Related papers: Computing with P Systems
It is common practice to compare the computational power of different models of computation. For example, the recursive functions are strictly more powerful than the primitive recursive functions, because the latter are a proper subset of…
To date, work on formalizing connectionist computation in a way that is at least Turing-complete has focused on recurrent architectures and developed equivalences to Turing machines or similar super-Turing models, which are of more…
Functioning and interaction of distributed devices and concurrent algorithms are analyzed in the context of the theory of algorithms. Our main concern here is how and under what conditions algorithmic interactive devices can be more…
The benchmark for computation is typically given as Turing computability; the ability for a computation to be performed by a Turing Machine. Many languages exploit (indirect) encodings of Turing Machines to demonstrate their ability to…
This paper is an attempt to incorporate the idea of spiking neural P systems as an early seed into the area of Operating System Design, regarding their capability to solve some classical computer science problems. It is reflecting the power…
This paper discusses "computational" systems capable of "computing" functions not computable by predefined Turing machines if the systems are not isolated from their environment. Roughly speaking, these systems can change their finite…
The $\textbf{P}$ vs. $\textbf{NP}$ problem is an important problem in contemporary mathematics and theoretical computer science. Many proofs have been proposed to this problem. This paper proposes a theoretic proof for $\textbf{P}$ vs.…
Approaching limitations of digital computing technologies have spurred research in neuromorphic and other unconventional approaches to computing. Here we argue that if we want to systematically engineer computing systems that are based on…
Probabilistic circuits (PCs) are a unifying representation for probabilistic models that support tractable inference. Numerous applications of PCs like controllable text generation depend on the ability to efficiently multiply two circuits.…
Computational problems are classified into computable and uncomputable problems. If there exists an effective procedure (algorithm) to compute a problem then the problem is computable otherwise it is uncomputable. Turing machines can…
This paper introduces a category theory-based framework to redefine physical computing in light of advancements in quantum computing and non-standard computing systems. By integrating classical definitions within this broader perspective,…
Computation is commonly defined as the execution of abstract algorithms over symbolic representations, with physical systems treated as substrates that realise predefined operations. While effective for engineered machines, this separation…
While it is well known that a Turing machine equipped with the ability to flip a fair coin cannot compute more that a standard Turing machine, we show that this is not true for a biased coin. Indeed, any oracle set $X$ may be coded as a…
Polar codes are recursive general concatenated codes. This property motivates a recursive formalization of the known decoding algorithms: Successive Cancellation, Successive Cancellation with Lists and Belief Propagation. Using such…
In this paper we give a framework for describing how abstract systems can be used to compute if no randomness or error is involved. Using this we describe a class of classical "physical" computation systems whose computational capabilities…
Chain-of-Thought (CoT) and Looped Transformers have been shown to empirically improve performance on reasoning tasks and to theoretically enhance expressivity by recursively increasing the number of computational steps. However, their…
We discuss some claims that certain UCOMP devices can perform hypercomputation (compute Turing-uncomputable functions) or perform super-Turing computation (solve NP-complete problems in polynomial time). We discover that all these claims…
Neuromorphic computing is a non-von Neumann computing paradigm that performs computation by emulating the human brain. Neuromorphic systems are extremely energy-efficient and known to consume thousands of times less power than CPUs and…
Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…
We introduce a novel scheme of quantum recursive programming, in which large unitary transformations, i.e. quantum gates, can be recursively defined using quantum case statements, which are quantum counterparts of conditionals and case…