Related papers: A New Term Rewriting Characterisation of ETIME fun…
We study a natural variant of scheduling that we call \emph{partial scheduling}: In this variant an instance of a scheduling problem along with an integer $k$ is given and one seeks an optimal schedule where not all, but only $k$ jobs, have…
Throughout this article we develop and change the definitions and the ideas in "arXiv:1006.4939", in order to consider the efficiency of functions and complexity time problems. The central idea here is effective enumeration and listing, and…
We introduce syntactic restrictions of the lexicographic path ordering to obtain the Light Lexicographic Path Ordering. We show that the light lexicographic path ordering leads to a characterisation of the functions computable in space…
A sound and complete algorithm for nominal unification of higher-order expressions with a recursive let is described, and shown to run in non-deterministic polynomial time. We also explore specializations like nominal letrec-matching for…
In this paper, we begin the exploration of vertex-ordering problems through the lens of exponential-time approximation algorithms. In particular, we ask the following question: Can we simultaneously beat the running times of the fastest…
Measuring how quickly iterative methods converge is essential in computational mathematics, but current approaches have significant limitations. Q-order analysis requires strict smoothness conditions, while R-order analysis lacks precision…
Polynomial optimization encompasses a broad class of problems in which both the objective function and constraints are polynomial functions of the decision variables. In recent years, a substantial body of research has focused on…
We generalise the termination method of higher-order polynomial interpretations to a setting with impredicative polymorphism. Instead of using weakly monotonic functionals, we interpret terms in a suitable extension of System F-omega. This…
The field of fine-grained complexity aims at proving conditional lower bounds on the time complexity of computational problems. One of the most popular assumptions, Strong Exponential Time Hypothesis (SETH), implies that SAT cannot be…
Reverse engineers would acquire valuable insights from descriptive function names, which are absent in publicly released binaries. Recent advances in binary function name prediction using data-driven machine learning show promise. However,…
We propose an extension of the framework for discussing the computational complexity of problems involving uncountably many objects, such as real numbers, sets and functions, that can be represented only through approximation. The key idea…
An important objective in scheduling literature is to minimize the sum of weighted flow times. We are given a set of jobs where each job is characterized by a release time, a processing time, and a weight. Our goal is to find a preemptive…
We define an enumerative function F(n,k,P,m) which is a generalization of binomial coefficients. Special cases of this function are also power function, factorials, rising factorials and falling factorials. The first section of the paper is…
The Product of Exponentials (PoE) formula is a mathematical tool that is used extensively in robotics. The virtue of using the exponential mapping, Lie Algebra and screw theory is that it allows an elegant and concise way of describing the…
In automated complexity analysis, noninterference-based type systems statically guarantee, via soundness, the property that well-typed programs compute functions of a given complexity class, e.g., the class FP of functions computable in…
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…
The best deterministic unconditionally proven integer factorization algorithms have exponential running time complexities of O(N^(1/4)) arithmetic operations, and conditional on the Riemann hypothesis, there is a deterministic algorithm of…
Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…
Quantum computing has been studied over the past four decades based on two computational models of quantum circuits and quantum Turing machines. To capture quantum polynomial-time computability, a new recursion-theoretic approach was taken…
The search for a logic capturing PTIME is a long standing open problem in finite model theory. One of the most promising candidate logics for this is Choiceless Polynomial Time with counting (CPT). Abstractly speaking, CPT is an…