Related papers: A Theory of Complexity, Condition and Roundoff
We investigate the descriptive complexity of the set of models of first-order theories. Using classical results of Knight and Solovay, we give a sharp condition for complete theories to have a $\pmb\Pi_\omega^0$-complete set of models. In…
The complexity class NP of decision problems that can be solved nondeterministically in polynomial time is of great theoretical and practical importance where the notion of polynomial-time reductions between NP-problems is a key concept for…
This paper illustrates the richness of the concept of regular sets of time bounds and demonstrates its application to problems of computational complexity. There is a universe of bounds whose regular subsets allow to represent several time…
We survey classical and recent developments in numerical linear algebra, focusing on two issues: computational complexity, or arithmetic costs, and numerical stability, or performance under roundoff error. We present a brief account of the…
In this article, we shall describe some of the most interesting topics in the subject of Complexity Science for a general audience. Anyone with a solid foundation in high school mathematics (with some calculus) and an elementary…
The purpose of this article is to examine and limit the conditions in which the P complexity class could be equivalent to the NP complexity class. Proof is provided by demonstrating that as the number of clauses in a NP-complete problem…
We extend classical methods of computational complexity to the realm of distributed computing, where they sometimes prove more effective than in their original context. Our focus is on decision problems in the LOCAL model, a setting in…
The computational complexity of winner determination under common voting rules is a classical and fundamental topic in the field of computational social choice. Previous work has established the NP-hardness of winner determination under…
We consider a class of optimization problems defined by a system of linear equations with min and max operators. This class of optimization problems has been studied under restrictive conditions, such as, (C1) the halting or stability…
Depth is a complexity measure for natural systems of the kind studied in statistical physics and is defined in terms of computational complexity. Depth quantifies the length of the shortest parallel computation required to construct a…
The first section starts with the basic definitions following mainly the notations of the book written by E. Kushilevitz and N. Nisan. At the end of the first section I examine tree-balancing. In the second section I summarize the…
I study the class of problems efficiently solvable by a quantum computer, given the ability to "postselect" on the outcomes of measurements. I prove that this class coincides with a classical complexity class called PP, or Probabilistic…
Except for crystalline or random structures, an agreed definition of complexity for intermediate and hence interesting cases does not exist. We fill this gap with a notion of complexity that characterises shapes formed by any finite number…
We define counting classes #P_R and #P_C in the Blum-Shub-Smale setting of computations over the real or complex numbers, respectively. The problems of counting the number of solutions of systems of polynomial inequalities over R, or of…
We use the powerful tools of counting complexity and generic oracles to help understand the limitations of the complexity of quantum computation. We show several results for the probabilistic quantum class BQP. 1. BQP is low for PP, i.e.,…
The authors discuss information-based complexity theory, which is a model of finite-precision computations with real numbers, and its applications to numerical analysis.
Halpern and Pearl introduced a definition of actual causality; Eiter and Lukasiewicz showed that computing whether X=x is a cause of Y=y is NP-complete in binary models (where all variables can take on only two values) and\…
We develop theory concerning non-uniform complexity in a setting in which the notion of single-pass instruction sequence considered in program algebra is the central notion. We define counterparts of the complexity classes P/poly and…
We present several known formalizations of theorems from computational complexity in bounded arithmetic and formalize the PCP theorem in the theory PV1 (no formalization of this theorem was known). This includes a formalization of the…
Continuing the study of complexity theory of Koepke's Ordinal Turing Machines (OTMs) that was started by Rin, L\"owe and the author, we prove the following results: (1) An analogue of Ladner's theorem for OTMs holds: That is, there are…