Related papers: The computational complexity of integer programmin…
Mixed-integer quadratic programming is the problem of optimizing a quadratic function over points in a polyhedral set where some of the components are restricted to be integral. In this paper, we prove that the decision version of…
In this paper we generalize N-fold integer programs and two-stage integer programs with N scenarios to N-fold 4-block decomposable integer programs. We show that for fixed blocks but variable N, these integer programs are polynomial-time…
Qualitative numerical planning is classical planning extended with non-negative real variables that can be increased or decreased "qualitatively", i.e., by positive indeterminate amounts. While deterministic planning with numerical…
The non-convex quadratic orogramming problem and the non-monotone linear complementarity problem are NP-complete problems. In this paper we first show taht the inverse problem of determinning a KKT point of the non-convex quadratic…
We prove that quantum computation is polynomially equivalent to classical probabilistic computation with an oracle for estimating the value of simple sums, quadratically signed weight enumerators. The problem of estimating these sums can be…
We convert, within polynomial-time and sequential processing, NP-Complete Problems into a problem of deciding feasibility of a given system S of linear equations with constants and coefficients of binary-variables that are 0, 1, or -1. S is…
We consider discrete bilevel optimization problems where the follower solves an integer program with a fixed number of variables. Using recent results in parametric integer programming, we present polynomial time algorithms for pure and…
We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an…
We prove that deciding whether a given input word contains as subsequence every possible permutation of integers $\{1,2,\ldots,n\}$ is coNP-complete. The coNP-completeness holds even when given the guarantee that the input word contains as…
We consider the following problem: Given a rational matrix $A \in \setQ^{m \times n}$ and a rational polyhedron $Q \subseteq\setR^{m+p}$, decide if for all vectors $b \in \setR^m$, for which there exists an integral $z \in \setZ^p$ such…
In 1978, Schaefer proved his famous dichotomy theorem for generalized satisfiability problems. He defined an infinite number of propositional satisfiability problems, showed that all these problems are either in P or NP-complete, and gave a…
We introduce a novel quantum programming language featuring higher-order programs and quantum controlflow which ensures that all qubit transformations are unitary. Our language boasts a type system guaranteeingboth unitarity and…
We show that multiplication can be done in polynomial time on a three counter machine that receives its input as the contents of two counters. The technique is generalized to functions of two variables computable by deterministic Turing…
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 study the computational complexity of fundamental problems over the $p$-adic numbers ${\mathbb Q}_p$ and the $p$-adic integers ${\mathbb Z}_p$. Gu\'epin, Haase, and Worrell proved that checking satisfiability of systems of linear…
The authors of ``A note on the complexity of a phaseless polynomial interpolation'' have shown that phaseless polynomial interpolation over $\mathbf{Q}$ is possible with $n+2$ points, where $n$ is the upper-bound on the degree of a…
Quantum computing is seeking to realize hardware-optimized algorithms for application-related computational tasks. NP (nondeterministic-polynomial-time) is a complexity class containing many important but intractable problems like the…
We consider the two categories of termination problems of quantum programs with nondeterminism: 1) Is an input of a program terminating with probability one under all schedulers? If not, how can a scheduler be synthesized to evidence the…
We show that one can enumerate the vertices of the convex hull of integer points in polytopes whose constraint matrices have bounded and nonzero subdeterminants, in time polynomial in the dimension and encoding size of the polytope. This…
The data-complexity of both satisfiability and finite satisfiability for the two-variable fragment with counting is NP-complete; the data-complexity of both query-answering and finite query-answering for the two-variable guarded fragment…