Related papers: A minimal representation for continuous functions
A fast nonparametric procedure for classifying functional data is introduced. It consists of a two-step transformation of the original data plus a classifier operating on a low-dimensional hypercube. The functional data are first mapped…
Partition functions of certain classes of "spin glass" models in statistical physics show strong connections to combinatorial graph invariants. Also known as homomorphism functions they allow for the representation of many such invariants,…
We investigate the possibility of a semantic account of the execution time (i.e. the number of \beta_v-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value {\lambda}-calculus. For…
The evaluation of a matrix exponential function is a classic problem of computational linear algebra. Many different methods have been employed for its numerical evaluation [Moler C and van Loan C 1978 SIAM Review 20 4], none of which…
We introduce a method for proving almost sure termination in the context of lambda calculus with continuous random sampling and explicit recursion, based on ranking supermartingales. This result is extended in three ways. Antitone ranking…
In combinatorial optimization, partial variable assignments are called persistent if they agree with some optimal solution. We propose persistency criteria for the multicut and max-cut problem as well as fast combinatorial routines to…
Bottom-up knowledge compilation is a paradigm for generating representations of functions by iteratively conjoining constraints using a so-called apply function. When the input is not efficiently compilable into a language - generally a…
The present article introduces ptarithmetic (short for "polynomial time arithmetic") -- a formal number theory similar to the well known Peano arithmetic, but based on the recently born computability logic (see…
A computer's clock rate ultimately determines the minimum time between sequential operations or instructions. Despite exponential advances in electronic computer performance owing to Moore's Law and increasingly parallel system…
In its most basic form, decision-making can be viewed as a computational process that progressively eliminates alternatives, thereby reducing uncertainty. Such processes are generally costly, meaning that the amount of uncertainty that can…
Datalog is a powerful yet elegant language that allows expressing recursive computation. Although Datalog evaluation has been extensively studied in the literature, so far, only loose upper bounds are known on how fast a Datalog program can…
Let $f:2^{E} \rightarrow \mathbb{Z}_+$ be a submodular function on a ground set $E = [n]$, and let $P(f)$ denote its extended polymatroid. Given a direction $d \in \mathbb{Z}^n$ with at least one positive entry, the line search problem is…
This paper introduces a generic framework that provides sufficient conditions for guaranteeing polynomial-time decidability of fixed-negation fragments of first-order theories that adhere to certain fixed-parameter tractability…
We discuss how the ideal formalism of Computational Mechanics can be adapted to apply to a non-infinite series of corrupted and correlated data, that is typical of most observed natural time series. Specifically, a simple filter that…
We establish new, and surprisingly tight, connections between propositional proof complexity and finite model theory. Specifically, we show that the power of several propositional proof systems, such as Horn resolution, bounded-width…
We present a theorem concerning the invariance of cross-correlation peak positions, which provides a foundation for a new method for time difference estimation that is potentially faster than the conventional fast Fourier transform (FFT)…
In many naturally occurring optimization problems one needs to ensure that the definition of the optimization problem lends itself to solutions that are tractable to compute. In cases where exact solutions cannot be computed tractably, it…
The properties of the stable distance over stable spacetimes are used as a reference to propose a simplified, abstract notion of spacetime. The discussion shows that spacetime, with its topology, causal order and (upper semi-continuous)…
Ising machines based on nonlinear analog systems are a promising method to accelerate computation of NP-hard optimization problems. Yet, their analog nature is also causing amplitude inhomogeneity which can deteriorate the ability to find…
A resource-bounded version of the statement "no algorithm recognizes all non-halting Turing machines" is equivalent to an infinitely often (i.o.) superpolynomial speedup for the time required to accept any coNP-complete language and also…