Related papers: Unconventional complexity classes in unconventiona…
Applications that require substantial computational resources today cannot avoid the use of heavily parallel machines. Embracing the opportunities of parallel computing and especially the possibilities provided by a new generation of…
A pseudoclassical model for P,T-invariant system of topologically massive U(1) gauge fields is analyzed. The model demonstrates a nontrivial relationship between continuous and discrete symmetries and reveals a phenomenon of ``classical…
We present characterisations of "exact" gap-definable classes, in terms of indeterministic models of computation which slightly modify the standard model of quantum computation. This follows on work of Aaronson [arXiv:quant-ph/0412187], who…
We propose a measure based upon the fundamental theoretical concept in algorithmic information theory that provides a natural approach to the problem of evaluating $n$-dimensional complexity by using an $n$-dimensional deterministic Turing…
We propose reactive Turing machines (RTMs), extending classical Turing machines with a process-theoretical notion of interaction, and use it to define a notion of executable transition system. We show that every computable transition system…
Infinite words, also known as streams, hold significant interest in computer science and mathematics, raising the natural question of how their complexity should be measured. We introduce cellular automaton reducibility as a measure of…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
Time-space tradeoff has been studied in a variety of models, such as Turing machines, branching programs, and finite automata, etc. While communication complexity as a technique has been applied to study finite automata, it seems it has not…
Turing machines and register machines have been used for decades in theoretical computer science as abstract models of computation. Also the $\lambda$-calculus has played a central role in this domain as it allows to focus on the notion of…
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…
The worst-case complexity of group-theoretic algorithms has been studied for a long time. Generic-case complexity, or complexity on random inputs, was introduced and studied relatively recently. In this paper, we address the average-case…
Quantum computing is concerned with computer technology based on the principles of quantum mechanics, with operations performed at the quantum level. Quantum computational models make it possible to analyze the resources required for…
One of the aims of Implicit Computational Complexity is the design of programming languages with bounded computational complexity; indeed, guaranteeing and certifying a limited resources usage is of central importance for various aspects of…
The article provides the theoretical framework of Probabilistic Shoenfield Machines (PSMs), an extension of the classical Shoenfield Machine that models randomness in the computation process. PSMs are introduced in contexts where…
The lambda-calculus is a peculiar computational model whose definition does not come with a notion of machine. Unsurprisingly, implementations of the lambda-calculus have been studied for decades. Abstract machines are implementations…
We present an original model of paraconsistent Turing machines (PTMs), a generalization of the classical Turing machines model of computation using a paraconsistent logic. Next, we briefl y describe the standard models of quantum…
Algorithms which learn environments represented by automata in the past have had complexity scaling with the number of states in the automaton, which can be exponentially large even for automata recognizing regular expressions with a small…
The well-known Turing machine is an example of a theoretical digital computer, and it was the logical basis of constructing real electronic computers. In the present paper we propose an alternative, namely, by formalising arithmetic…
A probabilistic database with attribute-level uncertainty consists of relations where cells of some attributes may hold probability distributions rather than deterministic content. Such databases arise, implicitly or explicitly, in the…
Descriptive complexity may be useful to design programs in a natural declarative way. This is important for parallel computation models such as cellular automata, because designing parallel programs is considered difficult. Our paper…