Related papers: Polynomial Path Orders
We model collapsible and ordered pushdown systems with term rewriting, by encoding higher-order stacks and multiple stacks into trees. We show a uniform inverse preservation of recognizability result for the resulting class of term…
The purpose of this article is to examine and limit the conditions in which the P complexity class could be equivalent to the NP complexity class. Proof is provided by demonstrating that as the number of clauses in a NP-complete problem…
An archetypal problem discussed in computer science is the problem of searching for a given number in a given set of numbers. Other than sequential search, the classic solution is to sort the list of numbers and then apply binary search.…
We propose a type system to analyze the time consumed by multi-threaded imperative programs with a shared global memory, which delineates a class of safe multi-threaded programs. We demonstrate that a safe multi-threaded program runs in…
The Windows Scheduling Problem, also known as the Pinwheel Problem, is to schedule periodic jobs subject to their processing frequency demands. Instances are given as a set of jobs that have to be processed infinitely often such that the…
We provide an implicit characterization of polynomial time computation in terms of ordinary differential equations: we characterize the class $\operatorname{PTIME}$ of languages computable in polynomial time in terms of differential…
Probabilistic circuits (PCs) are a unifying representation for probabilistic models that support tractable inference. Numerous applications of PCs like controllable text generation depend on the ability to efficiently multiply two circuits.…
In this paper, we define and study variants of several complexity classes of decision problems that are defined via some criteria on the number of accepting paths of an NPTM. In these variants, we modify the acceptance criteria so that they…
Polynomial regression is widely used and can help to express nonlinear patterns. However, considering very high polynomial orders may lead to overfitting and poor extrapolation ability for unseen data. The paper presents a method for…
This work studies the average complexity of solving structured polynomial systems that are characterized by a low evaluation cost, as opposed to the dense random model previously used. Firstly, we design a continuation algorithm that…
Global pooling is one of the most significant operations in many machine learning models and tasks, which works for information fusion and structured data (like sets and graphs) representation. However, without solid mathematical…
In this paper we present methods for the synthesis of polynomial invariants for probabilistic transition systems. Our approach is based on martingale theory. We construct invariants in the form of polynomials over program variables, which…
This contribution summarizes recent work of the authors that combines methods from dynamical systems theory (discrete Painlev\'e equations) and asymptotic analysis of orthogonal polynomial recurrences, to address long-standing questions in…
Techniques for the evaluation of complex polynomials with one and two variables are introduced. Polynomials arise in may areas such as control systems, image and signal processing, coding theory, electrical networks, etc., and their…
We develop a class of algebraic interpretations for many-sorted and higher-order term rewriting systems that takes type information into account. Specifically, base-type terms are mapped to \emph{tuples} of natural numbers and higher-order…
A type system is introduced for a generic Object Oriented programming language in order to infer resource upper bounds. A sound andcomplete characterization of the set of polynomial time computable functions is obtained. As a consequence,…
It has been shown that Linear Indexed Grammars can be processed in polynomial time by exploiting constraints which make possible the extensive use of structure-sharing. This paper describes a formalism that is more powerful than Linear…
In this paper we establish an automated amortised resource analysis for term rewrite systems. The method is presented in an annotated type system and gives rise to polynomial bounds on the innermost runtime complexity of the analysed term…
This paper introduces a more restrictive notion of feasibility of functionals on Baire space than the established one from second-order complexity theory. Thereby making it possible to consider functions on the natural numbers as running…
It is known that point searching in basic semialgebraic sets and the search for globally minimal points in polynomial optimization tasks can be carried out using $(s\,d)^{O(n)}$ arithmetic operations, where $n$ and $s$ are the numbers of…