Related papers: How long is a Proof? - A short note
This short note contains some definitions and formulas about the power of an observable in statistically separating different classes of events.
Wittgenstein's paradoxical theses that unproved propositions are meaningless, proofs form new concepts and rules, and contradictions are of limited concern, led to a variety of interpretations, most of them centered on the rule-following…
We introduce a logic for reasoning about evidence that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete…
This paper has been withdrawn because the part concerning the definition of global hyperbolicity has already been included in an expanded and clearer way in gr-qc/0611138. The remainder will be also extended and posted.
We present a simple new method for proving that languages are not regular. We prove the correctness of the method, illustrate the ease of using the method on well-known examples of nonregular languages, and prove two additional theorems on…
The separating words problem asks for the size of the smallest DFA needed to distinguish between two words of length <= n (by accepting one and rejecting the other). In this paper we survey what is known and unknown about the problem,…
Formalizing syntactic proofs of properties of logics, programming languages, security protocols, and other formal systems is a significant challenge, in large part because of the obligation to handle name-binding correctly. We present an…
After a short review on the use of time in various branches of physics, I suggest to change the interpretation of time, from a duration to a cut. A reassessment of terminology is also required to avoid meaning traps. I also address the…
This paper has been withdrawn.
The aim of this note is to show that Poincar\'e inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincar\'e inequalities are considered, too. The proof is short and does not involve covering…
Unilateral contracts, such as terms of service, play a substantial role in modern digital life. However, few users read these documents before accepting the terms within, as they are too long and the language too complicated. We propose the…
This paper has been withdrawn by the author due to an erro thereon line -2 of page 4.
This work evidences that a sentence cannot be denominated by P and written as P IS NOT TRUE. It demonstrates that in a system in which Q denominates the sentence Q IS NOT PROVABLE it is not provable that Q is true and not provable.
Presented here are over one hundred conjectures ranging from easy to difficult, from many mathematical fields. I also summarize briefly methods and tools that have led to this collection.
The aim of this short paper is to give a practical introduction to functional interpretation of proofs for computer scientists interested in synthesis.
By changing variables in a suitable way and using dominated convergence methods, this note gives a short proof of Stirling's formula and its refinement.
We develop a semantics for logics of imperfect information with respect to general models. Then we build a proof system and prove its soundness and completeness with respect to this semantics.
The large language models (LLMs) might produce a persuasive argument within mathematical and logical fields, although such argument often includes some minor missteps, including the entire omission of side conditions, invalid inference…
This submission has been withdrawn by arXiv administration.
The goal of this short note is to provide simple proofs for the "folklore facts" on the sample complexity of learning a discrete probability distribution over a known domain of size $k$ to various distances $\varepsilon$, with error…