Related papers: Unconventional complexity classes in unconventiona…
This paper exhibits a series of semantic characterisations of sublinear nondeterministic complexity classes. These results fall into the general domain of logic-based approaches to complexity theory and so-called implicit computational…
Cellular automata are discrete dynamical systems that consist of patterns of symbols on a grid, which change according to a locally determined transition rule. In this paper, we will consider cellular automata that arise from polynomial…
Classical machine learning algorithms often face scalability bottlenecks when they are applied to large-scale data. Such algorithms were designed to work with small data that is assumed to fit in the memory of one machine. In this report,…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
Probabilistic models based on continuous latent spaces, such as variational autoencoders, can be understood as uncountable mixture models where components depend continuously on the latent code. They have proven to be expressive tools for…
Deutsch proposed two sorts of models of quantum computers, quantum Turing machines (QTMs) and quantum circuit families (QCFs). In this paper we explore the computational powers of these models and re-examine the claim of the computational…
Computational complexity is a core theory of computer science, which dictates the degree of difficulty of computation. There are many problems with high complexity that we have to deal, which is especially true for AI. This raises a big…
Implicit computational complexity is a lively area of theoretical computer science, which aims to provide machine-independent characterizations of relevant complexity classes. % for uniformity with subsequent uses >> 1960s (but feel free to…
In this monograph, we study complexity classes that are defined using $O(\log n)$-space bounded non-deterministic Turing machines. We prove salient results of Computational Complexity in this topic such as the Immerman-Szelepcsenyi Theorem,…
We investigate the complexity of the separation problem associated to classes of regular languages. For a class C, C-separation takes two regular languages as input and asks whether there exists a third language in C which includes the…
This papers studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs). It presents a new framework using discrete ODEs as a central tool for computation and provides several implicit characterizations…
Different mathematical models of recognition processes are known. In the present paper we consider a pattern recognition algorithm as an oracle computation on a Turing machine. Such point of view seems to be useful in pattern recognition as…
We consider computations of a Turing machine subjected to noise. In every step, the action (the new state and the new content of the observed cell, the direction of the head movement) can differ from that prescribed by the transition…
A classical local cellular automaton can describe an interacting quantum field theory for fermions. We construct a simple classical automaton for a particular version of the Thirring model with imaginary coupling. This interacting fermionic…
We investigate the computational power of particle methods, a well-established class of algorit hms with applications in scientific computing and computer simulation. The computational power of a compute model determines the class of…
Metastability is a spurious mode of operation in digital signals, where an electrical signal fails to settle into a stable state within a specified time, leading to uncertainty and potentially failing downstream hardware. A system that…
Partial Differential Equations (PDEs) are fundamental tools for modeling physical phenomena, yet most PDEs of practical interest cannot be solved analytically and require numerical approximations. The feasibility of such numerical methods,…
This article introduces an analogue of permutation classes in the context of polyominoes. For both permutation classes and polyomino classes, we present an original way of characterizing them by avoidance constraints (namely, with excluded…
Computer science theory provides many different measures of complexity of a system including Kolmogorov complexity, logical depth, computational depth, and Levin complexity. However, these measures are all defined only for deterministic…
A fruitful way of obtaining meaningful, possibly concrete, algorithmically random numbers is to consider a potential behaviour of a Turing machine and its probability with respect to a measure (or semi-measure) on the input space of binary…