Related papers: A New Order-theoretic Characterisation of the Poly…
Partially observable Markov decision processes (POMDPs) provide an elegant mathematical framework for modeling complex decision and planning problems in stochastic domains in which states of the system are observable only indirectly, via a…
The software package BBCPOP is a MATLAB implementation of a hierarchy of sparse doubly nonnegative (DNN) relaxations of a class of polynomial optimization (minimization) problems (POPs) with binary, box and complementarity (BBC)…
This papers studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs). It presents a new framework using discrete ODEs as a central tool for computation and provides several implicit characterizations…
Short integer linear programs are programs with a relatively small number of constraints. We show how recent improvements on the running-times of solvers for such programs can be used to obtain fast pseudo-polynomial time algorithms for…
We investigate questions related to the set $\mathcal{SEP}_d$ consisting of the linear maps $\rho$ acting on $\mathbb{C}^d\otimes \mathbb{C}^d$ that can be written as a convex combination of rank one matrices of the form $xx^*\otimes yy^*$.…
Let $\un,$ be a quasi-definite linear functional defined on the space of polynomials $\mathbb{P}.$ For such a functional we can define a sequence of monic orthogonal polynomials (SMOP in short) $(P_n)_{n\geq 0},$ which satisfies a three…
Constrained pathfinding is a well-studied, yet challenging network optimisation problem that can be seen in a broad range of real-world applications. Pathfinding with multiple resource limits, which is known as the Resource Constrained…
Second-order polynomials generalize classical first-order ones in allowing for additional variables that range over functions rather than values. We are motivated by their applications in higher-order computational complexity theory,…
In this paper we give a framework for describing how abstract systems can be used to compute if no randomness or error is involved. Using this we describe a class of classical "physical" computation systems whose computational capabilities…
In the weighted flow-time problem on a single machine, we are given a set of n jobs, where each job has a processing requirement p_j, release date r_j and weight w_j. The goal is to find a preemptive schedule which minimizes the sum of…
Mapping is essential in robotics and autonomous systems because it provides the spatial foundation for path planning. Efficient mapping enables planning algorithms to generate reliable paths while ensuring safety and adapting in real time…
We introduce a new bounded theory RS^1_2 and show that the functions which are Sigma^b_1-representable in it are precisely random functions which can be computed in polynomial time. Concretely, we pass through a class of oracle functions…
Retrosynthetic planning is a critical task in organic chemistry which identifies a series of reactions that can lead to the synthesis of a target product. The vast number of possible chemical transformations makes the size of the search…
A new characterization of provably recursive functions of first-order arithmetic is described. Its main feature is using only terms consisting of 0, the successor S and variables in the quantifier rules, namely, universal elimination and…
For which sets A does there exist a mapping, computed by a total or partial recursive function, such that the mapping, when its domain is restricted to A, is a 1-to-1, onto mapping to $\Sigma^*$? And for which sets A does there exist such a…
We formalize the problem of selecting the optimal set of options for planning as that of computing the smallest set of options so that planning converges in less than a given maximum of value-iteration passes. We first show that the problem…
The general form of safe recursion (or ramified recurrence) can be expressed by an infinite graph rewrite system including unfolding graph rewrite rules introduced by Dal Lago, Martini and Zorzi, in which the size of every normal form by…
Operational semantics has established itself as a flexible but rigorous means to describe the meaning of programming languages. Oftentimes, it is felt necessary to keep a semantics small, for example to facilitate its use for model checking…
We propose a new polynomial-time deterministic algorithm that produces an approximated solution for the traveling salesperson problem. The proposed algorithm ranks cities based on their priorities calculated using a power function of means…
We propose an algorithm for quickly evaluating polynomials. It pre-conditions a complex polynomial $P$ of degree $d$ in time $O(d\log d)$, with a low multiplicative constant independent of the precision. Subsequent evaluations of $P$…