems that arise in the context of incomplete databases, i.e., relational databases that can contain unknown values in the form of labeled nulls. Specifically, we assume that the…
This paper studies the computational difficulty of clustering problems that are defined directly on a continuous probability density. Rather than working with finite samples, we assume the density is given as a polynomial and ask whether it…
In this work, we study two simple yet general complexity classes, based on logspace Turing machines, which provide a unifying framework for efficient query evaluation in areas like information extraction and graph databases, among others.…
Electoral control models ways of changing the outcome of an election via such actions as adding/deleting/partitioning either candidates or voters. To protect elections from such control attempts, computational complexity has been…
We study a new class of NP search problems, those which can be proved total using standard combinatorial reasoning based on approximate counting. Our model for this kind of reasoning is the bounded arithmetic theory $\mathrm{APC}_2$ of…
This paper considers the question of P = NP in context of the polynomial time SAT algorithm. It posits proposition dependent on existence of conjectured problem that even where the algorithm is shown to solve SAT in polynomial time it…
In this paper we are concerned with the classification of the finite groups admitting a bipartite DRR and a bipartite GRR. First, we find a natural obstruction in a finite group for not admitting a bipartite GRR. Then we give a complete…
Consider the following Stochastic Score Classification Problem. A doctor is assessing a patient's risk of developing a certain disease, and can perform $n$ tests on the patient. Each test has a binary outcome, positive or negative. A…
We study the connection between kappa calculus and probabilistic reasoning in diagnosis applications. Specifically, we abstract a probabilistic belief network for diagnosing faults into a kappa network and compare the ordering of faults…
This article provide new approach to solve P vs NP problem by using cardinality of bases function. About NP-Complete problems, we can divide to infinite disjunction of P-Complete problems. These P-Complete problems are independent of each…
Robust Principal Component Analysis (PCA) (Candes et al., 2011) and low-rank matrix completion (Recht et al., 2010) are extensions of PCA to allow for outliers and missing entries respectively. It is well-known that solving these problems…
The Managed Care system within Medicaid (US Healthcare) uses Request For Proposals (RFP) to award contracts for various healthcare and related services. RFP responses are very detailed documents (hundreds of pages) submitted by competing…