841 research outputs found
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
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 (boolean combination of
formulas having only 1 alternation) and (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
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
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
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 -varieties of languages to
positive -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
Mutation of Directed Graphs -- Corresponding Regular Expressions and Complexity of Their Generation
Directed graphs (DG), interpreted as state transition diagrams, are
traditionally used to represent finite-state automata (FSA). In the context of
formal languages, both FSA and regular expressions (RE) are equivalent in that
they accept and generate, respectively, type-3 (regular) languages. Based on
our previous work, this paper analyzes effects of graph manipulations on
corresponding RE. In this present, starting stage we assume that the DG under
consideration contains no cycles. Graph manipulation is performed by deleting
or inserting of nodes or arcs. Combined and/or multiple application of these
basic operators enable a great variety of transformations of DG (and
corresponding RE) that can be seen as mutants of the original DG (and
corresponding RE). DG are popular for modeling complex systems; however they
easily become intractable if the system under consideration is complex and/or
large. In such situations, we propose to switch to corresponding RE in order to
benefit from their compact format for modeling and algebraic operations for
analysis. The results of the study are of great potential interest to mutation
testing
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
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