Related papers: Most Programs Stop Quickly or Never Halt

We explore in the framework of Quantum Computation the notion of {\em Computability}, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm for Hilbert's tenth problem, which is equivalent to…

Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…

Probabilistic programming is a growing area that strives to make statistical analysis more accessible, by separating probabilistic modelling from probabilistic inference. In practice this decoupling is difficult. No single inference…

Termination is one of the basic liveness properties, and we study the termination problem for probabilistic programs with real-valued variables. Previous works focused on the qualitative problem that asks whether an input program terminates…

Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized…

We study the problem of deciding universal termination of linear and affine loops over the reals in the bit-model of real computation. We show that both problems are as close to decidable as one can expect them to be: there exist sound…

In this paper, we study quantitative properties of quantum programs. Properties of interest include (positive) almost-sure termination, expected runtime or expected cost, that is, for example, the expected number of applications of a given…

The difficulty of explaining non-local correlations in a fixed causal structure sheds new light on the old debate on whether space and time are to be seen as fundamental. Refraining from assuming space-time as given a priori has a number of…

Average-case analysis computes the complexity of an algorithm averaged over all possible inputs. Compared to worst-case analysis, it is more representative of the typical behavior of an algorithm, but remains largely unexplored in…

We present a heuristic framework for attacking the undecidable termination problem of logic programs, as an alternative to current termination/non-termination proof approaches. We introduce an idea of termination prediction, which predicts…

TThe problem is to identify a probability associated with a set of natural numbers, given an infinite data sequence of elements from the set. If the given sequence is drawn i.i.d. and the probability mass function involved (the target)…

This work presents an empirical analysis of exact algorithms for the unbounded knapsack problem, which includes seven algorithms from the literature, two commercial solvers, and more than ten thousand instances. The terminating step-off, a…

The subset sum problem is known to be an NP-hard problem in the field of computer science with the fastest known approach having a run-time complexity of $O(2^{0.3113n})$. A modified version of this problem is known as the perfect sum…

We study the relationship between the competitive ratio and the tail distribution of randomized online minimization problems. To this end, we define a broad class of online problems that includes some of the well-studied problems like…

There are numbers k and s and a URM program A(n,m) satisfying the following conditions. 1. If A(n,m) halts, then Cn(m) diverges. 2. For all n, C_k(n) = A(n,n) and C_s(n) = C_k(s). 3. A(k,s) halts and for all n, A(s,n) diverges. Here C_n(_)…

Partially ordered models of time occur naturally in applications where agents or processes cannot perfectly communicate with each other, and can be traced back to the seminal work of Lamport. In this paper we consider the problem of…

A decision problem is called parameterized if its input is a pair of strings. One of these strings is referred to as a parameter. The problem: given a propositional logic program P and a non-negative integer k, decide whether P has a stable…

This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…

Tailoring many-body interactions among a proper quantum system endows it with computing ability by means of static quantum computation in the sense that some of the physical degrees of freedom can be used to store binary information and the…

A long-standing open question in Integer Programming is whether integer programs with constraint matrices with bounded subdeterminants are efficiently solvable. An important special case thereof are congruency-constrained integer programs…