Related papers: Betwixt Turing and Kleene
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 Church-Turing thesis states that any sufficiently powerful computational model which captures the notion of algorithm is computationally equivalent to the Turing machine. This equivalence usually holds both at a computability level and…
Existing models of computation, such as a Turing machine (hereafter, TM), do not consider the agent involved in interpreting the outcome of the computation. We argue that a TM, or any other computation model, has no significance if its…
In this paper, the space complexity of nonuniform quantum computations is investigated. The model chosen for this are quantum branching programs, which provide a graphic description of sequential quantum algorithms. In the first part of the…
Demonstrating quantum advantage in machine learning tasks requires navigating a complex landscape of proposed models and algorithms. To bring clarity to this search, we introduce a framework that connects the structure of parametrized…
Encodings, that is, injective functions from words to words, have been studied extensively in several settings. In computability theory the notion of encoding is crucial for defining computability on arbitrary domains, as well as for…
The TTE approach to Computable Analysis is the study of so-called representations (encodings for continuous objects such as reals, functions, and sets) with respect to the notions of computability they induce. A rich variety of such…
The present paper introduces a novel notion of `(effective) computability', called viability, of strategies in game semantics in an intrinsic (i.e., without recourse to the standard Church-Turing computability), non-inductive and…
Our main models of computation (the Turing Machine and the RAM) make fundamental assumptions about which primitive operations are realizable. The consensus is that these include logical operations like conjunction, disjunction and negation,…
Non-monotone inductive definitions were studied in the late 1960's and early 1970's with the aim of understanding connections between the complexity of the formulas defining the induction steps and the size of the ordinals measuring the…
A fundamental question is whether Turing machines can model all reasoning processes. We introduce an existence principle stating that the perception of the physical existence of any Turing program can serve as a physical causation for the…
We present a Coq library about Kleene algebra with tests, including a proof of their completeness over the appropriate notion of languages, a decision procedure for their equational theory, and tools for exploiting hypotheses of a…
Finding a concrete use case for quantum computers in the near term is still an open question, with machine learning typically touted as one of the first fields which will be impacted by quantum technologies. In this work, we investigate and…
In the first of this pair of papers, it was proven that that no physical computer can correctly carry out all computational tasks that can be posed to it. The generality of this result follows from its use of a novel definition of…
The (meta)logic underlying classical theory of computation is Boolean (two-valued) logic. Quantum logic was proposed by Birkhoff and von Neumann as a logic of quantum mechanics more than sixty years ago. The major difference between Boolean…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…
Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the…
We initiate a formal study of logical inferences in context of the measure problem in cosmology or what we call cosmic logic. We describe a simple computational model of cosmic logic suitable for analysis of, for example, discretized…
We prove the Jordan curve theorem by generalizing the sweepline algorithm for trapezoidal decomposition of a polygon. Our proof uses Zorn's lemma (or, equivalently the axiom of choice). Though several proofs have been given for the Jordan…
The unit-derived method in coding theory is shown to be a unique optimal scheme for constructing and analysing codes. In many cases efficient and practical decoding methods are produced. Codes with efficient decoding algorithms at maximal…