237 research outputs found
A Faster Exact Algorithm for the Directed Maximum Leaf Spanning Tree Problem
Given a directed graph , the Directed Maximum Leaf Spanning Tree
problem asks to compute a directed spanning tree (i.e., an out-branching) with
as many leaves as possible. By designing a Branch-and-Reduced algorithm
combined with the Measure & Conquer technique for running time analysis, we
show that the problem can be solved in time \Oh^*(1.9043^n) using polynomial
space. Hitherto, there have been only few examples. Provided exponential space
this run time upper bound can be lowered to \Oh^*(1.8139^n)
minimum dominating set of queens: A trivial programming exercise?
Abstractminimum dominating set of queens is one of the typical programming exercises of a first year’s computer science course. However, little work has been published on the complexity of this problem. We analyse here several algorithms and show that advanced algorithmic techniques may dramatically speed up solving this problem
Accepting grammars and systems
We investigate several kinds of regulated rewriting (programmed,
matrix, with regular control, ordered, and variants thereof) and
of parallel rewriting mechanisms (Lindenmayer systems, uniformly
limited Lindenmayer systems, limited Lindenmayer systems and
scattered context grammars) as accepting devices, in contrast
with the usual generating mode.
In some cases, accepting mode turns out to be just as powerful as
generating mode, e.g. within the grammars of the Chomsky
hierarchy, within random context, regular control, L systems,
uniformly limited L systems, scattered context. Most of these
equivalences can be proved using a metatheorem on so-called
context condition grammars. In case of matrix grammars and
programmed grammars without appearance checking, a straightforward
construction leads to the desired equivalence result.
Interestingly, accepting devices are (strictly) more powerful than
their generating counterparts in case of ordered grammars,
programmed and matrix grammars with appearance checking (even
programmed grammarsm with unconditional transfer), and 1lET0L
systems. More precisely, if we admit erasing productions, we
arrive at new characterizations of the recursivley enumerable
languages, and if we do not admit them, we get new
characterizations of the context-sensitive languages.
Moreover, we supplement the published literature showing:
- The emptiness and membership problems are recursivley solvable
for generating ordered grammars, even if we admit erasing
productions.
- Uniformly limited propagating systems can be simulated by
programmed grammars without erasing and without appearance
checking, hence the emptiness and membership problems are
recursively solvable for such systems.
- We briefly discuss the degree of nondeterminism and the
degree of synchronization for devices with limited parallelism
Cooperating Distributed Grammar Systems of Finite Index Working in Hybrid Modes
We study cooperating distributed grammar systems working in hybrid modes in
connection with the finite index restriction in two different ways: firstly, we
investigate cooperating distributed grammar systems working in hybrid modes
which characterize programmed grammars with the finite index restriction;
looking at the number of components of such systems, we obtain surprisingly
rich lattice structures for the inclusion relations between the corresponding
language families. Secondly, we impose the finite index restriction on
cooperating distributed grammar systems working in hybrid modes themselves,
which leads us to new characterizations of programmed grammars of finite index.Comment: In Proceedings AFL 2014, arXiv:1405.527
Observations on grammar and language families
In this report, we emphasize the differences of grammar families
and their properties versus language families and their
properties. To this end, we investigate grammar families from an
abstract standpoint, developping a new framework of reasoning. In
particular when considering decidability questions, special care
must be taken when trying to use decidability results (which are,
in the first place, properties of grammar families) in order to
establish results (e.g. hierarchy results) on language families.
We illustrate this by inspecting some theorems and their proofs in
the field of regulated rewriting. In this way, we also correct the
formulation of an important theorem of Hinz and Dassow.
As an exercise, we show that there is no `effective\u27 grammatical
characterization of the family of recursive languages. Moreover,
we show how to prove the strictness of the Chomsky hierarchy using
decidability properties only. Most of the material of this report
will be published in `fundamenta informaticae\u27
Synchronization of Deterministic Visibly Push-Down Automata
We generalize the concept of synchronizing words for finite automata, which map all states of the automata to the same state, to deterministic visibly push-down automata. Here, a synchronizing word w does not only map all states to the same state but also fulfills some conditions on the stack content of each run after reading w. We consider three types of these stack constraints: after reading w, the stack (1) is empty in each run, (2) contains the same sequence of stack symbols in each run, or (3) contains an arbitrary sequence which is independent of the other runs. We show that in contrast to general deterministic push-down automata, it is decidable for deterministic visibly push-down automata whether there exists a synchronizing word with each of these stack constraints, more precisely, the problems are in EXPTIME. Under the constraint (1), the problem is even in P. For the sub-classes of deterministic very visibly push-down automata, the problem is in P for all three types of constraints. We further study variants of the synchronization problem where the number of turns in the stack height behavior caused by a synchronizing word is restricted, as well as the problem of synchronizing a variant of a sequential transducer, which shows some visibly behavior, by a word that synchronizes the states and produces the same output on all runs
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