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Quantum computers hold the promise of solving certain problems that lie beyond the reach of conventional computers. However, establishing this capability, especially for impactful and meaningful problems, remains a central challenge. Here,…
Suppose we are given a computably enumerable object arise from algorithmic randomness or computable analysis. We are interested in the strength of oracles which can compute an object that approximates this c.e. object. It turns out that,…
Even if Google AI's Sycamore processor is efficient for the particular task it has been designed for it fails to deliver universal computational capacity. Furthermore, even classical devices implementing transverse homoclinic orbits realize…
The classical algorithms for online learning and decision-making have the benefit of achieving the optimal performance guarantees, but suffer from computational complexity limitations when implemented at scale. More recent sophisticated…
Many unconventional computing models, including some that appear to be quite different from traditional ones such as Turing machines, happen to characterise either the complexity class P or PSPACE when working in deterministic polynomial…
We clarify the confusion, misunderstanding and misconception that the physical finiteness of the universe, if the universe is indeed finite, would rule out all hypercomputation, the kind of computation that exceeds the Turing computability,…
Regular functions of infinite words are (partial) functions realized by deterministic two-way transducers with infinite look-ahead. Equivalently, Alur et. al. have shown that they correspond to functions realized by deterministic Muller…
Two models of integral theory based on the concept of a differential as a certain infinitesimal quantity are considered. One theory treats an infinitesimal quantity as a zero-tending sequence. The second is as an infinitesimal Hyper-real.
The article contains an outline of a possible new direction for Computability Logic (see www.csc.villanova.edu/~japaridz/CL/ ), focused on computability without infinite memory or other impossible-to-possess computational resources. The new…
One of the fundamental results in computability is the existence of well-defined functions that cannot be computed. In this paper we study the effects of data representation on computability; we show that, while for each possible way of…
While computer programs and logical theories begin by declaring the concepts of interest, be it as data types or as predicates, network computation does not allow such global declarations, and requires *concept mining* and *concept…
Dependent types allow us to express precisely what a function is intended to do. Recent work on Quantitative Type Theory (QTT) extends dependent type systems with linearity, also allowing precision in expressing when a function can run.…
We prove that omega^2 strictly bounds the iterations required for modal definable functions to reach a fixed point across all countable structures. The result corrects and extends the previously claimed result by the first and third authors…
After two decades of research on indefinite causality, a philosophical lesson emerges: the tension between operational quantum theory and dynamical spacetime physics is unbridgeable if one believes both types of theories to be fundamental.…
We show that all--instances termination of chase is undecidable. More precisely, there is no algorithm deciding, for a given set $\cal T$ consisting of Tuple Generating Dependencies (a.k.a. Datalog$^\exists$ program), whether the $\cal…
Existing query languages for data discovery exhibit system-driven designs that emphasize database features and functionality over user needs. We propose a re-prioritization of the client through an introduction of a language-driven approach…
We generalise clones, which are sets of functions $f:A^n \rightarrow A$, to sets of mappings $f:A^n \rightarrow A^m$. We formalise this and develop language that we can use to speak about it. We then look at bijective mappings, which have…
This work establishes a rigorous theoretical foundation for analyzing deep learning systems by leveraging Infinite Time Turing Machines (ITTMs), which extend classical computation into transfinite ordinal steps. Using ITTMs, we reinterpret…
We revisit evaluation of logical formulas that allow both uninterpreted relations, constrained to be finite, as well as an interpreted vocabulary over an infinite domain. This formalism was denoted embedded finite model theory in the past.…
This paper clarifies the picture about Dense-choice Counter Machines, which have been less studied than (discrete) Counter Machines. We revisit the definition of "Dense Counter Machines" so that it now extends (discrete) Counter Machines,…