Related papers: A Measure of Space for Computing over the Reals
Let $\RR$ be a real closed field (e.g. the field of real numbers) and $\mathscr{S} \subset \RR^n$ be a semi-algebraic set defined as the set of points in $\RR^n$ satisfying a system of $s$ equalities and inequalities of multivariate…
We analyse the complexity of the satisfiability problem ssmSAT for State Space Models (SSM), which asks whether an input sequence can lead the model to an accepting configuration. We find that ssmSAT is undecidable in general, reflecting…
Computational feasibility is a widespread concern that guides the framing and modeling of biological and artificial intelligence. The specification of cognitive system capacities is often shaped by unexamined intuitive assumptions about the…
We study a class of functional problems reducible to computing $f^{(n)}(x)$ for inputs $n$ and $x$, where $f$ is a polynomial-time bijection. As we prove, the definition is robust against variations in the type of reduction used in its…
In several applications, input samples are more naturally represented in terms of similarities between each other, rather than in terms of feature vectors. In these settings, machine-learning algorithms can become very computationally…
In many learning theory problems, a central role is played by a hypothesis class: we might assume that the data is labeled according to a hypothesis in the class (usually referred to as the realizable setting), or we might evaluate the…
Robustness is a correctness notion for concurrent programs running under relaxed consistency models. The task is to check that the relaxed behavior coincides (up to traces) with sequential consistency (SC). Although computationally simple…
Modal logics are widely used in computer science. The complexity of modal satisfiability problems has been investigated since the 1970s, usually proving results on a case-by-case basis. We prove a very general classification for a wide…
Linearizability and progress properties are key correctness notions for concurrent objects. However, model checking linearizability has suffered from the PSPACE-hardness of the trace inclusion problem. This paper proposes to exploit…
Probabilistic Circuits (PCs) are a class of generative models that allow exact and tractable inference for a wide range of queries. While recent developments have enabled the learning of deep and expressive PCs, this increased capacity can…
It is known that the satisfiability problems of the product logics K4xS5 and S4xS5 and of the logic SSL of subset spaces are in N2EXPTIME. We improve this upper bound for the complexity of these problems by presenting ESPACE-algorithms for…
Equivalence checking of quantum circuits is a central verification task in quantum computing, ensuring the correctness of circuit optimizations, hardware mappings, and compilation pipelines. Among the primary symbolic methods for this…
We extend the framework by Kawamura and Cook for investigating computational complexity for operators occurring in analysis. This model is based on second-order complexity theory for functions on the Baire space, which is lifted to metric…
We provide a sparse version of the bounded degree SOS hierarchy BSOS [7] for polynomial optimization problems. It permits to treat large scale problems which satisfy a structured sparsity pattern. When the sparsity pattern satisfies the…
We study formal languages which are capable of fully expressing quantitative probabilistic reasoning and do-calculus reasoning for causal effects, from a computational complexity perspective. We focus on satisfiability problems whose…
Real-world systems, from aerospace to railway engineering, are modeled with partial differential equations (PDEs) describing the physics of the system. Estimating robust solutions for such problems is essential. Deep learning-based…
We give some reductions among problems in (nonnegative) weighted #CSP which restrict the class of functions that needs to be considered in computational complexity studies. Our reductions can be applied to both exact and approximate…
The \(L_1/L_2\) norm ratio has gained significant attention as a measure of sparsity due to three merits: sharper approximation to the \(L_0\) norm compared to the \(L_1\) norm, being parameter-free and scale-invariant, and exceptional…
Simulation of conditional master equations is important to describe systems under continuous measurement and for the design of control strategies in quantum systems. For large bosonic systems, such as BEC and atom lasers, full quantum field…
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a…