226 research outputs found
Minimal Forbidden Factors of Circular Words
Minimal forbidden factors are a useful tool for investigating properties of
words and languages. Two factorial languages are distinct if and only if they
have different (antifactorial) sets of minimal forbidden factors. There exist
algorithms for computing the minimal forbidden factors of a word, as well as of
a regular factorial language. Conversely, Crochemore et al. [IPL, 1998] gave an
algorithm that, given the trie recognizing a finite antifactorial language ,
computes a DFA recognizing the language whose set of minimal forbidden factors
is . In the same paper, they showed that the obtained DFA is minimal if the
input trie recognizes the minimal forbidden factors of a single word. We
generalize this result to the case of a circular word. We discuss several
combinatorial properties of the minimal forbidden factors of a circular word.
As a byproduct, we obtain a formal definition of the factor automaton of a
circular word. Finally, we investigate the case of minimal forbidden factors of
the circular Fibonacci words.Comment: To appear in Theoretical Computer Scienc
Degree of Sequentiality of Weighted Automata
Weighted automata (WA) are an important formalism to describe quantitative properties. Obtaining equivalent deterministic machines is a longstanding research problem. In this paper we consider WA with a set semantics, meaning that the semantics is given by the set of weights of accepting runs. We focus on multi-sequential WA that are defined as finite unions of sequential WA. The problem we address is to minimize the size of this union. We call this minimum the degree of sequentiality of (the relation realized by) the WA.
For a given positive integer k, we provide multiple characterizations of relations realized by a union of k sequential WA over an infinitary finitely generated group: a Lipschitz-like machine independent property, a pattern on the automaton (a new twinning property) and a subclass of cost register automata. When possible, we effectively translate a WA into an equivalent union of k sequential WA. We also provide a decision procedure for our twinning property for commutative computable groups thus allowing to compute the degree of sequentiality. Last, we show that these results also hold for word transducers and that the associated decision problem is PSPACE
-complete
Conjugacy and Equivalence of Weighted Automata and Functional Transducers
International audienceWe show that two equivalent K-automata are conjugate to a third one, when K is equal to B, N, Z, or any (skew) ¯eld and that the same holds true for functional tranducers as well
Characterization of mixing errors in a coupled physical biogeochemical model of the North Atlantic: implications for nonlinear estimation using Gaussian anamorphosis
In biogeochemical models coupled to ocean circulation models, vertical mixing is an important physical process which governs the nutrient supply and the plankton residence in the euphotic layer. However, vertical mixing is often poorly represented in numerical simulations because of approximate parameterizations of sub-grid scale turbulence, wind forcing errors and other mis-represented processes such as restratification by mesoscale eddies. Getting a sufficient knowledge of the nature and structure of these errors is necessary to implement appropriate data assimilation methods and to evaluate if they can be controlled by a given observation system. <br><br> In this paper, Monte Carlo simulations are conducted to study mixing errors induced by approximate wind forcings in a three-dimensional coupled physical-biogeochemical model of the North Atlantic with a 1/4&deg; horizontal resolution. An ensemble forecast involving 200 members is performed during the 1998 spring bloom, by prescribing perturbations of the wind forcing to generate mixing errors. The biogeochemical response is shown to be rather complex because of nonlinearities and threshold effects in the coupled model. The response of the surface phytoplankton depends on the region of interest and is particularly sensitive to the local stratification. In addition, the statistical relationships computed between the various physical and biogeochemical variables reflect the signature of the non-Gaussian behaviour of the system. It is shown that significant information on the ecosystem can be retrieved from observations of chlorophyll concentration or sea surface temperature if a simple nonlinear change of variables (anamorphosis) is performed by mapping separately and locally the ensemble percentiles of the distributions of each state variable on the Gaussian percentiles. The results of idealized observational updates (performed with perfect observations and neglecting horizontal correlations) indicate that the implementation of this anamorphosis method into sequential assimilation schemes can substantially improve the accuracy of the estimation with respect to classical computations based on the Gaussian assumption
Minimal Absent Words in Rooted and Unrooted Trees
We extend the theory of minimal absent words to (rooted and unrooted) trees, having edges labeled by letters from an alphabet of cardinality. We show that the set of minimal absent words of a rooted (resp. unrooted) tree T with n nodes has cardinality (resp.), and we show that these bounds are realized. Then, we exhibit algorithms to compute all minimal absent words in a rooted (resp. unrooted) tree in output-sensitive time (resp. assuming an integer alphabet of size polynomial in n
A Characterization of Bispecial Sturmian Words
A finite Sturmian word w over the alphabet {a,b} is left special (resp. right
special) if aw and bw (resp. wa and wb) are both Sturmian words. A bispecial
Sturmian word is a Sturmian word that is both left and right special. We show
as a main result that bispecial Sturmian words are exactly the maximal internal
factors of Christoffel words, that are words coding the digital approximations
of segments in the Euclidean plane. This result is an extension of the known
relation between central words and primitive Christoffel words. Our
characterization allows us to give an enumerative formula for bispecial
Sturmian words. We also investigate the minimal forbidden words for the set of
Sturmian words.Comment: Accepted to MFCS 201
On the Number of Synchronizing Colorings of Digraphs
We deal with -out-regular directed multigraphs with loops (called simply
\emph{digraphs}). The edges of such a digraph can be colored by elements of
some fixed -element set in such a way that outgoing edges of every vertex
have different colors. Such a coloring corresponds naturally to an automaton.
The road coloring theorem states that every primitive digraph has a
synchronizing coloring.
In the present paper we study how many synchronizing colorings can exist for
a digraph with vertices. We performed an extensive experimental
investigation of digraphs with small number of vertices. This was done by using
our dedicated algorithm exhaustively enumerating all small digraphs. We also
present a series of digraphs whose fraction of synchronizing colorings is equal
to , for every and the number of vertices large enough.
On the basis of our results we state several conjectures and open problems.
In particular, we conjecture that is the smallest possible fraction of
synchronizing colorings, except for a single exceptional example on 6 vertices
for .Comment: CIAA 2015. The final publication is available at
http://link.springer.com/chapter/10.1007/978-3-319-22360-5_1
On Functionality of Visibly Pushdown Transducers
Visibly pushdown transducers form a subclass of pushdown transducers that
(strictly) extends finite state transducers with a stack. Like visibly pushdown
automata, the input symbols determine the stack operations. In this paper, we
prove that functionality is decidable in PSpace for visibly pushdown
transducers. The proof is done via a pumping argument: if a word with two
outputs has a sufficiently large nesting depth, there exists a nested word with
two outputs whose nesting depth is strictly smaller. The proof uses technics of
word combinatorics. As a consequence of decidability of functionality, we also
show that equivalence of functional visibly pushdown transducers is
Exptime-Complete.Comment: 20 page
A Quadratic Upper Bound on the Size of a Synchronizing Word in One-Cluster Automata
Černý's conjecture asserts the existence of a synchronizing word of length at most (n - 1)2 for any synchronized n-state deterministic automaton. We prove a quadratic upper bound on the length of a synchronizing word for any synchronized n-state deterministic automaton satisfying the following additional property: there is a letter a such that for any pair of states p, q, one has p·ar = q·as for some integers r, s (for a state p and a word w, we denote by p·w the state reached from p by the path labeled w). As a consequence, we show that for any finite synchronized prefix code with an n-state decoder, there is a synchronizing word of length O(n2). This applies in particular to Huffman codes. © 2011 World Scientific Publishing Company
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