Related papers: On the Complexity of the Tiden-Arnborg Algorithm f…
Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that,…
We present an algorithm to solve a system of diagonal polynomial equations over finite fields when the number of variables is greater than some fixed polynomial of the number of equations whose degree depends only on the degree of the…
We consider the distributed optimization problem, where a group of agents work together to optimize a common objective by communicating with neighboring agents and performing local computations. For a given algorithm, we use tools from…
The quality of enumeration algorithms is often measured by their delay, that is, the maximal time spent between the output of two distinct solutions. If the goal is to enumerate $t$ distinct solutions for any given $t$, then another…
The problem of finding a nontrivial factor of a polynomial f(x) over a finite field F_q has many known efficient, but randomized, algorithms. The deterministic complexity of this problem is a famous open question even assuming the…
Polynomial multiplication is known to have quasi-linear complexity in both the dense and the sparse cases. Yet no truly linear algorithm has been given in any case for the problem, and it is not clear whether it is even possible. This…
The $\lambda$-calculus is a handy formalism to specify the evaluation of higher-order programs. It is not very handy, however, when one interprets the specification as an execution mechanism, because terms can grow exponentially with the…
It is undecidable in general whether a given finitely presented group is word hyperbolic. We use the concept of pregroups, introduced by Stallings, to define a new class of van Kampen diagrams, which represent groups as quotients of…
Deriving the time evolution of a distribution of probability (or a probability density matrix) is a problem encountered frequently in a variety of situations: for physical time, it could be a kinetic reaction study, while identifying time…
We study the precise computational complexity of deciding satisfiability of first-order quantified formulas over the theory of fixed-size bit-vectors with binary-encoded bit-widths and constants. This problem is known to be in EXPSPACE and…
The Sylvester's denumerant \( d(t; \boldsymbol{a}) \) is a quantity that counts the number of nonnegative integer solutions to the equation \( \sum_{i=1}^{N} a_i x_i = t \), where \( \boldsymbol{a} = (a_1, \dots, a_N) \) is a sequence of…
This paper studies distributed algorithms for the extended monotropic optimization problem, which is a general convex optimization problem with a certain separable structure. The considered objective function is the sum of local convex…
Generalized from the concept of consensus, this paper considers a group of edge agreements, i.e. constraints defined for neighboring agents, in which each pair of neighboring agents is required to satisfy one edge agreement constraint. Edge…
We consider fair allocation of indivisible items under additive utilities. When the utilities can be negative, the existence and complexity of an allocation that satisfies Pareto optimality and proportionality up to one item (PROP1) is an…
We study linear problems defined on tensor products of Hilbert spaces with an additional (anti-) symmetry property. We construct a linear algorithm that uses finitely many continuous linear functionals and show an explicit formula for its…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
Deterministic one-way time-bounded multi-counter automata are studied with respect to their ability to perform reversible computations, which means that the automata are also backward deterministic and, thus, are able to uniquely step the…
The numerical integration of the Schr\"odinger equation by discretization of time is explored for the curved manifolds arising from finite representations based on evolving basis states. In particular, the unitarity of the evolution is…
So-called separation automata are in the core of several recently invented quasi-polynomial time algorithms for parity games. An explicit $q$-state separation automaton implies an algorithm for parity games with running time polynomial in…
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…