Related papers: An efficient quantifier elimination procedure for …
We demonstrate a family of propositional formulas in conjunctive normal form so that a formula of size $N$ requires size $2^{\Omega(\sqrt[7]{N/logN})}$ to refute using the tree-like OBDD refutation system of Atserias, Kolaitis and Vardi…
Variational quantum algorithms are promising applications of noisy intermediate-scale quantum (NISQ) computers. These algorithms consist of a number of separate prepare-and-measure experiments that estimate terms in a Hamiltonian. The…
A numerical method is proposed for simulation of composite open quantum systems. It is based on Lindblad master equations and adiabatic elimination. Each subsystem is assumed to converge exponentially towards a stationary subspace, slightly…
This paper gives a decision procedure for the validity of en- tailment of symbolic heaps in separation logic with Presburger arithmetic and arrays. The correctness of the decision procedure is proved under the condition that sizes of arrays…
The so-called ``adiabatic elimination'' of fast decaying degrees of freedom in open quantum systems can be performed with a series expansion in the timescale separation. The associated computations are significantly more difficult when the…
We consider Presburger arithmetic (PA) extended by scalar multiplication by an algebraic irrational number $\alpha$, and call this extension $\alpha$-Presburger arithmetic ($\alpha$-PA). We show that the complexity of deciding sentences in…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
Reversible computation requires that intermediate data be explicitly undone rather than discarded. In quantum programming, this principle appears as uncomputation, usually treated as a technical cleanup mechanism. We instead present…
We generalize the framework of virtual substitution for real quantifier elimination to arbitrary but bounded degrees. We make explicit the representation of test points in elimination sets using roots of parametric univariate polynomials…
We model the algorithmic task of geometric elimination (e.g., quantifier elimination in the elementary field theories of real and complex numbers) by means of certain constraint database queries, called geometric queries. As a particular…
We give an algorithm determining whether a hermiticity-preserving superoperator is positive. In our approach we apply techniques of quantifier elimination theory for real numbers. Furthermore, we argue that quantifier elimination theory…
We present a quantum algorithm to solve systems of linear equations of the form $A\mathbf{x}=\mathbf{b}$, where $A$ is a tridiagonal Toeplitz matrix and $\mathbf{b}$ results from discretizing an analytic function, with a circuit complexity…
In this paper we extend a decision procedure for the Boolean algebra of finite sets with cardinality constraints ($\mathcal{L}_{\lvert\cdot\rvert}$) to a decision procedure for $\mathcal{L}_{\lvert\cdot\rvert}$ extended with set terms…
This paper presents two enhancements to cylindrical algebraic decomposition (CAD) based quantifier elimination (QE) for cases in which multiple equational constraints are present in the given input formula $\phi^*$. The first enhancement…
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…
We consider the extension of two variable logic with quantifiers that state that the number of elements where a formula holds should belong to a given ultimately periodic set. We show that both satisfiability and finite satisfiability of…
This note is intended to foster a discussion about the extent to which typical problems arising in quantum information theory are algorithmically decidable (in principle rather than in practice). Various problems in the context of…
Decision procedures can be either theory-specific, e.g., Presburger arithmetic, or theory-generic, applying to an infinite number of user-definable theories. Variant satisfiability is a theory-generic procedure for quantifier-free…
In this paper we present an alternative approach to formalize the theory of logic programming. In this formalization we allow existential quantified variables and equations in queries. In opposite to standard approaches the role of answer…
A central problem in quantum computation is to understand which quantum circuits are useful for exponential speed-ups over classical computation. We address this question in the setting of query complexity and show that for almost any…