On regular languages determined by nondeterministic directable automata

It is known that the languages consisting of directing words of deterministic and nondeterministic automata are regular. Here these classes of regular languages are studied and compared. By introducing further three classes of regular languages, it is proved that the 8 classes considered form a semilattice with respect to intersection

Quotient Complexity of Ideal Languages

The final publication is available at Elsevier via http://dx.doi.org/10.1016/j.tcs.2012.10.055 © 2013. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/A language L over an alphabet Σ is a right (left) ideal if it satisfies L=LΣ∗ (L=Σ∗L). It is a two-sided ideal if L=Σ∗LΣ∗, and an all-sided ideal if L=Σ∗L, the shuffle of Σ∗ with L. Ideal languages are not only of interest from the theoretical point of view, but also have applications to pattern matching. We study the state complexity of common operations in the class of regular ideal languages, but prefer to use the equivalent term “quotient complexity”, which is the number of distinct left quotients of a language. We find tight upper bounds on the complexity of each type of ideal language in terms of the complexity of an arbitrary generator and of the minimal generator, and also on the complexity of the minimal generator in terms of the complexity of the language. Moreover, tight upper bounds on the complexity of union, intersection, set difference, symmetric difference, concatenation, star, and reversal of ideal languages are derived.Natural Sciences and Engineering Research Council of Canada grant [OGP0000871]VEGA grant 2/0111/0

Opinion dynamics and decision of vote in bipolar political systems

A model of the opinion dynamics underlying the political decision is proposed. The analysis is restricted to a bipolar scheme with a possible third political area. The interaction among voters is local but the final decision strongly depends on global effects such as, for example, the rating of the governments. As in the realistic case, the individual decision making process is determined by the most relevant personal interests and problems. The phenomenological analysis of the national vote in Italy and Germany has been carried out and a prediction of the next Italian vote as a function of the government rating is presented.Comment: 8 pages, 1 figure. To be published in International Journal of Modern Physics

Something to Talk About: Interactions as Descriptive Schema

A “conceptual schema” is a model or pattern of ideas imposed on reality or experience. A “descriptive schema” is a conceptual schema used to communicate. Because we use these schemas very frequently, a large amount of our knowledge comes to resemble the patterns implicit in them. Because the received descriptive schema is a linear reductionist model of the world, it is unreflective of the emergent features of interaction. I will introduce and develop a new descriptive schema based on these emergent properties of interaction rather than on the reductive properties of individual entities. I will show how this new schema fills in the descriptive gap left by the current schema. Finally, I will speculate about the implications this new schema has for understanding ourselves and the universe in which we live