Related papers: Decision Problems for Additive Regular Functions
Recently, research on explainable recommender systems has drawn much attention from both academia and industry, resulting in a variety of explainable models. As a consequence, their evaluation approaches vary from model to model, which…
In the study of random access machines (RAMs) it has been shown that the availability of an extra input integer, having no special properties other than being sufficiently large, is enough to reduce the computational complexity of some…
Pandora's problem is a fundamental model in economics that studies optimal search strategies under costly inspection. In this paper we initiate the study of Pandora's problem with combinatorial costs, capturing many real-life scenarios…
A linear quadratic optimal stochastic control problem with random coefficients and indefinite state/control weight costs is usually linked to an indefinite stochastic Riccati equation (SRE) which is a matrix-valued quadratic backward…
Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. This paper considers both minimax and adaptive estimation of the principal subspace in the high dimensional…
Saturation is a fundamental game-semantic property satisfied by strategies that interpret higher-order concurrent programs. It states that the strategy must be closed under certain rearrangements of moves, and corresponds to the intuition…
The development lifecycle of generative AI systems requires continual evaluation, data acquisition, and annotation, which is costly in both resources and time. In practice, rapid iteration often makes it necessary to rely on synthetic…
In this paper a class of single machine scheduling problems is considered. It is assumed that job processing times and due dates can be uncertain and they are specified in the form of discrete scenario set. A probability distribution in the…
An index for a finite automaton is a powerful data structure that supports locating paths labeled with a query pattern, thus solving pattern matching on the underlying regular language. In this paper, we solve the long-standing problem of…
We compute the integral of a function or the expectation of a random variable with minimal cost and use, for our new algorithm and for upper bounds of the complexity, i.i.d. samples. Under certain assumptions it is possible to select a…
This paper studies an online replication problem for distributed data access. The goal is to dynamically create and delete data copies in a multi-server system as time passes to minimize the total storage and network cost of serving access…
In the fillable array problem one must maintain an array A[1..n] of $w$-bit entries subject to random access reads and writes, and also a $\texttt{fill}(\Delta)$ operation which sets every entry of to some $\Delta\in\{0,\ldots,2^w-1\}$. We…
We address single machine problems with optional jobs - rejection, studied recently in Zhang et al. [21] and Cao et al. [2]. In these papers, the authors focus on minimizing regular performance measures, i.e., functions that are…
The problem of deciding whether one point in a program is data dependent upon another is fundamental to program analysis and has been widely studied. In this paper we consider this problem at the abstraction level of program schemas in…
A robot can invoke heterogeneous computation resources such as CPUs, cloud GPU servers, or even human computation for achieving a high-level goal. The problem of invoking an appropriate computation model so that it will successfully…
A cryptarithm is a mathematical puzzle where given an arithmetic equation written with letters rather than numerals, a player must discover an assignment of numerals on letters that makes the equation hold true. In this paper, we propose a…
We concern with a special class of binary cellular automata, i.e., the so-called particle cellular automata (PCA) in the present paper. We first propose max-plus expressions to PCA of 4 neighbors. Then, by utilizing basic operations of the…
Regular expressions with backreferences (regex, for short), as supported by most modern libraries for regular expression matching, have an NP-complete matching problem. We define a complexity parameter of regex, called active variable…
Elementary cellular automata (ECA) is a widely studied one-dimensional processing methodology where the successive iteration of the automaton may lead to the recreation of a rich pattern dynamic. Recently, cellular automata have been…
The assembly index of assembly theory quantifies the minimal number of composition steps required to construct an object from elementary components. The study proves that the decision version of the assembly index problem is NP-complete,…