Related papers: A note on the complexity of the causal ordering pr…
Variational quantum algorithms are proposed to solve relevant computational problems on near term quantum devices. Popular versions are variational quantum eigensolvers and quantum ap- proximate optimization algorithms that solve ground…
We consider the temporal logic with since and until modalities. This temporal logic is expressively equivalent over the class of ordinals to first-order logic by Kamp's theorem. We show that it has a PSPACE-complete satisfiability problem…
We investigate the power of quantum computers when they are required to return an answer that is guaranteed to be correct after a time that is upper-bounded by a polynomial in the worst case. We show that a natural generalization of Simon's…
Discovery of causal relations is fundamental for understanding the dynamics of complex systems. While causal interactions are well defined for acyclic systems that can be separated into causally effective subsystems, a mathematical…
We develop a theory of complexity for numerical computations that takes into account the condition of the input data and allows for roundoff in the computations. We follow the lines of the theory developed by Blum, Shub, and Smale for…
In this vision paper, we explore the challenges and opportunities of a form of computation that employs an empirical (rather than a formal) approach, where the solution of a computational problem is returned as empirically most likely…
Structural equation models and Bayesian networks have been widely used to analyze causal relations between continuous variables. In such frameworks, linear acyclic models are typically used to model the datagenerating process of variables.…
Investigating the role of causal order in quantum mechanics has recently revealed that the causal distribution of events may not be a-priori well-defined in quantum theory. While this has triggered a growing interest on the theoretical…
Recent advances in artificial intelligence reveal the limits of purely predictive systems and call for a shift toward causal and collaborative reasoning. Drawing inspiration from the revolution of Grothendieck in mathematics, we introduce…
Causal modeling has long been an attractive topic for many researchers and in recent decades there has seen a surge in theoretical development and discovery algorithms. Generally discovery algorithms can be divided into two approaches:…
In the paper we present results to develop an irreducible theory of complex systems in terms of self-organization processes of prime integer relations. Based on the integers and controlled by arithmetic only the self-organization processes…
When solving the Hamiltonian path problem it seems natural to be given additional precedence constraints for the order in which the vertices are visited. For example one could decide whether a Hamiltonian path exists for a fixed starting…
We study a polynomial-time decision problem in which each input encodes a depth-$N$ causal execution in which a single non-duplicable token must traverse an ordered sequence of steps, revealing at most $O(1)$ bits of routing information at…
Abduction is a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining how the world behaves it aims at finding an explanation for some observed manifestation. In this paper we focus on propositional…
Causal discovery aims to recover information about an unobserved causal graph from the observable data it generates. Layerings are orderings of the variables which place causes before effects. In this paper, we provide ways to recover…
Effecting coordination across remote sites in a distributed system is an essential part of distributed computing, and also an inherent challenge. In 1978, an analysis of communication in asynchronous systems was suggested by Leslie Lamport.…
Causality defines the relationship between cause and effect. In multivariate time series field, this notion allows to characterize the links between several time series considering temporal lags. These phenomena are particularly important…
In this study, we present a novel constraint-based algorithm for causal structure learning specifically designed for nonlinear autoregressive time series. Our algorithm significantly reduces computational complexity compared to existing…
In this paper, we determine the complexity of the satisfiability problem for various logics obtained by adding numerical quantifiers, and other constructions, to the traditional syllogistic. In addition, we demonstrate the incompleteness of…
This is the latest in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. In the previous papers, we have proved that the sat CNF problem is polynomially reduced to the problem of finding a…