Related papers: Separating the complexity classes NL and NP
A relevant thesis is that for the family of complete first order theories with NIP (i.e. without the independence property) there is a substantial theory, like the family of stable (and the family of simple) first order theories. We examine…
We show that reconstructing a tree from order information on triples is NP-hard. This is in contrast to the case for ultra-metrics and for subtree information on quadruples which are both known to allow polynomial time reconstruction.
We propose to consider non confluence with respect to implicit complexity. We come back to some well known classes of first-order functional program, for which we have a characterization of their intentional properties, namely the class of…
In this paper, we study a class of bilevel optimization program (BP), where the feasible set of the lower level program is independent of the upper level variable. For bilevel programs it is known that the first order approach requires the…
We show that time complexity analysis of higher-order functional programs can be effectively reduced to an arguably simpler (although computationally equivalent) verification problem, namely checking first-order inequalities for validity.…
The point of this note is to prove that a language is in the complexity class PP if and only if the strings of the language encode valid inferences in a Bayesian network defined using function-free first-order logic with equality.
Given a function based on the computation of an NP machine, can one in general eliminate some solutions? That is, can one in general decrease the ambiguity? This simple question remains, even after extensive study by many researchers over…
For a sequence of random structures with $n$-element domains over a relational signature, we define its first order (FO) complexity as a certain subset in the Banach space $\ell^{\infty}/c_0$. The well-known FO zero-one law and FO…
We construct a reduction which proves that the fooling set number and the determinantal rank of a Boolean matrix are NP-hard to compute.
Modern neural network architectures for large-scale learning tasks have substantially higher model complexities, which makes understanding, visualizing and training these architectures difficult. Recent contributions to deep learning…
We show how the complexity of higher-order functional programs can be analysed automatically by applying program transformations to a defunctionalized versions of them, and feeding the result to existing tools for the complexity analysis of…
We consider the quantum complexities of the following three problems: searching an ordered list, sorting an un-ordered list, and deciding whether the numbers in a list are all distinct. Letting N be the number of elements in the input list,…
We show that the two main reduction notions in arithmetic circuit complexity, p-projections and c-reductions, differ in power. We do so by showing unconditionally that there are polynomials that are VNP-complete under c-reductions but not…
This paper has been withdrawn due to a crucial error in the proof of the main theorem
Withdrawn; results will appear elsewhere.
Weak-head normalization is inconsistent with functional extensionality in the call-by-name $\lambda$-calculus. We explore this problem from a new angle via the conflict between extensionality and effects. Leveraging ideas from work on the…
We introduce a notion of weak definability of first order structures, show that various classification-theoretic properties are or are not preserved under it, and that the properties which are preserved can also be characterized in terms of…
Supervised learning is often computationally easy in practice. But to what extent does this mean that other modes of learning, such as reinforcement learning (RL), ought to be computationally easy by extension? In this work we show the…
The method of parameter variation for linear differential equations is extended to classes of second order nonlinear differential equations. This allows to reduce the latter to first order differential equations. Known classical equations…
This article has been withdrawn due to an error in a proof of the main result.