97 research outputs found
Interactive L systems with almost interactionless behaviour
A restricted version of interactive L systems is introduced. A P2L system is called an essentially growing 2L-systems (e-G2L system) if every length-preserving production is interactionless (context-free). It is shown that the deterministic e-G2L systems can be simulated by codings of propagating interactionless systems, and that this is not possible for the nondeterministic version. Some interesting properties of e-GD2L systems are established, the main result being the decidability of the sequence equivalence problem for them
Locally Periodic Versus Globally Periodic Infinite Words
AbstractWe call a one-way infinite word w over a finite alphabet (ρ,l)-repetitive if all long enough prefixes of w contain as a suffix a ρth power (or more generally a repetition of order ρ) of a word of length at most l. We show that each (2,4)-repetitive word is ultimately periodic, as well as that there exist continuum many, and hence also nonultimately periodic, (2,5)-repetitive words. Further, we characterize nonultimately periodic (2,5)-repetitive words both structurally and algebraically
k-Abelian Pattern Matching
Two words are called -abelian equivalent, if they share the same multiplicities for all factors of length at most . We present an optimal linear time algorithm for identifying all occurrences of factors in a text that are -abelian equivalent to some pattern. Moreover, an optimal algorithm for finding the largest for which two words are -abelian equivalent is given. Solutions for various online versions of the -abelian pattern matching problem are also proposed
Degrees of infinite words, polynomials and atoms
Our objects of study are finite state transducers and their power for transforming infinite words. Infinite sequences of symbols are of paramount i
Transition Property For Cube-Free Words
We study cube-free words over arbitrary non-unary finite alphabets and prove
the following structural property: for every pair of -ary cube-free
words, if can be infinitely extended to the right and can be infinitely
extended to the left respecting the cube-freeness property, then there exists a
"transition" word over the same alphabet such that is cube free. The
crucial case is the case of the binary alphabet, analyzed in the central part
of the paper.
The obtained "transition property", together with the developed technique,
allowed us to solve cube-free versions of three old open problems by Restivo
and Salemi. Besides, it has some further implications for combinatorics on
words; e.g., it implies the existence of infinite cube-free words of very big
subword (factor) complexity.Comment: 14 pages, 5 figure
Computing the -binomial complexity of the Thue--Morse word
Two words are -binomially equivalent whenever they share the same
subwords, i.e., subsequences, of length at most with the same
multiplicities. This is a refinement of both abelian equivalence and the Simon
congruence. The -binomial complexity of an infinite word maps
the integer to the number of classes in the quotient, by this -binomial
equivalence relation, of the set of factors of length occurring in
. This complexity measure has not been investigated very much. In
this paper, we characterize the -binomial complexity of the Thue--Morse
word. The result is striking, compared to more familiar complexity functions.
Although the Thue--Morse word is aperiodic, its -binomial complexity
eventually takes only two values. In this paper, we first obtain general
results about the number of occurrences of subwords appearing in iterates of
the form for an arbitrary morphism . We also thoroughly
describe the factors of the Thue--Morse word by introducing a relevant new
equivalence relation
A Sufficient Condition for Hanna Neumann Property of Submonoids of a Free Monoid
Using automata-theoretic approach, Giambruno and Restivo have investigated on
the intersection of two finitely generated submonoids of the free monoid over a
finite alphabet. In particular, they have obtained Hanna Neumann property for a
special class of submonoids generated by finite prefix sets. This work
continues their work and provides a sufficient condition for Hanna Neumann
property for the entire class of submonoids generated by finite prefix sets. In
this connection, a general rank formula for the submonoids which are accepted
by semi-flower automata is also obtained
On Solving Word Equations Using SAT
We present Woorpje, a string solver for bounded word equations (i.e.,
equations where the length of each variable is upper bounded by a given
integer). Our algorithm works by reformulating the satisfiability of bounded
word equations as a reachability problem for nondeterministic finite automata,
and then carefully encoding this as a propositional satisfiability problem,
which we then solve using the well-known Glucose SAT-solver. This approach has
the advantage of allowing for the natural inclusion of additional linear length
constraints. Our solver obtains reliable and competitive results and,
remarkably, discovered several cases where state-of-the-art solvers exhibit a
faulty behaviour
Equivalence of Deterministic Nested Word to Word Transducers
International audienceWe study the equivalence problem of deterministic nested word to word transducers and show it to be surprisingly robust. Modulo polynomial time reductions, it can be identified with 4 equivalence problems for diverse classes of deterministic non-copying order-preserving transducers. In particular, we present polynomial time back and fourth reductions to the morphism equivalence problem on context free languages, which is known to be solvable in polynomial time
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