Related papers: On low for speed oracles
We consider the computation of Bernoulli, Tangent (zag), and Secant (zig or Euler) numbers. In particular, we give asymptotically fast algorithms for computing the first n such numbers in O(n^2.(log n)^(2+o(1))) bit-operations. We also give…
Extending the lambda-calculus with a construct for sharing, such as let expressions, enables a special representation of terms: iterated applications are decomposed by introducing sharing points in between any two of them, reducing to the…
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…
Grover's algorithm is a primary algorithm offered as evidence that quantum computers can provide an advantage over classical computers. It involves an "oracle" specified for a given application whose structure is not part of the formal…
The work is devoted to Computability Logic (CoL) -- the philosophical/mathematical platform and long-term project for redeveloping classical logic after replacing truth} by computability in its underlying semantics (see…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…
Pairwise "same-cluster" queries are one of the most widely used forms of supervision in semi-supervised clustering. However, it is impractical to ask human oracles to answer every query correctly. In this paper, we study the influence of…
We revisit the question (most famously) initiated by Turing: can human intelligence be completely modeled by a Turing machine? We show that the answer is \emph{no}, assuming a certain weak soundness hypothesis. More specifically we show…
In this paper we explore fundamental concepts in computational complexity theory and the boundaries of algorithmic decidability. We examine the relationship between complexity classes \textbf{P} and \textbf{NP}, where $L \in \textbf{P}$…
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…
This paper establishes for the first time the predictive performance of speed priors and their computational complexity. A speed prior is essentially a probability distribution that puts low probability on strings that are not efficiently…
A proof of quantumness is a protocol through which a classical machine can test whether a purportedly quantum device, with comparable time and memory resources, is performing a computation that is impossible for classical computers.…
Large language models achieve strong reasoning performance, but inference strategies such as Self-Consistency (SC) are computationally expensive, as they fully expand all reasoning traces. We introduce PoLR (Path of Least Resistance), the…
It is an established fact that for many of the interesting problems quantum algorithms based on queries of the standard oracle bring no significant improvement in comparison to known classical algorithms. It is conceivable that there are…
Can a computer which runs for time $\omega^2$ compute more than one which runs for time $\omega$? No. Not, at least, for the infinite computer we describe. Our computer gets more powerful when the set of its steps gets larger. We prove that…
Linear temporal logic (LTL) is a specification language for finite sequences (called traces) widely used in program verification, motion planning in robotics, process mining, and many other areas. We consider the problem of learning LTL…
To expand a fundamental theory of context-free languages, we equip nondeterministic one-way pushdown automata with additional oracle mechanisms, which naturally induce various nondeterministic reducibilities among formal languages. As a…
Algorithms with unitary oracles can be nested, which makes them extremely versatile. An example is the phase estimation algorithm used in many candidate algorithms for quantum speed-up. The search for new quantum algorithms benefits from…
Let $f$ denote length preserving function on words. A classical algorithm can be considered as $T$ iterated applications of black box representing $f$, beginning with input word $x$ of length $n$. It is proved that if $T=O(2^{n/(7+e)}), e…
Finding the global minimum of non-convex functions is one of the main and most difficult problems in modern optimization. In the first part of the paper, we consider a certain class of "good" non-convex functions that can be bounded above…