Related papers: Lower bounds and complete problems in nondetermini…
Reasoning with minimal models has always been at the core of many knowledge representation techniques, but we still have only a limited understanding of this problem in Description Logics (DLs). Minimization of some selected predicates,…
In this paper we consider a nondeterministic computation by deterministic multi-head 2-way automata having a read-only access to an auxiliary memory. The memory contains additional data (a guess) and computation is successful iff it is…
An established measure of the expressive power of a given ReLU neural network is the number of linear regions into which it partitions the input space. There exist many different, non-equivalent definitions of what a linear region actually…
In the framework of computational complexity and in an effort to define a more natural reduction for problems of equivalence, we investigate the recently introduced kernel reduction, a reduction that operates on each element of a pair…
We consider the two categories of termination problems of quantum programs with nondeterminism: 1) Is an input of a program terminating with probability one under all schedulers? If not, how can a scheduler be synthesized to evidence the…
We study a basic algorithmic problem in algebraic geometry, which we call NNL, of constructing a normalizing map as per Noether's Normalization Lemma. For general explicit varieties, as formally defined in this paper, we give a randomized…
In this paper we introduce a class of constraint logic programs such that their termination can be proved by using affine level mappings. We show that membership to this class is decidable in polynomial time.
Bilevel linear programs (BLPs) form a class of hierarchical decision-making problems in which both the upper-level and the lower-level decision-makers, known as the leader and the follower, respectively, solve linear optimization problems.…
Decentralized optimization with time-varying networks is an emerging paradigm in machine learning. It saves remarkable communication overhead in large-scale deep training and is more robust in wireless scenarios especially when nodes are…
We study the problem of non-preemptively scheduling $n$ jobs, each job $j$ with a release time $t_j$, a deadline $d_j$, and a processing time $p_j$, on $m$ parallel identical machines. Cieliebak et al. (2004) considered the two constraints…
The problem of attaining energy efficiency in distributed systems is of importance, but a general, non-domain-specific theory of energy-minimal scheduling is far from developed. In this paper, we classify the problems of energy-minimal…
We provide a logical characterization of non-deterministic polynomial time defined by BSS machines over semirings via existential second-order logic interpreted in the semiring semantics developed by Gr\"adel and Tannen. Furthermore, we…
We examine the computational complexity of testing and finding small plans in probabilistic planning domains with succinct representations. We find that many problems of interest are complete for a variety of complexity classes: NP, co-NP,…
A subset of Q^n is called semilinear (or piecewise linear) if it is Boolean combination of linear half-spaces. We study the computational complexity of the constraint satisfaction problem (CSP) over the rationals when all the constraints…
We revisit the minimum-link path problem: Given a polyhedral domain and two points in it, connect the points by a polygonal path with minimum number of edges. We consider settings where the vertices and/or the edges of the path are…
In this monograph, we study complexity classes that are defined using $O(\log n)$-space bounded non-deterministic Turing machines. We prove salient results of Computational Complexity in this topic such as the Immerman-Szelepcsenyi Theorem,…
The community is increasingly exploring linear RNNs (LRNNs) as language models, motivated by their expressive power and parallelizability. While prior work establishes the expressivity benefits of LRNNs over transformers, it is unclear what…
We investigate the computational complexity of various problems for simple recurrent neural networks (RNNs) as formal models for recognizing weighted languages. We focus on the single-layer, ReLU-activation, rational-weight RNNs with…
Many learning algorithms are formulated in terms of finding model parameters which minimize a data-fitting loss function plus a regularizer. When the regularizer involves the l0 pseudo-norm, the resulting regularization path consists of a…
We prove the #P-hardness of the counting problems associated with various satisfiability, graph and combinatorial problems, when restricted to planar instances. These problems include \begin{romannum} \item[{}] {\sc 3Sat, 1-3Sat, 1-Ex3Sat,…