Checking Whether an Automaton Is Monotonic Is NP-complete

An automaton is monotonic if its states can be arranged in a linear order that is preserved by the action of every letter. We prove that the problem of deciding whether a given automaton is monotonic is NP-complete. The same result is obtained for oriented automata, whose states can be arranged in a cyclic order. Moreover, both problems remain hard under the restriction to binary input alphabets.Comment: 13 pages, 4 figures. CIAA 2015. The final publication is available at http://link.springer.com/chapter/10.1007/978-3-319-22360-5_2

Testing the Equivalence of Regular Languages

The minimal deterministic finite automaton is generally used to determine regular languages equality. Antimirov and Mosses proposed a rewrite system for deciding regular expressions equivalence of which Almeida et al. presented an improved variant. Hopcroft and Karp proposed an almost linear algorithm for testing the equivalence of two deterministic finite automata that avoids minimisation. In this paper we improve the best-case running time, present an extension of this algorithm to non-deterministic finite automata, and establish a relationship between this algorithm and the one proposed in Almeida et al. We also present some experimental comparative results. All these algorithms are closely related with the recent coalgebraic approach to automata proposed by Rutten

Data Portraits and Intermediary Topics: Encouraging Exploration of Politically Diverse Profiles

In micro-blogging platforms, people connect and interact with others. However, due to cognitive biases, they tend to interact with like-minded people and read agreeable information only. Many efforts to make people connect with those who think differently have not worked well. In this paper, we hypothesize, first, that previous approaches have not worked because they have been direct -- they have tried to explicitly connect people with those having opposing views on sensitive issues. Second, that neither recommendation or presentation of information by themselves are enough to encourage behavioral change. We propose a platform that mixes a recommender algorithm and a visualization-based user interface to explore recommendations. It recommends politically diverse profiles in terms of distance of latent topics, and displays those recommendations in a visual representation of each user's personal content. We performed an "in the wild" evaluation of this platform, and found that people explored more recommendations when using a biased algorithm instead of ours. In line with our hypothesis, we also found that the mixture of our recommender algorithm and our user interface, allowed politically interested users to exhibit an unbiased exploration of the recommended profiles. Finally, our results contribute insights in two aspects: first, which individual differences are important when designing platforms aimed at behavioral change; and second, which algorithms and user interfaces should be mixed to help users avoid cognitive mechanisms that lead to biased behavior.Comment: 12 pages, 7 figures. To be presented at ACM Intelligent User Interfaces 201

Quotient Complexity of Regular Languages

The past research on the state complexity of operations on regular languages is examined, and a new approach based on an old method (derivatives of regular expressions) is presented. Since state complexity is a property of a language, it is appropriate to define it in formal-language terms as the number of distinct quotients of the language, and to call it "quotient complexity". The problem of finding the quotient complexity of a language f(K,L) is considered, where K and L are regular languages and f is a regular operation, for example, union or concatenation. Since quotients can be represented by derivatives, one can find a formula for the typical quotient of f(K,L) in terms of the quotients of K and L. To obtain an upper bound on the number of quotients of f(K,L) all one has to do is count how many such quotients are possible, and this makes automaton constructions unnecessary. The advantages of this point of view are illustrated by many examples. Moreover, new general observations are presented to help in the estimation of the upper bounds on quotient complexity of regular operations

Going higher in the First-order Quantifier Alternation Hierarchy on Words

We investigate the quantifier alternation hierarchy in first-order logic on finite words. Levels in this hierarchy are defined by counting the number of quantifier alternations in formulas. We prove that one can decide membership of a regular language to the levels $\mathcal{B}\Sigma_2$ (boolean combination of formulas having only 1 alternation) and $\Sigma_3$ (formulas having only 2 alternations beginning with an existential block). Our proof works by considering a deeper problem, called separation, which, once solved for lower levels, allows us to solve membership for higher levels

Delineation of a unique protein-protein interaction site on the surface of the estrogen receptor

Recent studies have identified a series of estrogen receptor (ER)interacting peptides that recognize sites that are distinct from the classic coregulator recruitment (AF2) region. Here, we report the structural and functional characterization of an ER alpha-specific peptide that binds to the liganded receptor in an AF2-independent manner. The 2-angstrom crystal structure of the ER/peptide complex reveals a binding site that is centered on a shallow depression on the beta-hairpin face of the ligand-binding domain. The peptide binds in an unusual extended conformation and makes multiple contacts with the ligand-binding domain. The location and architecture of the binding site provides an insight into the peptide's ER subtype specificity and ligand interaction preferences. In vivo, an engineered coactivator containing the peptide motif is able to strongly enhance the transcriptional activity of liganded ER alpha, particularly in the presence of 4-hydroxytamoxifen. Furthermore, disruption of this binding surface alters ER's response to the coregulator TIF2. Together, these results indicate that this previously unknown interaction site represents a bona fide control surface involved in regulating receptor activity

On Varieties of Ordered Automata

The Eilenberg correspondence relates varieties of regular languages to pseudovarieties of finite monoids. Various modifications of this correspondence have been found with more general classes of regular languages on one hand and classes of more complex algebraic structures on the other hand. It is also possible to consider classes of automata instead of algebraic structures as a natural counterpart of classes of languages. Here we deal with the correspondence relating positive $\mathcal C$-varieties of languages to positive $\mathcal C$-varieties of ordered automata and we present various specific instances of this correspondence. These bring certain well-known results from a new perspective and also some new observations. Moreover, complexity aspects of the membership problem are discussed both in the particular examples and in a general setting