Related papers: Polynomial Path Orders
Probabilistic circuits compute multilinear polynomials that represent multivariate probability distributions. They are tractable models that support efficient marginal inference. However, various polynomial semantics have been considered in…
Tail recursive functions allow for a wider range of optimisations than general recursive functions. For this reason, much research has gone into the transformation and optimisation of this family of functions, in particular those written in…
This work considers polynomial optimization problems where the objective admits a low-rank canonical polyadic tensor decomposition. We introduce LRPOP (low-rank polynomial optimization), a new hierarchy of semidefinite programming…
A backdoor set is a set of variables of a propositional formula such that fixing the truth values of the variables in the backdoor set moves the formula into some polynomial-time decidable class. If we know a small backdoor set we can…
Recombining trinomial trees are a workhorse for modeling discrete-event systems in option pricing, logistics, and feedback control. Because each node stores a state-dependent quantity, a depth-$D$ tree naively yields $\mathcal{O}(3^{D})$…
We consider a capacitated job shop problem with order acceptance. This research is motivated by the management of a research and development project pipeline for a company in the agricultural industry whose success depends on regularly…
We introduce the method of path-sums which is a tool for exactly evaluating a function of a discrete matrix with possibly non-commuting entries, based on the closed-form resummation of infinite families of terms in the corresponding Taylor…
We prove that orthogonal constructor term rewrite systems and lambda-calculus with weak (i.e., no reduction is allowed under the scope of a lambda-abstraction) call-by-value reduction can simulate each other with a linear overhead. In…
We study a scheduling problem in which jobs may be split into parts, where the parts of a split job may be processed simultaneously on more than one machine. Each part of a job requires a setup time, however, on the machine where the job…
A basic model in sequential decision making is the Markov decision process (MDP), which is extended to Robust MDPs (RMDPs) by allowing uncertainty in transition probabilities and optimizing against the worst-case transition probabilities…
Rule set learning has long been studied and has recently been frequently revisited due to the need for interpretable models. Still, existing methods have several shortcomings: 1) most recent methods require a binary feature matrix as input,…
Interpreting three-leaf binary trees or {\em rooted triples} as constraints yields an entailment relation, whereby binary trees satisfying some rooted triples must also thus satisfy others, and thence a closure operator, which is known to…
We examine two different ways of encoding a counting function, as a rational generating function and explicitly as a function (defined piecewise using the greatest integer function). We prove that, if the degree and number of input…
We investigate the relationship between several enumeration complexity classes and focus in particular on problems having enumeration algorithms with incremental and polynomial delay (IncP and DelayP respectively). We show that, for some…
Conformal prediction (CP) quantifies the uncertainty of machine learning models by constructing sets of plausible outputs. These sets are constructed by leveraging a so-called conformity score, a quantity computed using the input point of…
It is well known that modal satisfiability is PSPACE-complete (Ladner 1977). However, the complexity may decrease if we restrict the set of propositional operators used. Note that there exist an infinite number of propositional operators,…
We introduce the topological complexity of the work map associated to a robot system. In broad terms, this measures the complexity of any algorithm controlling, not just the motion of the configuration space of the given system, but the…
We define a compilation scheme for a constructor-based, strongly-sequential, graph rewriting system which shortcuts some needed steps. The object code is another constructor-based graph rewriting system. This system is normalizing for the…
The analysis of observable phenomena (for instance, in biology or physics) allows the detection of dynamical behaviors and, conversely, starting from a desired behavior allows the design of objects exhibiting that behavior in engineering.…
We study the problem of verifiable polynomial evaluation in the user-server and multi-party setups. We propose {INTERPOL}, an information-theoretically verifiable algorithm that allows a user to delegate the evaluation of a polynomial to a…