On the Expressiveness of LARA: A Unified Language for Linear and Relational Algebra

We study the expressive power of the Lara language - a recently proposed unified model for expressing relational and linear algebra operations - both in terms of traditional database query languages and some analytic tasks often performed in machine learning pipelines. We start by showing Lara to be expressive complete with respect to first-order logic with aggregation. Since Lara is parameterized by a set of user-defined functions which allow to transform values in tables, the exact expressive power of the language depends on how these functions are defined. We distinguish two main cases depending on the level of genericity queries are enforced to satisfy. Under strong genericity assumptions the language cannot express matrix convolution, a very important operation in current machine learning operations. This language is also local, and thus cannot express operations such as matrix inverse that exhibit a recursive behavior. For expressing convolution, one can relax the genericity requirement by adding an underlying linear order on the domain. This, however, destroys locality and turns the expressive power of the language much more difficult to understand. In particular, although under complexity assumptions the resulting language can still not express matrix inverse, a proof of this fact without such assumptions seems challenging to obtain

Juan Bautista Alberdi: modernidad y modernizaciones en el siglo xix / Juan Bautista Alberdi: modernity and modernization in XIX century

El artículo distingue conceptualmente modernidad y modernizaciones en un contexto decimonónico, para luego examinar la trayectoria del pensamiento de Juan Bautista Alberdi (1810-1884), estableciendo tres etapas según el énfasis que el autor hace en distintos componentes de la modernización. Se focaliza en uno de los ensayos finales de Alberdi, su libro sobre un empresario norteamericano: La vida y los trabajos industriales de William Wheelwright en la América del Sud (1876),  texto que se analiza poniendo de relieve lo que esta etapa de su pensamiento  revela y lo que oculta.the article discusses the concepts of modernity and modernization in a decimononic context. We examine three stages in Juan Bautista Alberdi´s  thought, using as a variable the differents components of modernization. Finally the article focuses on Alberdi’s book on an american entrepreneur: Life and industrial Works of William Wheelwright in South America (1876), using this text to reveal the third and final stage of Alberdi’s thought

The Computational Complexity of Evil Hangman

The game of Hangman is a classical asymmetric two player game in which one player, the setter, chooses a secret word from a language, that the other player, the guesser, tries to discover through single letter matching queries, answered by all occurrences of this letter if any. In the Evil Hangman variant, the setter can change the secret word during the game, as long as the new choice is consistent with the information already given to the guesser. We show that a greedy strategy for Evil Hangman can perform arbitrarily far from optimal, and most importantly, that playing optimally as an Evil Hangman setter is computationally difficult. The latter result holds even assuming perfect knowledge of the language, for several classes of languages, ranging from Finite to Turing Computable. The proofs are based on reductions to Dominating Set on 3-regular graphs and to the Membership problem, combinatorial problems already known to be computationally hard

Wordle is NP-hard

Wordle is a single player word-guessing game where the goal is to discover a secret word $w$ that has been chosen from a dictionary $D$. In order to discover $w$, the player can make at most $\ell$ guesses, which must also be words from $D$, all words in $D$ having the same length $k$. After each guess, the player is notified of the positions in which their guess matches the secret word, as well as letters in the guess that appear in the secret word in a different position. We study the game of Wordle from a complexity perspective, proving NP-hardness of its natural formalization: to decide given a dictionary $D$ and an integer $\ell$ if the player can guarantee to discover the secret word within $\ell$ guesses. Moreover, we prove that hardness holds even over instances where words have length $k = 5$, and that even in this case it is NP-hard to approximate the minimum number of guesses required to guarantee discovering the secret word (beyond a certain constant). We also present results regarding its parameterized complexity and offer some related open problems.Comment: Accepted at FUN202