Related papers: Termination of Triangular Polynomial Loops

We show that finding rank-$R$ decompositions of a 3D tensor, for $R\le 4$, over a fixed finite field can be done in polynomial time. However, if some cells in the tensor are allowed to have arbitrary values, then rank-2 is NP-hard over the…

We prove lower bounds of order $n\log n$ for both the problem to multiply polynomials of degree $n$, and to divide polynomials with remainder, in the model of bounded coefficient arithmetic circuits over the complex numbers. These lower…

This paper is concerned with certifying that a given point is near an exact root of an overdetermined or singular polynomial system with rational coefficients. The difficulty lies in the fact that consistency of overdetermined systems is…

Termination properties of actual Prolog systems with constraints are fragile and difficult to analyse. The lack of the occurs-check, moded and overloaded arithmetical evaluation via is/2 and the occasional nontermination of finite domain…

We prove that it is $\#\mathsf{P}$-complete to count the triangulations of a (non-simple) polygon.

We consider the problem of learning low-rank tensors from partial observations with structural constraints, and propose a novel factorization of such tensors, which leads to a simpler optimization problem. The resulting problem is an…

This work investigates the algorithmic complexity of non-classical logics, focusing on superintuitionistic and modal systems. It is shown that propositional logics are usually polynomial-time reducible to their fragments with at most two…

Polynomial interpretations are a useful technique for proving termination of term rewrite systems. They come in various flavors: polynomial interpretations with real, rational and integer coefficients. As to their relationship with respect…

In the past few years, the slice-rank lemma of Tao has been applied successfully to many problems in extremal combinatorics. In this paper, first, we define a new notion of triangular tensors which generalizes that of triangular matrices…

The structure of the F5 algorithm to compute Gr\"obner bases makes it very efficient. However, while it is believed to terminate for so-called regular sequences, it is not clear whether it terminates for all inputs. This paper has two major…

Tensor completion is a natural higher-order generalization of matrix completion where the goal is to recover a low-rank tensor from sparse observations of its entries. Existing algorithms are either heuristic without provable guarantees,…

We study the termination problem for nondeterministic recursive probabilistic programs. First, we show that a ranking-supermartingales-based approach is both sound and complete for bounded terminiation (i.e., bounded expected termination…

Reversible Boolean Circuits are an interesting computational model under many aspects and in different fields, ranging from Reversible Computing to Quantum Computing. Our contribution is to describe a specific class of Reversible Boolean…

A regularity lemma for polynomials provides a decomposition in terms of a bounded number of approximately independent polynomials. Such regularity lemmas play an important role in numerous results, yet suffer from the familiar shortcoming…

This paper presents the following results on sets that are complete for NP. 1. If there is a problem in NP that requires exponential time at almost all lengths, then every many-one NP-complete set is complete under length-increasing…

This paper uses Brin and Thickstun's theory of end reductions of non-compact 3-manifolds to study groups of covering translations of irreducible contractible open 3-manifolds W which are not homeomorphic to R^3. We associate to W an object…

Nonassociative finite simple Moufang loops are exactly the loops constructed by Paige from Zorn vector matrix algebras. We prove this result anew, using geometric loop theory. In order to make the paper accessible to a broader audience, we…

Termination analysis of linear loops plays a key r\^{o}le in several areas of computer science, including program verification and abstract interpretation. Already for the simplest variants of linear loops the question of termination…

In this paper, we consider the satisfiability problem for string logic with equations, regular membership and Presburger constraints over length functions. The difficulty comes from multiple occurrences of string variables making…

In recent years there has been considerable interest in theories over string equations, length function, and string-number conversion predicate within the formal verification, software engineering, and security communities. SMT solvers for…