Related papers: From matrix interpretations over the rationals to …

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…

All current investigations to analyze the derivational complexity of term rewrite systems are based on a single termination method, possibly preceded by transformations. However, the exclusive use of direct criteria is problematic due to…

Recently it was shown that it is undecidable whether a term rewrite system can be proved terminating by a polynomial interpretation in the natural numbers. In this paper we show that this is also the case when restricting the…

We study the termination problem for probabilistic term rewrite systems. We prove that the interpretation method is sound and complete for a strengthening of positive almost sure termination, when abstract reduction systems and term rewrite…

Over the past decades, classification models have proven to be essential machine learning tools given their potential and applicability in various domains. In these years, the north of the majority of the researchers had been to improve…

The termination method of weakly monotonic algebras, which has been defined for higher-order rewriting in the HRS formalism, offers a lot of power, but has seen little use in recent years. We adapt and extend this method to the alternative…

We introduce a novel resource analysis for typed term rewrite systems based on a potential-based type system. This type system gives rise to polynomial bounds on the innermost runtime complexity. We relate the thus obtained amortised…

In this paper, we revisit implicit regularization from the ground up using notions from dynamical systems and invariant subspaces of Morse functions. The key contributions are a new criterion for implicit regularization---a leading…

We establish a natural translation from word rewriting systems to strictly positive polymodal logics. Thereby, the latter can be considered as a generalization of the former. As a corollary we obtain examples of undecidable strictly…

This work investigates if the current neural architectures are adequate for learning symbolic rewriting. Two kinds of data sets are proposed for this research -- one based on automated proofs and the other being a synthetic set of…

In this paper we derive a representation of an arbitrary real matrix M as the difference of a real matrix A and the transpose of its inverse. This expression may prove useful for progressing beyond known results for which the appearance of…

We present a framework for the construction of linearizations for scalar and matrix polynomials based on dual bases which, in the case of orthogonal polynomials, can be described by the associated recurrence relations. The framework…

Our goal is to study the feasibility of porting termination analysis techniques developed for one programming paradigm to another paradigm. In this paper, we show how to adapt termination analysis techniques based on polynomial…

We take matrix decompositions that are usually applied to matrices over the real numbers or complex numbers, and extend them to matrices over an algebra called the double numbers. In doing so, we unify some matrix decompositions: For…

Multidimensional systems are becoming increasingly important as they provide a promising tool for estimation, simulation and control, while going beyond the traditional setting of one-dimensional systems. The analysis of multidimensional…

Matrices over the ring of formal power series are considered. Normal forms with respect to various sub-groups of the two-sided transformations are constructed. The construction is based on the special property of the action: it induces a…

It is proved that the roots of combinations of matrix polynomials with real roots can be recast as eigenvalues of combinations of real symmetric matrices, under certain hypotheses. The proof is based on recent solution of the Lax…

Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional…

We provide sufficient conditions for systems of polynomial equations over general (real or complex) algebras to have a solution. This generalizes known results on quaternions, octonions and matrix algebras. We also generalize the…

Combining a standard proof search method, such as resolution or tableaux, and rewriting is a powerful way to cut off search space in automated theorem proving, but proving the completeness of such combined methods may be challenging. It may…