1,179 research outputs found
Complexity of Left-Ideal, Suffix-Closed and Suffix-Free Regular Languages
A language over an alphabet is suffix-convex if, for any words
, whenever and are in , then so is .
Suffix-convex languages include three special cases: left-ideal, suffix-closed,
and suffix-free languages. We examine complexity properties of these three
special classes of suffix-convex regular languages. In particular, we study the
quotient/state complexity of boolean operations, product (concatenation), star,
and reversal on these languages, as well as the size of their syntactic
semigroups, and the quotient complexity of their atoms.Comment: 20 pages, 11 figures, 1 table. arXiv admin note: text overlap with
arXiv:1605.0669
Large Aperiodic Semigroups
The syntactic complexity of a regular language is the size of its syntactic
semigroup. This semigroup is isomorphic to the transition semigroup of the
minimal deterministic finite automaton accepting the language, that is, to the
semigroup generated by transformations induced by non-empty words on the set of
states of the automaton. In this paper we search for the largest syntactic
semigroup of a star-free language having left quotients; equivalently, we
look for the largest transition semigroup of an aperiodic finite automaton with
states.
We introduce two new aperiodic transition semigroups. The first is generated
by transformations that change only one state; we call such transformations and
resulting semigroups unitary. In particular, we study complete unitary
semigroups which have a special structure, and we show that each maximal
unitary semigroup is complete. For there exists a complete unitary
semigroup that is larger than any aperiodic semigroup known to date.
We then present even larger aperiodic semigroups, generated by
transformations that map a non-empty subset of states to a single state; we
call such transformations and semigroups semiconstant. In particular, we
examine semiconstant tree semigroups which have a structure based on full
binary trees. The semiconstant tree semigroups are at present the best
candidates for largest aperiodic semigroups.
We also prove that is an upper bound on the state complexity of
reversal of star-free languages, and resolve an open problem about a special
case of state complexity of concatenation of star-free languages.Comment: 22 pages, 1 figure, 2 table
Symmetric Groups and Quotient Complexity of Boolean Operations
The quotient complexity of a regular language L is the number of left
quotients of L, which is the same as the state complexity of L. Suppose that L
and L' are binary regular languages with quotient complexities m and n, and
that the transition semigroups of the minimal deterministic automata accepting
L and L' are the symmetric groups S_m and S_n of degrees m and n, respectively.
Denote by o any binary boolean operation that is not a constant and not a
function of one argument only. For m,n >= 2 with (m,n) not in
{(2,2),(3,4),(4,3),(4,4)} we prove that the quotient complexity of LoL' is mn
if and only either (a) m is not equal to n or (b) m=n and the bases (ordered
pairs of generators) of S_m and S_n are not conjugate. For (m,n)\in
{(2,2),(3,4),(4,3),(4,4)} we give examples to show that this need not hold. In
proving these results we generalize the notion of uniform minimality to direct
products of automata. We also establish a non-trivial connection between
complexity of boolean operations and group theory
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
Bulletin 2220: Best Management Practices for Small Scale Poultry Producers in Maine
Written for small-scale poultry producers. University specialists, Extension educators, and agriculture service providers from New England and New York developed this list of Best Management Practices to assist small-scale poultry growers to provide the best of care for their birds, minimize losses due to disease and predation, as well as minimizing the impact on the environment while assuring a high quality, wholesome product for their family and customers.https://digitalcommons.library.umaine.edu/extension_ag/1004/thumbnail.jp
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
Static Trace-Based Deadlock Analysis for Synchronous Mini-Go
We consider the problem of static deadlock detection for programs in the Go
programming language which make use of synchronous channel communications. In
our analysis, regular expressions extended with a fork operator capture the
communication behavior of a program. Starting from a simple criterion that
characterizes traces of deadlock-free programs, we develop automata-based
methods to check for deadlock-freedom. The approach is implemented and
evaluated with a series of examples
The Magic Number Problem for Subregular Language Families
We investigate the magic number problem, that is, the question whether there
exists a minimal n-state nondeterministic finite automaton (NFA) whose
equivalent minimal deterministic finite automaton (DFA) has alpha states, for
all n and alpha satisfying n less or equal to alpha less or equal to exp(2,n).
A number alpha not satisfying this condition is called a magic number (for n).
It was shown in [11] that no magic numbers exist for general regular languages,
while in [5] trivial and non-trivial magic numbers for unary regular languages
were identified. We obtain similar results for automata accepting subregular
languages like, for example, combinational languages, star-free, prefix-,
suffix-, and infix-closed languages, and prefix-, suffix-, and infix-free
languages, showing that there are only trivial magic numbers, when they exist.
For finite languages we obtain some partial results showing that certain
numbers are non-magic.Comment: In Proceedings DCFS 2010, arXiv:1008.127
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
Probe spectroscopy in an operating magneto-optical trap: the role of Raman transitions between discrete and continuum atomic states
We report on cw measurements of probe beam absorption and four-wave-mixing
spectra in a Rb magneto-optical trap taken while the trap is in
operation. The trapping beams are used as pump light. We concentrate on the
central feature of the spectra at small pump-probe detuning and attribute its
narrow resonant structures to the superposition of Raman transitions between
light-shifted sublevels of the ground atomic state and to atomic recoil
processes. These two contributions have different dependencies on trap
parameters and we show that the former is inhomogeneously broadened. The strong
dependence of the spectra on the probe-beam polarization indicates the
existence of large optical anisotropy of the cold-atom sample, which is
attributed to the recoil effects. We point out that the recoil-induced
resonances can be isolated from other contributions, making pump-probe
spectroscopy a highly sensitive diagnostic tool for atoms in a working MOT.Comment: 9 pages, 8 figure
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