Related papers: Some Remarks on Real-Time Turing Machines
In this paper, we consider Turing machines based on unsharp quantum logic. For a lattice-ordered quantum multiple-valued (MV) algebra E, we introduce E-valued non-deterministic Turing machines (ENTMs) and E-valued deterministic Turing…
In this paper, we have introduced the deterministic variant of parallel communicating Watson-Crick automata systems. We show that similar to the non-deterministic version, the deterministic version can also recognise some non-regular…
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…
Although temporal tagging is still dominated by rule-based systems, there have been recent attempts at neural temporal taggers. However, all of them focus on monolingual settings. In this paper, we explore multilingual methods for the…
It is well known that the "store language" of every pushdown automaton -- the set of store configurations (state and stack contents) that can appear as an intermediate step in accepting computations -- is a regular language. Here many…
There are several forms of irreducibility in computing systems, ranging from undecidability to intractability to nonlinearity. This paper is an exploration of the conceptual issues that have arisen in the course of investigating speed-up…
Results on the problem of stabilizing a nonlinear continuous-time system by a finite number of control or measurement values are presented. The basic tool is a discontinuous version of the so-called semi-global backstepping lemma. We derive…
Multiple extensions of Recurrent Neural Networks (RNNs) have been proposed recently to address the difficulty of storing information over long time periods. In this paper, we experiment with the capacity of Neural Turing Machines (NTMs) to…
This paper presents a probabilistic model validation methodology for nonlinear systems in time-domain. The proposed formulation is simple, intuitive, and accounts both deterministic and stochastic nonlinear systems with parametric and…
Modern tokenizers employ deterministic algorithms to map text into a single "canonical" token sequence, yet the same string can be encoded as many non-canonical tokenizations using the tokenizer vocabulary. In this work, we investigate the…
Designing models that are both expressive and preserve known invariances of tasks is an increasingly hard problem. Existing solutions tradeoff invariance for computational or memory resources. In this work, we show how to leverage…
Any class of languages $\mathbf{L}$ accepted in time $\mathbf{T}$ has a counterpart $\mathbf{NL}$ accepted in nondeterministic time $\mathbf{NT}$. It follows from the definition of nondeterministic languages that $\mathbf{L} \subseteq…
Mathematically, ternary coding is more efficient than binary coding. It is little used in computation because technology for binary processing is already established and the implementation of ternary coding is more complicated, but remains…
We show that equivalence of deterministic top-down tree-to-string transducers is decidable, thus solving a long standing open problem in formal language theory. We also present efficient algorithms for subclasses: polynomial time for total…
A better understanding of the emergent computation and problem-solving capabilities of recent large language models is of paramount importance to further improve them and broaden their applicability. This work investigates how a language…
In a recent paper, Altenbernd, Thomas and W\"ohrle have considered acceptance of languages of infinite two-dimensional words (infinite pictures) by finite tiling systems, with the usual acceptance conditions, such as the B\"uchi and Muller…
We prove that any Turing machine running on inputs of arbitrary length can be simulated by a constant bit-size transformer, as long as the context window is sufficiently long. This improves previous works, which require scaling up either…
Progress in language and image understanding by machines has sparkled the interest of the research community in more open-ended, holistic tasks, and refueled an old AI dream of building intelligent machines. We discuss a few prominent…
The advent of recurrent neural networks for handwriting recognition marked an important milestone reaching impressive recognition accuracies despite the great variability that we observe across different writing styles. Sequential…
We introduce a novel quantum programming language featuring higher-order programs and quantum controlflow which ensures that all qubit transformations are unitary. Our language boasts a type system guaranteeingboth unitarity and…