Related papers: Logical depth for reversible Turing machines with …
The Turing machine is one of the simple abstract computational devices that can be used to investigate the limits of computability. In this paper, they are considered from several points of view that emphasize the importance and the…
In [1] it is shown that recurrent neural networks (RNNs) can learn - in a metric entropy optimal manner - discrete time, linear time-invariant (LTI) systems. This is effected by comparing the number of bits needed to encode the…
We provide a unifying framework where artificial neural networks and their architectures can be formally described as particular cases of a general mathematical construction--machines of finite depth. Unlike neural networks, machines have a…
Reversible computing is a paradigm of computation that reflects physical reversibility, one of the fundamental microscopic laws of Nature. In this survey, we discuss topics on reversible logic elements with memory (RLEM), which can be used…
It is now widely accepted that the CMOS technology implementing irreversible logic will hit a scaling limit beyond 2016, and that the increased power dissipation is a major limiting factor. Reversible computing can potentially require…
We study the problem of truthfully scheduling $m$ tasks to $n$ selfish unrelated machines, under the objective of makespan minimization, as was introduced in the seminal work of Nisan and Ronen [STOC'99]. Closing the current gap of…
Reversible computing can reduce the energy dissipation of computation, which can improve cost-efficiency in some contexts. But the practical applicability of this method depends sensitively on the space and time overhead required by…
We describe the basic theory of infinite time Turing machines and some recent developments, including the infinite time degree theory, infinite time complexity theory, and infinite time computable model theory. We focus particularly on the…
Recently, small models with latent recursion have obtained promising results on complex reasoning tasks. These results are typically explained by the theory that such recursion increases a networks depth, allowing it to compactly emulate…
Logically constrained rewrite systems (LCTRSs) are a versatile and efficient rewriting formalism that can be used to model programs from various programming paradigms, as well as simplification systems in compilers and SMT solvers. In this…
Using nonstandard analysis, we will extend the classical Turing machines into the internal Turing machines. The internal Turing machines have the capability to work with infinite ($*$-finite) number of bits while keeping the finite…
We prove essentially optimal fine-grained lower bounds on the gap between a data structure and a partially retroactive version of the same data structure. Precisely, assuming any one of three standard conjectures, we describe a problem that…
Reversible debugging is becoming increasingly popular for locating the source of errors. This technique proposes a more natural approach to debugging, where one can explore a computation from the observable misbehaviour backwards to the…
The emphasis is made on the juxtaposition of (quantum~theorem) proving versus quantum (theorem~proving). The logical contents of verification of the statements concerning quantum systems is outlined. The Zittereingang (trembling input)…
Deep neural networks have seen tremendous success over the last years. Since the training is performed on digital hardware, in this paper, we analyze what actually can be computed on current hardware platforms modeled as Turing machines,…
We examine the minimum amount of memory for real-time, as opposed to one-way, computation accepting nonregular languages. We consider deterministic, nondeterministic and alternating machines working within strong, middle and weak space, and…
Recent progress in large language models (LLMs) has focused on test-time scaling to improve reasoning via increased inference computation, but often at the cost of efficiency. We revisit test-time behavior and uncover a simple yet…
In the last decades, great achievements have been made in the development of computing machines. However, due to exponential growth of transistor density and in particular due to tremendously increasing power consumption, researchers expect…
The aim of this paper is to undertake an experimental investigation of the trade-offs between program-size and time computational complexity. The investigation includes an exhaustive exploration and systematic study of the functions…
The Tsetlin Machine (TM) is a recent machine learning algorithm with several distinct properties, such as interpretability, simplicity, and hardware-friendliness. Although numerous empirical evaluations report on its performance, the…