‎in this paper some properties of weak regular injectivity for $s$-posets‎, ‎where $s$ is a pomonoid‎, ‎are studied‎. ‎the behaviour‎ ‎of different kinds of weak regular injectivity with products‎, ‎coproducts and direct sums is considered‎. ‎also‎, ‎some‎ ‎characterizations of pomonoids over which all $s$-posets are of‎ ‎some kind of weakly regular injective are obtained‎. ‎further‎, ‎we‎ ‎giv...

We present a method for the detection and representation of polysemous nouns, a phenomenon that has received little attention in NLP. The method is based on the exploitation of the semantic information preserved in Word Embeddings. We first prove that polysemous nouns instantiating a particular sense alternation form a separate class when clustering nouns in a lexicon. Such a class, however, do...

An n-ary query over trees takes an input tree t and returns a set of ntuples of the nodes of t. In this paper, a compact data structure is introduced for representing the answer sets of n-ary queries defined by tree automata. Despite that the number of the elements of the answer set can be as large as |t|, our representation allows to store the set using only O(3|t|) space. Several basic operat...

We follow language theoretic approach to synchronizing automata and Černý’s conjecture initiated in a series of recent papers. We find a precise lower bound for the reset complexity of a principal ideal languages. Also we show a strict connection between principal left ideals and synchronizing automata. We characterize regular languages whose minimal deterministic finite automaton is synchroniz...

Naturalistic textures with an intermediate degree of statistical regularity can capture key structural features of natural images (Freeman and Simoncelli, 2011). V2 and later visual areas are sensitive to these features, while primary visual cortex is not (Freeman et al., 2013). Here we expand on this work by investigating a class of textures that have maximal formal regularity, the 17 crystall...

We present a new technique to encode a deterministic nite automaton (DFA). Based on the speciic properties of Glushkov's nondeterministic nite automaton (NFA) construction algorithm, we are able to encode the DFA using (m + 1)(2 m+1 + jj) bits, where m is the number of characters (excluding operator symbols) in the regular expression and is the alphabet. This compares favorably against the wors...

We present a uniform version of Di Nola Theorem, this enables to embed all MV-algebras of a bounded cardinality in an algebra of functions with values in a single non-standard ultrapower of the real interval [0, 1]. This result also implies the existence, for any cardinal α, of a single MValgebra in which all infinite MV-algebras of cardinality at most α embed. Recasting the above construction ...

Abstract. We consider semidefinite programming problems on which a permutation group is acting. We describe a general technique to reduce the size of such problems, exploiting the symmetry. The technique is based on a low-order matrix ∗-representation of the commutant (centralizer ring) of the matrix algebra generated by the permutation matrices. We apply it to extending a method of de Klerk et...