Decision Problems for Subclasses of Rational Relations over Finite and Infinite Words

We consider decision problems for relations over finite and infinite words defined by finite automata. We prove that the equivalence problem for binary deterministic rational relations over infinite words is undecidable in contrast to the case of finite words, where the problem is decidable. Furthermore, we show that it is decidable in doubly exponential time for an automatic relation over infinite words whether it is a recognizable relation. We also revisit this problem in the context of finite words and improve the complexity of the decision procedure to single exponential time. The procedure is based on a polynomial time regularity test for deterministic visibly pushdown automata, which is a result of independent interest.Comment: v1: 31 pages, submitted to DMTCS, extended version of the paper with the same title published in the conference proceedings of FCT 2017; v2: 32 pages, minor revision of v1 (DMTCS review process), results unchanged; v3: 32 pages, enabled hyperref for Figure 1; v4: 32 pages, add reference for known complexity results for the slenderness problem; v5: 32 pages, added DMTCS metadat

A primordial, mathematical, logical and computable, demonstration (proof) of the family of conjectures known as Goldbach´s

licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.In this document, by means of a novel system model and first order topological, algebraic and geometrical free-­‐context formal language (NT-­‐FS&L), first, we describe a new signature for a set of the natural numbers that is rooted in an intensional inductive de-­‐embedding process of both, the tensorial identities of the known as “natural numbers”, and the abstract framework of theirs locus-­‐positional based symbolic representations. Additionally, we describe that NT-­‐FS&L is able to: i.-­‐ Embed the De Morgan´s Laws and the FOL-­‐Peano´s Arithmetic Axiomatic. ii.-­‐ Provide new points of view and perspectives about the succession, precede and addition operations and of their abstract, topological, algebraic, analytic geometrical, computational and cognitive, formal representations. Second, by means of the inductive apparatus of NT-­‐FS&L, we proof that the family of conjectures known as Glodbach’s holds entailment and truth when the reasoning starts from the consistent and finitary axiomatic system herein describedWe wish to thank the Organic Chemistry Institute of the Spanish National Research Council (IQOG/CSIC) for its operative and technical support to the Pedro Noheda Research Group (PNRG). We also thank the Institute for Physical and Information Technologies (ITETI/CSIC) of the Spanish National Research Council for their hospitality. We also thank for their long years of dedicated and kind support Dr. Juan Martínez Armesto (VATC/CSIC), Belén Cabrero Suárez (IQOG/CSIC, Administration), Mar Caso Neira (IQOG/CENQUIOR/CSIC, Library) and David Herrero Ruíz (PNRG/IQOG/CSIC). We wish to thank to Bernabé-­‐Pajares´s brothers (Dr. Manuel Bernabé-­‐Pajares, IQOG/CSIC Structural Chemistry & Biochemistry; Magnetic Nuclear Resonance and Dr. Alberto Bernabé Pajares (Greek Philology and Indo-­‐European Linguistics/UCM), for their kind attention during numerous and kind discussions about space, time, imaging and representation of knowledge, language, transcription mistakes, myths and humans always holding us familiar illusion and passion for knowledge and intellectual progress. We wish to thank Dr. Carlos Cativiela Marín (ISQCH/UNIZAR) for his encouragement and for kind listening and attention. We wish to thank Miguel Lorca Melton for his encouragement and professional point of view as Patent Attorney. Last but not least, our gratitude to Nati, María and Jaime for the time borrowed from a loving husband and father. Finally, we apologize to many who have not been mentioned today, but to whom we are grateful. Finally, let us point out that we specially apologize to many who have been mentioned herein for any possible misunderstanding regarding the sense and intension of their philosophic, scientific and/or technical hard work and milestone ideas; we hope that at least Goldbach, Euler and Feymann do not belong to this last human´s collectivity.Peer reviewe

Recognisable languages over monads

The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of composing structures into bigger structures. It so happens that category theory has an abstract concept for this, namely a monad. The goal of this paper is to propose monads as a unifying framework for discussing existing algebras and designing new algebras

General Catalog 1998-2000

Contains course descriptions, University college calendar, and college administration.https://digitalcommons.usu.edu/universitycatalogs/1121/thumbnail.jp

General Catalog 2002-2004

Contains course descriptions, University college calendar, and college administrationhttps://digitalcommons.usu.edu/universitycatalogs/1123/thumbnail.jp

General Catalog 2007-2009

Contains course descriptions, University college calendar, and college administrationhttps://digitalcommons.usu.edu/universitycatalogs/1127/thumbnail.jp

Gabriel Vacariu (c2023 to 2014) The UNBELIEVABLE similarities between the ideas of some people (2006-2016) and my ideas (2002-2008) in physics (quantum mechanics, cosmology), cognitive neuroscience, philosophy of mind, and philosophy

Unbelievable similar ideas to my ideas published long before..

(b2023 to 2014) The UNBELIEVABLE similarities between the ideas of some people (2006-2016) and my ideas (2002-2008) in physics (quantum mechanics, cosmology), cognitive neuroscience, philosophy of mind, and philosophy (this manuscript would require a REVOLUTION in international academy environment!)

(b2023 to 2014) The UNBELIEVABLE similarities between the ideas of some people (2006-2016) and my ideas (2002-2008) in physics (quantum mechanics, cosmology), cognitive neuroscience, philosophy of mind, and philosophy (this manuscript would require a REVOLUTION in international academy environment!

(2023 to 2014) The UNBELIEVABLE similarities between the ideas of some people (2006-2016) and my ideas (2002-2008) in physics (quantum mechanics, cosmology), cognitive neuroscience, philosophy of mind, and philosophy (this manuscript would require a REVOLUTION in international academy environment!)

The main ideas of the EDWs perspective are in Gabriel Vacariu’s PhD thesis posted online by UNSW (Australia) in 2007!!! I have realized the GREATEST discovery in the history of human knowledge: the EDWs! With discovering the EDWs, I have changed everything in Philosophy, Physics and Cognitive Neuroscience! This has been the main reason, so many people have published UNBELIEVABLE similar ideas to my ideas, many years I published my first works! UNBELIEVABLE, many (hundreds) “great” or small thinkers did the same thing in 2006-2007 and later: they published the same ideas, UNBELIEVABLE similar to my ideas from 2002-2005! They believe they would be considered co-authors of the same new framework of thinking. They did not know that many “professors” would do the same thing: they plagiarized my ideas and they hurry up to published their work as soon as possible (in 2006-2007, depending when they discovered my article 2005). So, in the same 2 years, many people “discovered” the same new framework of thinking, the EDWs perspective, each of them did not think that there would be so many other people doing the same thing, that is, many people “discovered” the same new framework (the greatest challenge in the history of human thinking!) in the same period! Such coincidences (the discovery of the EDWs in the same two years!!!) are quite IMPOSSIBLE!! This is the reason nobody quoted my name, but nobody quoted any name who PLAGIARIZED my ideas… In 2006-2007, I was wondering why nobody quote my name, but in fact, they plagiarized my ideas. Nobody discovered this framework of thinking 2500 years, and in 2-3 years, many people discovered it!!!! IMPOSSIBLE!!!! There were some "professors" who published articles/chapters very close to Bohr's complementarity, Dirac, de Broglie's dualism before 2005 (for instance Carlo Rovelli 1996 or Ladyman), but their works were constructed within the "unicorn world" (Universe/world), therefore, these works had nothing in common with the EDWs perspective!!!! In reality, all of them plagiarized my ideas! It was like many people composed Beethoven Fifth’s Symphony, claiming that they never listen Beethoven! Who would be so stupid to believe them